Cooling of electronic components using arrays of microjets

Transcription

UNIVERSITY OF CALIFORNIA
Los Angeles
Cooling of Electronic Components Using Arrays of
Microjets
A dissertation submitted in partial satisfaction of the
requirements of the degree of Doctor of Philosophy in
Mechanical and Aerospace Engineering
by
Matteo Fabbri
2004
1
© Copyright by
Matteo Fabbri
2004
ii
The dissertation of Matteo Fabbri is approved.
____________________________________
Jason Woo
____________________________________
Ivan Catton
____________________________________
Anthony F. Mills
____________________________________
Vijay K. Dhir, Committee Chair
University of California, Los Angeles
2004
ii
To my parents, my family, and my friends whom I immensely missed during all these
years.
iii
TABLE OF CONTENTS
TABLE OF CONTENTS.................................................................................................. IV
LIST OF FIGURES .........................................................................................................VII
LIST OF TABLES...........................................................................................................XII
NOMENCLATURE ...................................................................................................... XXI
ACKNOWLEDGEMENTS........................................................................................ XXIV
VITA .............................................................................................................................XXV
PUBLICATIONS AND PRESENTATIONS ...............................................................XXV
ABSTRACT OF THE DISSERTATION .................................................................. XXVII
CCHAPTER
HAPTER 11 ....................................................................................................................... 1
INTRODUCTION .............................................................................................................. 1
1.1
System description .............................................................................................. 5
1.2
Literature review................................................................................................. 8
1.2.1
Single phase ................................................................................................ 8
1.2.2
Boiling....................................................................................................... 15
1.2.3
Overview................................................................................................... 20
CCHAPTER
HAPTER 22 ..................................................................................................................... 21
COOLING MODULE ...................................................................................................... 21
2.1
Experimental Apparatus.................................................................................... 21
2.2
Experimental procedure and data acquisition. .................................................. 27
2.3
Results............................................................................................................... 29
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2.4
Summary ........................................................................................................... 38
CCHAPTER
HAPTER 33 ..................................................................................................................... 39
MICROJET ARRAYS: HEAT TRANSFER IN AN OPEN SYSTEM
CONFIGURATION.......................................................................................................... 39
3.1
3.2
Experimental Procedure.................................................................................... 43
3.3
Data Reduction.................................................................................................. 45
3.4
Results and Discussion ..................................................................................... 48
3.5
Effect of the orifice plate to heater distance ..................................................... 61
3.6
Optimal jet configuration.................................................................................. 63
3.7
Summary ........................................................................................................... 72
CCHAPTER
HAPTER 44 ..................................................................................................................... 74
MICROJET ARRAYS: HEAT TRANSFER IN A CLOSED SYSTEM
CONFIGURATION.......................................................................................................... 74
4.1
4.2
Experimental Procedure.................................................................................... 79
4.3
Data Reduction.................................................................................................. 81
4.4
Results and Discussion ..................................................................................... 82
4.4.1
Single phase data....................................................................................... 82
4.4.2
Two phase data ......................................................................................... 86
4.4.3
High heat flux data.................................................................................... 93
4.5
Summary ......................................................................................................... 108
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CCHAPTER
HAPTER 55 ................................................................................................................... 110
COMPARISON BETWEEN JET ARRAYS AND DROPLET SPRAYS..................... 110
5.1
Introduction..................................................................................................... 110
5.2
Results and discussion .................................................................................... 116
5.3
Summary ......................................................................................................... 124
CCHAPTER
HAPTER 66 ................................................................................................................... 125
CONCLUSIONS AND FUTURE WORK ..................................................................... 125
6.1
Conclusions..................................................................................................... 125
6.2
Future work..................................................................................................... 129
A
PPENDIX A
APPENDIX
A................................................................................................................. 130
A
PPENDIX BB ................................................................................................................. 134
APPENDIX
A
PPENDIX CC ................................................................................................................. 177
APPENDIX
C.1
Closed system - variable air content data ....................................................... 178
C.2
Closed system - high heat flux data ................................................................ 193
A
PPENDIX D
APPENDIX
D................................................................................................................. 210
D.1
Uncertainty on the cooling module data ......................................................... 210
D.2
Uncertainty on the open system data .............................................................. 211
D.3
Uncertainty on the closed system and high heat flux data.............................. 214
REFERENCES ............................................................................................................... 216
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LIST OF FIGURES
Figure 1.1 Schematic of a possible cooling module ........................................................... 6
Figure 2.1 Cooling module. .............................................................................................. 23
Figure 2.2 Details of the diode and of the jets. ................................................................. 24
Figure 2.3 Cooling module set up..................................................................................... 25
Figure 2.4 Schematic of the RTDs placement. ................................................................. 26
Figure 2.5 Cooling module test results ( 4 x 6 array of jets, dn = 140 μm, s = 2 mm ): heat
flux versus Tw - Tliq. .................................................................................................. 31
Figure 2.6 Heat flux as a function of wall superheat. ....................................................... 32
Figure 2.7 Equivalent thermal circuit for the cooling module.......................................... 33
Figure 2.8 Cooling module test results: external resistance versus air flowrate............... 35
Figure 2.9 Cooling module test results: internal resistance versus mass fraction of air
contained in the module. ........................................................................................... 36
Figure 2.10 Cooling module test results: process efficiency. ........................................... 37
Figure 3.1 Schematic of the experimental setup............................................................... 40
Figure 3.2 60o slice of each orifice plate: details of the jet’s area of influence. ............... 42
Figure 3.3 Details of the test section................................................................................. 43
Figure 3.4 Data repeatability............................................................................................. 46
Figure 3.5 Data repeatability............................................................................................. 47
Figure 3.6 Comparison between the heat transfer under arrays of microjets and the results
by Oliphant et al. [8]................................................................................................. 48
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Figure 3.7 Comparison of the experimental and predicted Nusselt number..................... 51
Figure 3.8 Variation of Nu with Redn for varying Pr and s/dn. ......................................... 53
Figure 3.9 Variation of Nu with Pr for varying Redn and s/dn. ......................................... 54
Figure 3.10 Variation of Nu with s/dn for varying Redn and Pr. ....................................... 55
Figure 3.11 Comparison of the Nusselt number predicted by various correlations as a
function of Redn for s/dn = 26.1 and Pr = 3.6. ........................................................... 56
function of Redn for s/dn = 6.7 and Pr = 3.6. ............................................................. 57
function of Redn for s/dn = 26.1 and Pr = 30.5. ......................................................... 57
function of Redn for s/dn = 13.3 and Pr = 30.5. ......................................................... 58
Figure 3.17 Comparison of the effect of s/dn on the Nusselt number in the present work
and those of Pan and Webb [4] and Yonehara and Ito [7]........................................ 60
Figure 3.18 Effect of different spray distance on the heat transfer................................... 62
Figure 3.19 Normalized pressure drop across the orifice plates....................................... 65
Figure 3.20 Qpumping as a function of dn for a specific Qremoved/(Tw - Tjets). ....................... 67
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Figure 3.21 Variation of the optimal Qpumping as a function of dn for different Qremoved/(Tw Tjets) and s.................................................................................................................. 68
Figure 3.22 Flowrate versus dn for different s. ................................................................. 69
Figure 4.1 Schematic of the experimental rig for the closed system tests........................ 76
Figure 4.2 Test chamber for the closed system configuration experiments. .................... 77
Figure 4.3 Heat flux versus Tw – Tjets for different Xair. s = 1 mm, dn = 118μm, V = 516
ml/min [29.4 μl/mm2s].............................................................................................. 83
Figure 4.4 Heat flux versus Tw – Tjets for different Xair. s = 3 mm, dn = 116.3μm, V = 233
ml/min [13.27 μl/mm2s]............................................................................................ 84
ml/min [19.93 μl/mm2s]............................................................................................ 84
ml/min [13.1 μl/mm2s].............................................................................................. 85
ml/min [20.51 μl/mm2s]............................................................................................ 85
Figure 4.8 Heat flux versus Tw – Tsat for different Xair or liquid subcooling s = 1mm, dn =
118.7 μm, V = 516 ml/min [29.4 μl/mm2s]. ............................................................ 87
118.7 μm, V = 516 ml/min [29.4 μl/mm2s] ............................................................. 87
Figure 4.10 Heat flux versus Tw – Tsat for different Xair or liquid subcooling s = 3 mm, dn
= 116.3 μm, V = 233 ml/min [13.27 μl/mm2s]. ....................................................... 88
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= 116.3 μm, V = 233 ml/min [13.27 μl/mm2s]. ....................................................... 88
= 116.3 μm, V = 350 ml/min [19.94 μl/mm2s]. ....................................................... 89
= 116.3 μm, V = 350 ml/min [19.94 μl/mm2s]. ....................................................... 89
Figure 4.14 Heat flux versus Tw – Tjets for different Xair or liquid subcooling s = 3 mm, dn
= 173.6 μm, V = 230 ml/min [13.1 μl/mm2s]. ......................................................... 90
Figure 4.15 Heat flux versus Tw – Tjets for different Xair or liquid subcooling s = 3 mm, dn
= 173.6 μm, V = 230 ml/min [13.1 μl/mm2s]. ......................................................... 90
= 173.6 μm, V = 360 ml/min [20.51 μl/mm2s]. ....................................................... 91
= 173.6 μm, V = 360 ml/min [20.51 μl/mm2s]. ....................................................... 91
Figure 4.18 Heat flux versus Tw – Tsat for two different flowrates, and jet diameters (Tjets
≈ 100 oC). .................................................................................................................. 92
Figure 4.19 Heat flux versus Tw – Tsat for two different flowrates, and jet diameters (Tjets
≈ 93 oC). .................................................................................................................... 92
Figure 4.20 Details of the test section modified to accommodate high heat fluxes. ........ 93
Figure 4.21 Heat flux versus Tw – Tjets for different flowrates, s = 1 mm, dn = 69.3 μm. 96
Figure 4.22 Heat flux versus Tw – Tjets for different flowrates, s = 1 mm, dn = 118.7 μm.
................................................................................................................................... 97
x
................................................................................................................................... 97
Figure 4.24 Heat flux versus Tw – Tjet for different flowrates, s = 3 mm, dn = 173.6 μm. 98
Figure 4.25 Effect of jet velocity on single-phase heat transfer. ...................................... 99
Figure 4.26 Effect of jet velocity on two-phase heat transfer......................................... 100
Figure 4.27 Effect of liquid subcooling on boiling......................................................... 101
Figure 4.28 Effect of change in system pressure ............................................................ 102
Figure 4.29 Effect of system pressure in on two-phase heat transfer ............................. 103
Figure 4.30 Effect of system pressure............................................................................. 104
Figure 4.31 Fully developed boiling data and prediction from other correlations. ........ 105
Figure 4.32 Area of influence of a jet and characteristic length..................................... 106
Figure 5.1 Comparison of spray data for two flowrates (a) 50.56 ml/min [2.87μl/mm2s]
and (b) 81.56 ml/min [4.63μl/mm2s], with the predictions of Holman et al. [30,31]
and Cho et al. [33]. ................................................................................................. 118
Figure 5.2 Comparison between spray and micro jets performance for two flowrates (a)
50.56 ml/min [2.87μl/mm2s] and (b) 81.56 ml/min [4.63 μl/mm2s]....................... 119
Figure 5.3 Comparison of process efficiency between spray and micro jets for two
flowrates (a) 50.56 ml/min [2.87μl/mm2s] and (b) 81.56 ml/min [4.63 μl/mm2s] . 120
Figure 5.4 Comparison between spray and micro jets performance for the same pumping
power....................................................................................................................... 122
Figure 5.5 Comparison of the present data with the results by Oliphant et al.[8]. ......... 123
Figure D.1 Temperature profile in the copper block. Values taken from Table B1. ...... 212
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LIST OF TABLES
Table 1.1 Correlations for fully developed boiling under impinging jets......................... 16
Table 3.1 Orifice plate details........................................................................................... 41
Table 3.2 Prediction error on the experimental data......................................................... 50
Table 3.3 Number of jets impinging on a circular surface of 292.5 mm2......................... 67
Table 3.4 Qremoved, vjets, ΔP for a flowrate of 2·10-6 m3/s of water. Tw-Tjets = 60 oC, Tjets
=18.6 oC, Area = 292 mm2 (6.84 μl/mm2s), tplate = 0.51 mm.................................... 71
Table 4.1 Test configurations. .......................................................................................... 82
Table 4.2 List of orifice plate tested. ................................................................................ 95
Table 4.3 Comparison of CHF data (s = 3, dn = 263μm) with predictions from other
correlations.............................................................................................................. 106
Table 5.1 Range of parameters for the experimental work of Ghodbane et al. [30] and
Holman et al. [31] ................................................................................................... 113
Table A.1......................................................................................................................... 131
Table A.2......................................................................................................................... 131
Table A.3......................................................................................................................... 132
Table A.4......................................................................................................................... 132
Table A.5......................................................................................................................... 132
Table A.6......................................................................................................................... 133
Table B.1......................................................................................................................... 135
Table B.2......................................................................................................................... 135
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Table B.3......................................................................................................................... 136
Table B.4......................................................................................................................... 136
Table B.5......................................................................................................................... 137
Table B.6......................................................................................................................... 137
Table B.7......................................................................................................................... 137
Table B.8......................................................................................................................... 138
Table B.9......................................................................................................................... 138
Table B.10....................................................................................................................... 139
Table B.11....................................................................................................................... 139
Table B.12....................................................................................................................... 140
Table B.13....................................................................................................................... 140
Table B.14....................................................................................................................... 141
Table B.15....................................................................................................................... 141
Table B.16....................................................................................................................... 142
Table B.17....................................................................................................................... 142
Table B.18....................................................................................................................... 143
Table B.19....................................................................................................................... 143
Table B.20....................................................................................................................... 144
Table B.21....................................................................................................................... 144
Table B.22....................................................................................................................... 144
Table B.23....................................................................................................................... 145
Table B.24....................................................................................................................... 145
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Table B.25....................................................................................................................... 146
Table B.26....................................................................................................................... 146
Table B.27....................................................................................................................... 147
Table B.28....................................................................................................................... 147
Table B.29....................................................................................................................... 148
Table B.30....................................................................................................................... 148
Table B.31....................................................................................................................... 149
Table B.32....................................................................................................................... 149
Table B.33....................................................................................................................... 150
Table B.34....................................................................................................................... 150
Table B.35....................................................................................................................... 151
Table B.36....................................................................................................................... 151
Table B.37....................................................................................................................... 152
Table B.38....................................................................................................................... 152
Table B.39....................................................................................................................... 153
Table B.40....................................................................................................................... 153
Table B.41....................................................................................................................... 154
Table B.42....................................................................................................................... 154
Table B.43....................................................................................................................... 155
Table B.44....................................................................................................................... 155
Table B.45....................................................................................................................... 156
Table B.46....................................................................................................................... 156
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Table B.47....................................................................................................................... 156
Table B.48....................................................................................................................... 157
Table B.49....................................................................................................................... 157
Table B.50....................................................................................................................... 158
Table B.51....................................................................................................................... 158
Table B.52....................................................................................................................... 159
Table B.53....................................................................................................................... 159
Table B.54....................................................................................................................... 160
Table B.55....................................................................................................................... 160
Table B.56....................................................................................................................... 161
Table B.57....................................................................................................................... 161
Table B.58....................................................................................................................... 161
Table B.59....................................................................................................................... 162
Table B.60....................................................................................................................... 162
Table B.61....................................................................................................................... 162
Table B.62....................................................................................................................... 163
Table B.63....................................................................................................................... 163
Table B.64....................................................................................................................... 163
Table B.65....................................................................................................................... 164
Table B.66....................................................................................................................... 164
Table B.67....................................................................................................................... 164
Table B.68....................................................................................................................... 165
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Table B.69....................................................................................................................... 165
Table B.70....................................................................................................................... 165
Table B.71....................................................................................................................... 166
Table B.72....................................................................................................................... 166
Table B.73....................................................................................................................... 166
Table B.74....................................................................................................................... 167
Table B.75....................................................................................................................... 167
Table B.76....................................................................................................................... 167
Table B.77....................................................................................................................... 168
Table B.78....................................................................................................................... 168
Table B.79....................................................................................................................... 168
Table B.80....................................................................................................................... 169
Table B.81....................................................................................................................... 169
Table B.82....................................................................................................................... 169
Table B.83....................................................................................................................... 170
Table B.84....................................................................................................................... 170
Table B.85....................................................................................................................... 170
Table B.86....................................................................................................................... 171
Table B.87....................................................................................................................... 171
Table B.88....................................................................................................................... 171
Table B.89....................................................................................................................... 172
Table B.90....................................................................................................................... 172
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Table B.91....................................................................................................................... 172
Table B.92....................................................................................................................... 173
Table B.93....................................................................................................................... 173
Table B.94....................................................................................................................... 174
Table B.95....................................................................................................................... 174
Table B.96....................................................................................................................... 174
Table B.97....................................................................................................................... 175
Table B.98....................................................................................................................... 175
Table B.99....................................................................................................................... 176
Table B.100..................................................................................................................... 176
Table B.101 Calibration data (T1-T4 are the thermocouples in the copper block, 1 being
the closest to the free surface and 4 the farthest away)........................................... 176
Table C.1......................................................................................................................... 178
Table C.2......................................................................................................................... 179
Table C.3......................................................................................................................... 179
Table C.4......................................................................................................................... 180
Table C.5......................................................................................................................... 180
Table C.6......................................................................................................................... 181
Table C.7......................................................................................................................... 181
Table C.8......................................................................................................................... 182
Table C.9......................................................................................................................... 182
Table C.10....................................................................................................................... 183
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Table C.11....................................................................................................................... 183
Table C.12....................................................................................................................... 184
Table C.13....................................................................................................................... 184
Table C.14....................................................................................................................... 185
Table C.15....................................................................................................................... 185
Table C.16....................................................................................................................... 186
Table C.17....................................................................................................................... 186
Table C.18....................................................................................................................... 187
Table C.19....................................................................................................................... 187
Table C.20....................................................................................................................... 188
Table C.21....................................................................................................................... 188
Table C.22....................................................................................................................... 189
Table C.23....................................................................................................................... 189
Table C.24....................................................................................................................... 190
Table C.25....................................................................................................................... 190
Table C.26....................................................................................................................... 191
Table C.27....................................................................................................................... 191
Table C.28....................................................................................................................... 192
Table C.29....................................................................................................................... 192
Table C.30....................................................................................................................... 193
Table C.31....................................................................................................................... 193
Table C.32....................................................................................................................... 194
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Table C.33....................................................................................................................... 194
Table C.34....................................................................................................................... 195
Table C.35....................................................................................................................... 195
Table C.36....................................................................................................................... 196
Table C.37....................................................................................................................... 197
Table C.38....................................................................................................................... 198
Table C.39....................................................................................................................... 199
Table C.40....................................................................................................................... 200
Table C.41....................................................................................................................... 200
Table C.42....................................................................................................................... 201
Table C.43....................................................................................................................... 202
Table C.44....................................................................................................................... 202
Table C.45....................................................................................................................... 203
Table C.46....................................................................................................................... 203
Table C.47....................................................................................................................... 204
Table C.48....................................................................................................................... 204
Table C.49....................................................................................................................... 205
Table C.50....................................................................................................................... 206
Table C.51....................................................................................................................... 207
Table C.52....................................................................................................................... 208
Table C.53....................................................................................................................... 209
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Table C.54 Calibration data (T1-T4 are the thermocouples in the copper block, 1 being
the closest to the free surface and 4 the farthest away)........................................... 209
Table D.1 Max and min uncertainties for the open system configuration...................... 212
Table D.2 Variable values and their uncertainty ............................................................ 213
Table D.3 Max and min uncertainties for the closed system configuration. .................. 214
Table D.4 Max and min uncertainties for the high heat flux data. ................................. 215
xx
NOMENCLATURE
A
area [m2]
cp
specific heat [J/kgK]
d
jet or droplet diameter [m]
D
diameter
ΔP
pressure drop across the nozzle or the orifice plate [Pa]
ΔT
temperature difference [K]
h
heat transfer coefficient [W/m2K], h = q/(Tw-Tliq)
hfg
latent heat of vaporization [J/kg]
k
thermal conductivity [W/mK]
L
heater characteristic length [m]
L*
length of the radial flow region [m]
N
number of jets
Nu
Nusselt number Nu = hdn/k
Pr
Prandtl number
q
heat flux [W/m2]
Q
power [W]
R
Thermal resistance [K/W]
Re
Reynolds number
s
pitch between the jets [m]
t
thickness [m]
xxi
T
temperature [K]
v
velocity [m/s]
V
volumetric flowrate [m3/s]
We
Weber number
z
nozzle to heater distance [m]
Greek symbols
α
thermal diffusivity [m2/s]
β
standard spray angle [deg]
μ
dynamic viscosity [kg/ms]
ν
kinematic viscosity [m2/s]
ρ
density [kg/m3]
σ
surface tension [N/m]
Subscripts
br
breakup
chip
surface of the chip
d
droplet
ext
external
H
heater
i
at the impinging point
int
internal
jets
jets
L
based on the heater’s characteristic length
xxii
liq
sprayed liquid
n
at nozzle or orifice plate exit
plate
of the orifice plate
w
wall or surface
¯
area averaged
sub
subcooling
sat
saturation or superheat
xxiii
ACKNOWLEDGEMENTS
This work received support from DARPA within the HERETIC project.
A particular thank to:
Garry Rohystein, Miguel Lozano, Dale Cooper, Steve Grubweiser, and the other guys at
the machine shop for their help with my experimental work;
Jim Mcgee and John Boiko for being patient with my long term borrowing of the tools
and late afternoon purchase orders;
Lennox Mackenzie for his quick deliveries of packages;
Lex Kopfer and his boys Hugo and Jesse for helping me make sure that nobody
electrocuted himself in the lab;
Coral Castro, Janice Bedig, Angie Castillo, Lili Bulholes, Marcia Terranova, Abel Lebon,
Stacey Morse for bearing me and taking care of all my mess with the various paperwork;
David Riley for the “lunch” he never gave me;
Gopinath Warrier for his help with the experiments and the guys in the lab for putting up
with all the crap I brought up during all these years;
Prof. Anthony Mills and Prof. Ivan Catton for their advice and their friendship;
Cindy Gilbert for her invaluable help and friendship, even though I’m an Angels fan;
All those who supported me all this time.
xxiv
VITA
February 2, 1971
Born, Parma, Italy
1997
Laurea in Mechanical Engineering
University of Parma
Parma, Italy
1999
M.S., Mechanical Engineering
Univ. of California Los Angeles
Los Angeles, California
1998-2000
Teaching Assistant
Mechanical and Aerospace Department
1997-2004
Research Assistant
Mechanical and Aerospace Department
PUBLICATIONS AND PRESENTATIONS
•
Dhir, V.K., Warrier, G.R., Fabbri, M., and Jiang, S., “Heat Removal With Flow in
Microchannels, Microjets, and Microdroplets,” NATO Advanced Study Institute on
Microscale Heat Transfer Fundamentals and Applications in Biological and
Microelectromechanical Systems, Cesme/Izmir, Turkey, July 2004.
•
Fabbri M., Jiang S., and Dhir V.K., “Comparative study of spray and multiple
micro jets cooling for high power density electronic applications ” Proceeding of the
2003 ASME International Mechanical Engineering Congress & Exposition, Washington,
D.C., November 2003.
xxv
•
Fabbri M., Jiang S., and Dhir V.K., “Experimental investigation of single-phase
micro jets impingement cooling for electronic applications,” Proceedings of the 2003
ASME Summer Heat Transfer Conference, Las Vegas, Nevada, USA, July 2003.
•
Catton, I., Merilo, E., and Fabbri, M., “Experimental Study of Two-Phase Flow in
Microchannels”, Honeywell Technical Report, 2003.
•
Shaw, M.C., Waldrop, J.R., Chandrasekaran, S., Kagalwala, B., Jing, X., Brown,
E.R., Dhir, V.K. and Fabbri, M., 2002, “Enhanced thermal management by direct water
spray of high-voltage, high power devices in a three phase, 18-hp AC motor drive
demonstration”, Proceedings of the 8th Intersociety Conference on Thermal and
Thermomechanical Phenomena in Electronic Systems, San Diego, CA.
•
Fabbri M., Jiang S., and Dhir V.K., “Experimental Investigation of a Micro Jets –
based Cooling Package for Electronic Applications,” Proceedings of the 12th
International Heat Transfer Conference, Grenoble, France, August 2002.
•
Fabbri M., and Dhir V.K., “Experimental Study of a Natural Convection in
Volumetrically Heated Pools Contained in a Cylindrical Cavity,” EPRI Technical Report,
EPRI, Palo Alto, CA: 2001 (1003187).
•
Fabbri M., and Dhir V.K., “Experimental Study of a Natural Convection in
Volumetrically Heated Pools Contained in a Cylindrical Cavity,” Proceedings of the 34th
National Heat Transfer Conference, Pittsburgh, Pennsylvania, August 2000.
xxvi
ABSTRACT OF THE DISSERTATION
Cooling of Electronic Components Using Arrays of
Microjets
by
Matteo Fabbri
Doctor of Philosophy in Mechanical and Aerospace
Engineering
University of California, Los Angeles, 2004
Professor Vijay K. Dhir, Chair
Electronic cooling has become a subject of interest in recent
years due to the constantly increasing speed and sustainable power
of microchips. Conventional forced air cooling techniques can not
satisfy the new cooling requirements and new methods have to be
sought. Jet cooling has been used in other industrial fields and it
has demonstrated the capability of sustaining high heat transfer
rates.
xxvii
The goal of this work was to investigate the heat transfer under
arrays of microjets. Ten different arrays have been tested using
deionized water and FC40 as test fluids. The data have been
correlated using only three nondimensional groups, in a manner
similar to that used in the literature. An optimal configuration of
the main geometrical parameters can be established for given
cooling requirements of the electronic component.
The effect of varying noncondensable gas content in the
ambient surrounding the jets on the heat transfer under microjet
arrays has also been investigated and no significant enhancement
has been found as the volume fraction of noncondensable gas is
decreased for the range of flowrates investigated.
This work demonstrates that jet cooling can be used for
electronic cooling. For that purpose a prototype of a closed system
cooling module based on microjet arrays has been built and
successfully tested.
A comparison of the results with those obtained using droplet
sprays has shown that the microjet arrays can provide the same
heat transfer rates, but a lower energy cost.
xxviii
C
CH
HA
AP
PT
TE
ER
R 11
INTRODUCTION
With time, the demand for high performance electronics has increased. More and
more applications require the electronic components to be faster, smaller, able to handle a
higher amount of power, and be more reliable than before. Small size and high power
unfortunately lead to high heat fluxes that need to be removed from the components to
avoid failure; speed and reliability improve as the surface temperature of the device
decreases. To obtain an idea of how seriously the electronic world is looking for more
effective cooling methods, one just has to note that even personal computers, which are
not considered as power electronic applications, and whose speed is increasing constantly
are reaching the point where traditional cooling techniques (i.e., air cooling) are not
sufficient. Even greater are the problems in power electronics, where the limitations of
the present cooling methods impose a constraint on the amount of power that a
component can handle.
A great amount of research to develop more effective cooling techniques for
electronic purposes has been performed during the last 25 years. Most of it has
concentrated on enhancing the performance of air-cooling by means of new fin
geometries, and materials.
Another branch has directed its attention to the usage of liquid coolants instead of
air. Liquid cooled “cold plates” are already available on the market as well as heat pipes.
1
Studies have been conducted on micro-channel cooling including both single, and two
phase flow. Pool boiling studies have also interested the researchers because of the high
heat transfer rates, which characterize the nucleate boiling region.
A promising technique, which has received particular attention, is spray cooling.
Spray cooling can be implemented by means of liquid jets or liquid droplets. This method
presents, while still providing very high heat flux removal capabilities, the possibility of
minimizing the amount of liquid employed and pumping power needed in the cooling
process. The pressure drop across the nozzle or orifice needed to form the spray or jets
does not depend on the mechanism of heat transfer at the surface. In contrast, in channel
cooling, when boiling occurs on the heat transfer surface, the pressure drop across the
channel increases drastically. Thus, the ratio between power spent for the cooling process
and the heat removed decreases faster for spray cooling than for channel cooling, when
surface temperature is increased. Furthermore, spraying directly on the heating source
eliminates the thermal resistance represented by the bonding layer on which the device is
usually attached. All the reasons mentioned above make the idea of using spray cooling
for electronic applications very attractive.
In order to implement this concept into a cooling module, a closed loop system
has to be considered. Ultimately, the heat stored in the hot liquid and vapor produced by
spraying of the hot surface must be transferred to the ambient. To accomplish this task an
air cooled condenser is needed; and a pump to propel the liquid through the nozzle is also
required.
2
Extensive studies have been conducted on air cooled augmented heat transfer
surfaces to find more promising configurations, and plenty of data for both heat transfer
and pressure drop are available in the literature. Unfortunately, the manufacturing
difficulty, and the high costs associated with it have not always been considered since the
purpose was only to improve the heat exchange.
Condensation has been studied broadly since Nusselt did his work in 1916.
Models are available in the literature to predict the condensation rate on a variety of
surfaces, with and without noncondensable gases. Enhanced surfaces to improve the
condensation rate have been developed and tested, even though not many of them were
designed to improve the performance when noncondensables were present.
One critical issue that must be addressed when employing liquid cooling for
electronic components is the choice of cooling fluid. The ideal fluid for this type of
application would have high thermal conductivity, high specific heat, high latent heat of
vaporization, and zero electrical conductivity. Water would be the best fluid if only the
first three properties were to be considered, because it has values that are higher than
most fluids. Unfortunately, there is a problem with the electrical conductivity. Deionized
water has a very low electrical conductivity, but it has at the same time the tendency of
extracting ions from the materials it gets in contact with, which makes it, after a while,
electrically conductive. Refrigerants such as Freon R-113 or Fluorinet FC-72 behave
optimally from an electrical point of view, but have much lower values for the other
physical properties mentioned before.
3
The choice between water and a refrigerant definitely depends on the heat flux
that has to be removed, and on the possibility of electrically insulating the device that has
to be cooled. One solution could be to coat the device with an insulating layer.
Unfortunately, this means introducing an undesired thermal resistance in the circuit.
Obviously, not only is it necessary that the desired amount of heat be removed
from the electronic component, but it must also be accomplished with the least amount of
pumping power needed to implement the scheme.
4
1.1 System description
As mentioned before, an impinging jets based cooling module would require three
primary components: an orifice plate for forming jets; a container to hold the nozzle, the
heat source and the cooling liquid, which also serves as a heat exchanger to the ambient;
and a pump which recirculates the coolant. A fan could be used to improve the heat
transfer to the ambient, and that would also allow the use of a smaller container.
From a thermal management point of view, the heat is first transferred from the
heat source (the electronic component), to the sprayed liquid which will in part evaporate,
and then from the hot liquid and vapor to the ambient by conduction through the
container’s walls. Figure 1.1 shows a schematic of a possible configuration of a microjets
based cooling module.
5
HEAT
HEAT
HEAT
HEAT
HEAT
HEAT
VAPOR + AIR HEAT
HEAT
NOZZLE
HEAT
JETS
HEAT
HEAT
CHIP
FAN
PUMP
Figure 1.1 Schematic of a possible cooling module
The microjets deposit a thin liquid layer on top of the microchip-heat source. The
heat is transferred from the chip to the liquid that flows over it. The heat transfer is
primarily by convection. In certain conditions the evaporation which occurs at the
interface between the liquid film and the ambient surrounding the chip may become
important. The amount of noncondensable gases present in the chamber can however
hinder the evaporative process.
The vapor produced in the cooling process condenses on the walls of the chamber,
thus transferring the heat. The remaining liquid flows away from the chip mainly along
the bottom wall of the chamber to a drain and back to the pump that recirculates it. The
noncondensable gases can also greatly decrease the vapor condensation rate on the
6
chamber side. The heat transfer to the walls depends on the geometry and design of the
chamber and on the amount of noncondensable gases present inside the chamber. The
presence of fins on the inner walls of the chamber would allow a better condensation rate
for the vapor, when noncondensables gases are present in the chamber or when the liquid
film flowing on the surface would be otherwise quite thick.
The excess liquid from the sprays, which does not become vapor, must still be
cooled. This can be accomplished in different ways. For a cooling module configuration
similar to that illustrated in Figure 1.1, part of the inner walls could be covered with a
wick which sucks the hot liquid present at the bottom of the chamber up along the
chamber walls. Another way could be to place the chip at a higher location with respect
to the rest of the chamber: the liquid would fall from the chip directly onto the walls.
The heat is conducted through the walls to the outside of the chamber, where it is
transferred to the ambient by forced convection. It is possible to improve the heat transfer
by using fins on the outer walls.
7
1.2 Literature review
1.2.1 Single phase
Jet impingement cooling has been studied by many researchers and because of the
high heat transfer rates that are achievable, it is used in a variety of applications from the
metal sheet industry to cooling of laser and electronic equipment. The jet can be
submerged, which means that it flows within the same fluid in the same state (i.e. gas into
gas or liquid into liquid), or free surface, which means that the liquid jet is injected into a
gaseous environment. Gaseous jets, that obviously have low heat transfer potential, and
submerged liquid jets are not considered in this work. The focus of this study is only on
free surface liquid jets.
Extensive studies have been performed in the past particularly on single-phase
single jet configurations, and most of the experimental data available have been obtained
for values of the jet Reynolds number (Redn) that fall in the turbulent regime, (Redn >
2000) . An important conclusion from these studies is that the local heat transfer
decreases sharply as one moves radially outward from the stagnation region to the
periphery [1]. Elison and Webb [2] experimentally investigated the heat transfer
associated with a single water jet. They tested three different pipe type nozzles with
diameters of 0.584, 0.315, and 0.246 mm. The nozzles were long enough to allow a fully
developed velocity profile in any regime. The range of Redn was between 300 and 7000.
Their major finding was that in the laminar regime (Redn < 2000), the Nusselt number
(Nu) varied as Redn0.8, whereas previous studies had shown that Nu ∝ Redn0.5. They
8
attributed this enhancement to surface tension effects at the nozzle exit, which increased
the actual jet diameter.
Most of the theoretical work has involved laminar jets, and a good summary of
the results is presented in [1]. The major conclusions are that the jet impingement flow
can be divided in four regions. Region 1 is the stagnation zone, where it was found that
the thickness of the hydrodynamic and thermal boundary layers is constant. In the second
region, both boundary layers are developing and have not reached the free surface.
Region 3 is characterized by the fact that the hydrodynamic boundary layer has reached
the free surface, whereas the thermal boundary layer has not. Finally in region 4 both
boundary layers have reached the free surface of the liquid film. If the Prandtl number
(Pr) is less than unity the thermal boundary layer develops faster than the hydrodynamic
and the two thicknesses are interchanged in regions 2 and 3. Criteria are given for the
transition from one region to the other. The theoretical results matched reasonably well
with the experimental data.
Multiple jets impinging on a heater surface can improve the spatial uniformity of
the heat transfer coefficient on the surface. Jiji and Dagan [3] studied the heat transfer
associated with multiple single-phase free surface jets impinging on an array of
microelectronic heat sources. They tested square arrays of 1, 4, and 9 jets using FC77 as
the working fluid on multiple heat sources of size 12.7x12.7 mm2. They found that the
surface temperature uniformity improved as the spacing between the jets decreased, and
that the heat transfer rate was independent of the ratio of the nozzle to heater distance (z)
and the jets’ diameter (dn) in the range between 3 and 15. They correlated their data as,
9
Nu L = Re dn
1
2
1
⎛
⎞
L
Pr 3 3.84 ⎜ 0.08 N + 1⎟
dn
⎝
⎠
(1.1)
where L is the heater length and N is the number of jets.
This correlation was developed based on the following parameters: jet pitch (s) to
diameter ratios (s/dn) of 5.08 and 10.16, two jets diameters, 0.5 and 1.0 mm, jets
velocities (vjet) between 2.2 and 14.5 m/s, and Redn between 2800 and 12600. They had
only two data points with water as the test liquid with a single jet of 1 mm diameter for
Redn of 10000 and 20000. They concluded that, for flow rates less than 20 ml/s and a
heater area of 1.61 cm2, the thermal resistance is of the order of 1 K/W when the coolant
is FC77, and of the order of 0.1 K/W when the coolant is water. Using the correlation
they developed, it was predicted that with FC77 a heat flux approximately 100 W/cm2
could be achieved with an array of nine jets of 0.3 mm diameter at a flow rate of 10 ml/s,
when the temperature difference between the impinged surface and the jet was 60°C.
Pan and Webb [4] conducted experiments on water jet arrays. They studied two
configurations in particular: a 3 x 3 inline array and a seven jet staggered configuration.
Infrared thermography was used to find the local characteristics of the heat transfer
process. They concluded that the stagnation Nu was independent of the interjet spacing,
but it exhibited a dependence on the nozzle to plate spacing. The local heat transfer for
the two different configurations had only minor differences, mainly in the radial flow
region between the jets. They also observed a transition for the central jet from being
10
confined and submerged at z/dn = 2 to a free surface jet as z/dn was increased to 5. They
correlated their data for the average heat transfer coefficient as,
2
1
Nudn = 0.225 Re dn3 Pr 3 e
−0.095⎛⎜ s ⎟⎞
⎝ dn ⎠
(1.2)
This correlation is valid for the following range of parameters: 2 ≤ s/dn ≤ 8, 2 ≤
z/dn ≤ 5, 5000 ≤ Redn ≤ 20000. The jet diameters used in these tests were 1, 2, and 3 mm.
Womac et al. [5] performed experiments on 2 x 2 and 3 x 3 jet arrays using water
and FC77. The impinging surface was 12.7 x 12.7 mm2 in size and was made of copper.
Only two jet diameters were tested, 0.513 and 1.02 mm, and only two pitches were used,
5.08 and 10.16 mm. In this investigation they covered a wide range of parameters: 500 ≤
Redn ≤ 20000, 4.98 ≤ s/dn ≤ 19.8, 9.9 ≤ z/dn ≤ 20, and 7 ≤ Pr ≤ 24. They found that
varying z/dn had negligible effect on the heat transfer, and that for a given flow rate, the
heat transfer improved with an increase in jet velocity. They also pointed out that the
reduction in the heat transfer that occurs with lowering the flow rate became more
pronounced at very low flow rates. This was attributed to the bulk heating of the fluid (a
condition that occurs when the thermal boundary layer reaches the free surface of the
liquid film). Unfortunately, they did not provide any evidence to support their claim. The
data were correlated by using an area weighted combination of correlations associated
with the impingement and wall jet region following the same procedure as Womac et. al
[6] had applied in a previous work on single jets. The final correlation was given as,
11
⎡
⎤ 0.4
⎛L⎞
0.579 ⎛ L ⎞
NuL = ⎢0.516 Re0.5
⎟ Ar + 0.344 Re L* ⎜ * ⎟ (1 − Ar ) ⎥ Pr
di ⎜
⎝L ⎠
⎝ di ⎠
⎣
⎦
where Ar = N
πdi2
4L2
(
, Vi = V + 2gz
2
n
)
0.5
(1.3)
0.5
⎛ Vn d n2 ⎞
⎟⎟ , L is the heater length, and L* is an
, di = ⎜⎜
⎝ Vi ⎠
estimate of the average distance associated with radial flow in the wall jet regions of the
heater and is given by L* =
( 2 + 1) s − 2di
.
4
Yonehara and Ito [7] carried out an analytical study of the heat transfer under a
square array of impinging free surface liquid jets on an isothermal surface. The resulting
correlation was given as,
Nu = 2.38 Re Pr ⎛⎜ s ⎞⎟
⎝ dn ⎠
2
3
dn
1
3
( −4 3 )
(1.4)
They also performed experiments to validate their model and found good
2
agreement between experimental and theoretical data for Re dn ⎛⎜ s ⎞⎟ ≥ 5 . The tests
⎝ dn ⎠
were conducted for the following range of parameters: 13.8 ≤ s/dn ≤ 330, 7100 ≤ Redn ≤
48000.
Another study involving arrays of jets was carried out by Oliphant et al. [8], in
which the performance of sprays and arrays of liquid jets were compared to each other.
12
They utilized arrays of 4 and 7 jets of deionized water impinging on top of a 1.9 cm
diameter aluminum cylinder. A cartridge heater provided heat to the aluminum cylinder
and 6 thermocouples measured the temperatures under the wetted surface allowing the
calculation of heat flux, surface temperature, and heat losses. Two jet diameters were
used: 1 and 1.59 mm. The jet Reynolds numbers investigated in the study ranged between
3150 and 11300 (41.8 - 178.46 kg/m2s). The jets were spaced such that each covered an
equal fraction of the total heat transfer area.
In order to produce the spray, the orifice plate used to generate the jets was
substituted with a full-cone, air-assist atomizer (Delavan Airo Type B). Mass fluxes
between 1 and 30 kg/m2s were investigated. The manufacturer’s specified mean Sauter
diameter for the droplets was 50 μm. From a plot of jets and spray heat transfer
coefficient versus mass flux, they concluded that spray and jets have heat transfer
coefficients of the same order of magnitude, but the spray obtained it using a lower mass
flux. They also stated that if the data for the spray are extrapolated into the same mass
flux range as that of the jets, “the spray impingement is significantly more effective than
the liquid jet arrays”. However, no particular effort was made towards investigating or
understanding the effect of the parameters which affect the heat transfer under liquid jet
arrays. From the above literature survey, it can be concluded that in single-phase
impingement cooling with multiple jets, the heat transfer improves when either the liquid
mass flow rate, or the jet velocity of the liquid, or the number of jets is increased. The
nozzle to heater distance has no significant effect on the heat transfer unless it is
decreased to the point where the jets become submerged. The higher the number of jets
13
the more uniform is the surface temperature. Also, the presence of noncondensibles can
hinder the heat transfer rate considerably.
It also appears to be better to use a large number of smaller jets than a single large
jet to cool a flat surface. Also, since the motivation behind this work is high power
electronic cooling, the use of an array of small jets makes it possible to selectively spray
the liquid at the locations where the heat is generated. Lastly, all the previous studies
have employed flow rates of coolant which appear considerably high for cooling of a
small microchip.
14
1.2.2 Boiling
Multi jets impingement cooling with boiling allows the removal of very high heat
fluxes at relatively low surface temperatures. Boiling heat transfer under impinging jets
has been thoroughly reviewed by Wolf et al. [11]. In their review they concluded that the
jet velocity has no effect the heat transfer underfully developed nucleate boiling for a
circular free surface jet. They also reported that Monde and Okuma [14] during an
investigation of the heat transfer from a saturated jet of R-113 found that the effect of jet
velocity increased with decreasing jet to heater diameter ratio when the liquid flowrates
are low. They observed that behavior consistently when the total power removed
approximately equaled the amount of energy necessary to evaporate the entire liquid
flowrate.
Wolf et al. [11] also discussed the effect of liquid subcooling. It can be concluded
that although some researchers found lower surface temperature to occur for higher
degree of subcooling at low wall superheat, the subcooling plays no role at high wall
superheat and all the boiling curves collapse onto the one obtained with saturated liquid.
Different jet diameter to heater diameter ratios were not found to affect the heat transfer
by several researchers, with the exception of the case reported by Monde and Okuma
mentioned earlier. The nozzle to heater distance was found to play no role in the heat
transfer under a circular free jet. A list of some the most important nucleat boiling heat
transfer correlations of experimental data reported by Wolf et al. in their review, is
presented in Table 1.1.
15
Table 1.1 Correlations for fully developed boiling under impinging jets.
(
= C ΔT ( C )
m )
Author
Copeland [13]
Katsuta and Kurose [17]
Katto and Kunihiro [18]
Katto and Monde [19]
Monde and Katto [24]
Monde [22]
Monde and Katto [23]
Ruch and Holman [20]
Fluid
C
Water
740
R-113 2.93·10-6
Water
340
Water
450
n
2.3
7.4
2.7
2.7
Range of ΔTsat
8-31
24-31
18-38
18-46
R-113
R-113
2.0
1.95
15-30
17-44
q W
o
2
790
467
n
sat
Nonn et al. [10] [15] presented two studies of one, four and nine jets of 0.5 and 1
mm diameter, impinging on a 12.7 x 12.7 mm2 surface. The test fluid was FC 72 in the
first case and a mixture of FC72 and FC87 in the second. In both cases they detected an
effect of velocity on the heat transfer for the four and nine jet configurations when boiling
occurs on the surface; lower surface temperatures occurred at higher jet velocities for the
same heat flux. Also the boiling incipience point and the critical heat flux value were seen
to occur at higher heat fluxes as the velocity was increased. The liquid subcooling
affected the heat transfer, particularly at low heat fluxes. A higher degree of subcooling
corresponded to a higher heat flux for same wall superheat. Nonn et al. [10] [15] found
that a correlation by Lee et al. [12] for CHF on short heating lengths predicted well the
experimental results from both studies. The correlation was given as,
qCHF
⎛ρ
= 0.0742 ρ f h fg vn ⎜ f
⎜ρ
⎝ g
⎞
⎟⎟
⎠
−0.239
⎛ ρ f vn2 L ⎞
⎜⎜
⎟⎟
⎝ σ ⎠
−0.365
⎛
⎛ρ
⎜ 1 + 0.952 ⎜ f
⎜ρ
⎜
⎝ g
⎝
where L was the maximum flow length for each jet.
16
⎞
⎟⎟
⎠
0.118
1.414
⎛ c p f ΔTsub ⎞
⎜⎜
⎟⎟
⎝ h fg ⎠
⎞
⎟
⎟
⎠
(1.5)
Lay and Dhir [16], in an investigation of nucleate boiling heat transfer
enhancement by means of macro and micro structured surfaces cooled by an impinging
jet also tested a plane surface. The cooled surface had a diameter of 17.6 mm and it was
one side of a copper cylinder 25 mm long. The temperature profile measured by
thermocouples embedded in the slug along the middle axis allowed the calculation of
heat flux and surface temperature. The heating was provided by means of an electric arc
applied on the other side of the copper block. They used two jet diameters of 1.1 and 2.2
mm, and one water flowrate of 5.26 cm3/s. The liquid subcooling was maintained at
70oC. The maximum heat flux removed was 500 W/cm2 at 30oC of wall superheat.
Wolf et al. [11] reviewed a large number of studies on critical heat flux under
impinging jets. Most of the studies investigated a single saturated liquid impinging jet. It
was concluded that CHF increases with increasing jet velocity and liquid subcooling.
Physical properties and jet to surface diameter ratio were found to affect the magnitude of
CHF and their effects appear clearly in all the correlations of experimental data reported
in the literature. Among the various correlations available to predict CHF under saturated
jets, Wolf et al. particularly recommended three of them. One by Katto and Yokoya [26]
that was obtained using a large amount of data from studies by different researchers; one
by Monde et al. [22] and one by Sharan and Lienhard [28]. The correlations, with the
applicable range of parameters, recommended by Wolf et al. are reported below. Katto
and Yokoya’s correlation was given as,
qCHF
⎛ρ
= ρ g h fg vn ⎜ f
⎜
⎝ ρg
⎞⎛
⎛ ρf
⎟⎟ ⎜ 0.0166 + 7.00 ⎜⎜
⎠ ⎝⎜
⎝ ρg
17
⎞
⎟⎟
⎠
−1.12
−ξ
⎞ ⎛ ρ v 2 ( D − d ) ⎞ −ξ
⎛ D⎞
n
⎟⎜ f n
+
1
⎟⎟ ⎜
⎟
⎟ ⎝⎜
σ
⎝ d⎠
⎠
⎠
(1.6)
⎛ρ
where ξ = 0.374 ⎜ f
⎜ ρg
⎝
⎞
⎟⎟
⎠
−0.0155
It is applicable for 5 ≤
⎛ρ
for ⎜ f
⎜ ρg
⎝
⎞
⎛ ρf
⎟⎟ ≥ 248 and ξ = 0.532 ⎜⎜
⎠
⎝ ρg
⎞
⎟⎟
⎠
−0.0794
⎛ρ
for ⎜ f
⎜ ρg
⎝
⎞
⎟⎟ ≤ 248 .
⎠
ρf
D
≤ 53.9 , and 0.3 ≤ vn ≤ 60
≤ 1603 , 10 ≤ D ≤ 60.1 mm, 3.9 ≤
dn
ρg
m/s.
Monde et al. [22]correlation was expressed as,
qCHF
⎛ρ
= 0.280 ρ g h fg vn ⎜ f
⎜ ρg
⎝
⎞
⎟⎟
⎠
0.645
⎛ ρ f vn2 ( D − d n ) ⎞
⎜⎜
⎟⎟
σ
⎝
⎠
−0.343
⎛ D⎞
⎜1 + ⎟
d⎠
⎝
−0.364
(1.7)
Wolf et al. estimated the applicable range of parameters to be 15 ≤
10 ≤ D ≤ 60.1 mm, 5 ≤
ρf
≤ 1603 ,
ρg
D
≤ 57.1 , and 0.2 ≤ vn ≤ 60 m/s.
dn
Sharan and Lienhard [28] correlation was given as,
qCHF
where
⎛
⎛ ρf
= ρ g h fg vn ⎜ 0.21 + 0.00171⎜
⎜ρ
⎜
⎝ g
⎝
⎛ρ
ξ = 0.486 + 0.06052 ln ⎜ f
⎜ρ
⎝ g
applicable for 5 ≤
−ξ
⎞ ⎞ ⎛ ρ f vn2 D ⎞ ⎛ D ⎞ −
⎟⎟ ⎟ ⎜⎜
⎟⎟ ⎜ ⎟
⎟
⎠ ⎠ ⎝ 1000σ ⎠ ⎝ d ⎠
⎡ ⎛ ρf
⎞
⎟⎟ − 0.0378 ⎢ln ⎜⎜
⎢⎣ ⎝ ρ g
⎠
1
3
2
⎡ ⎛ ρf
⎞⎤
⎟⎟ ⎥ + 0.00362 ⎢ ln ⎜⎜
⎢⎣ ⎝ ρ g
⎠ ⎥⎦
(1.8)
3
⎞⎤
⎟⎟ ⎥ .
⎠ ⎥⎦
It
is
ρf
D
≤ 36.4 , and 0.3 ≤ vn ≤ 60 m/s.
≤ 1603 , 10 ≤ D ≤ 25.5 mm, 5 ≤
dn
ρg
Monde et al. [24] also investigated the effect of subcooling on the critical heat
flux under a free surface jet. Such effect was accounted for in the correlation of the
experimental data through a subcooling factor. The correlation was given as,
18
qCHF
where ε sub
⎛ρ
= 2.7 ⎜ f
⎜ ρg
⎝
⎛ρ
= 0.0745 ρ g h fg vn ⎜ f
⎜ρ
⎝ g
⎞
⎟⎟
⎠
0.725
⎛ ρ f vn2 D ⎞
⎜⎜
⎟⎟
⎝ σ ⎠
−1
3
(1 + ε sub )
(1.9)
2
⎞ ⎛ c p f ΔTsub ⎞
⎟⎟ ⎜⎜
⎟⎟ accounts for the subcooling effect.
h
g
⎠⎝
⎠
The effect of pressure on CHF was investigated by Katto and Shimizu [25] and by
Monde et al. [26], as reported by Wolf et al.. Experiments were conducted using R-12 as
test liquid with system pressures ranging from approximately 6 to 28 bars. It was found
that CHF weakly increases as the pressure is decreased.
Monde et al. [21] investigated CHF under multiple impinging jets. They studied
CHF under two and four jets. Saturated water and R-113 were the test fluids. Upward and
downward impinging configurations were tested, as well as configurations where the jets
impinged on the edge of the heater. When the jets impinged inside the heater boundaries,
CHF started at the edges.All the data for such cases were correlated as,
⎛ ρf
qCHF = 0.150 ρ g h fg vn ⎜
⎜ρ
⎝ g
⎞
⎟⎟
⎠
0.615
⎛ ρfv L⎞
⎜⎜
⎟⎟
⎝ σ ⎠
2
n
−1
3
⎛
⎞
⎜
⎟
1
⎟
⎜
2 ⎟
⎜
⎜ 1 + 0.00113 ⎛ 2 L ⎞ ⎟
⎜
⎟ ⎟
⎜
⎝ dn ⎠ ⎠
⎝
where L, the characteristic length, is the maximum flow length..
19
(1.10)
1.2.3 Overview
The first part of this work shows how the idea of a microjets based cooling
module is implemented. A prototype is built and tested as shown in Chapter 2. Then, the
focus will shift in Chapter 3 on the study of the heat transfer under microjets and on to
find an optimal configuration of the jet parameters.
In Chapter 4 the heat transfer under microjets is studied in a closed system
configuration, and an attempt to determine the effect of the presence of noncondensable
gas in the system on the heat transfer is made. Also, a modification to the experimental
set up allowed the study of boiling heat transfer under microjets.
In Chapter 5 a comparison between the heat transfer under microjets and under
droplet sprays is carried out. All the raw data are listed in the appendices as well as the
uncertainty analysis.
20
C
CH
HA
AP
PT
TE
ER
R 22
COOLING MODULE
In this Chapter, it is shown how the idea of using microjets has been converted
into a closed loop cooling module. A prototype was built and tested, and a procedure to
predict the performance was also established.
2.1 Experimental Apparatus
An impinging jets based cooling module requires three primary components: an
orifice plate for forming jets; a containment vessel to hold the nozzle, the heat source and
the cooling liquid, which also serves as a heat exchanger to the ambient; and a pump
which recirculates the coolant. A fan could be used to improve the heat transfer to the
ambient, and that would also allow the use of a smaller container. From a thermal
management point of view, the heat is first transferred from the heat source (the
electronic component), to the sprayed liquid. This causes part of the liquid to evaporate.
Heat is transferred from the hot liquid and vapor to the ambient by conduction through
the container’s walls. Details of a cooling module based on this idea are discussed below.
The cooling module, shown in Figure 2.1, consists of an aluminum box with
internal dimensions of 50 x 50 x 65 mm and wall thickness of 3.175 mm. At the bottom,
the box is closed with a 3.175 mm thick stainless steel plate. A 6.25 mm thick aluminum
21
flange, welded to the box walls, provides the interface for the bottom plate and the space
for an o-ring.
Inside the container, a stainless steel orifice plate is installed on a support located
above the heat source, as shown in Figure 2.2. The heat source consists of a diode used in
current controlled mode to avoid high voltages. The diode is mounted on a Direct Bond
Copper (DBC) substrate layer, which is in turn glued on top of a G10 insulating base (not
shown in Figure 2.2). The diode is 8.68 x 4.97 mm in size. The electrical connections are
provided by means of two copper rods, 3.175 mm in diameter. Four threaded rods hold
both the diode and the orifice plate assembly together and allow adjustment of the
relative distance between the diode and the orifice plate. The threaded rods are screwed
into the stainless steel plate, which forms the bottom of the box.
The orifice plate, 0.5 mm thick, has 24 holes (140 μm in diameter), distributed on
a square array pattern with 2 mm spacing. Details of the orifice plate are given below. A
3.175 mm OD stainless steel tube connects the orifice plate to the outlet of the pump. The
loop is closed with a 6.25 mm OD stainless steel tube connecting the bottom plate to the
pump inlet.
22
Electrical
Connection
Water
inlet
To Vacuum
Pump
Orifice
Plate
Fins
Diode
Electrical
connection
outlet
RTD
wire
Water
outlet
Pressure
Wire
Transd. and
outlet
Thermocouple
outlet
Figure 2.1 Cooling module.
23
Orifice
Plate
Jets
Diode
Copper
Rod
DBC
Substrate
Stainless
Steel
Support
Figure 2.2 Details of the diode and of the jets.
Aluminum pin fins, 20 mm long and 3.175 mm in diameter, are installed on the
outside of the container in a 45o staggered pattern with both pitches equal to 10.16 mm.
The fin tips are inserted into holes drilled into four aluminum plates, which are welded at
the corners and form an external shroud. A small DC fan is mounted at the bottom which
pushes ambient air over the fins. The air is forced only over the fins, since the gaps in the
corners between the external shroud and the fin array were blocked off. Figure 2.3 shows
a schematic of the experimental apparatus.
24
Thermocouple
Flowmeter
Filter
Pressure
Transducer
Valve
Fins
Gear
Pump
Jets
Diode
Valve
Module
Fan
Figure 2.3 Cooling module set up.
K-type thermocouples are used to measure the air temperature at the inlet and
outlet of the fin array, the inlet water temperature, and the temperature of the environment
in the chamber. Two RTD’s are used to measure the temperatures on the top of the diode
and on the back of the DBC, as shown in Figure 2.4.
25
Electrical
Connections
RTD
Diode
DBC Substrate
RTD
G10 base
Figure 2.4 Schematic of the RTDs placement.
An absolute pressure transducer is also installed to measure the pressure in the
chamber. An outlet for the RTD’s connecting wires and the electrical connections is
provided on the top of the box. To check the liquid level inside the box a short piece of
Tygon tubing is installed on the outside between the top and the bottom of the box.
Two pressure taps are present on one of the external plates and are connected to a
differential pressure transducer, which measures the pressure drop across the fins. A
variable speed gear pump is used to pump the liquid through the pipes and the orifice
plate. The liquid flow rate is measured using a rotameter. The overall dimensions of the
whole module, including the fan, are: 100 x 100 x 130 mm.
26
2.2 Experimental procedure and data acquisition.
Before the experiment was started, the thermocouples were calibrated by
submerging them in a pool of boiling water and in an ice bath, whose temperatures were
measured with a mercury thermometer with an accuracy of ± 0.1 oC. The absolute
pressure transducer (accuracy ±325 Pa) reading was used to find in the steam tables the
saturation temperature of water and this was then compared with the value given by the
thermometer submerged in a pool of boiling water. The two values were found to be
within ± 0.1 oC.
The module was first charged with 40.8 ml of deionized water at room
temperature. Subsequently the pump was started and the flow rate was set to the desired
value. Thereafter, the internal pressure of the chamber was reduced by means of a
vacuum pump. At steady-state chamber conditions, the vapor partial pressure was
calculated, using steam tables, assuming the temperature measured in the chamber is
equal to the vapor saturation temperature at the computed vapor partial pressure.
Thereafter, power was supplied to the diode and the data were recorded.
Assuming that the relative humidity inside the chamber is equal to 100%, the air
partial pressure can be calculated using Dalton’s law, as the difference between the total
pressure and the vapor partial pressure. The thermocouples, RTDs and chamber pressure
readings were recorded with a 16-bit Strawberry Tree data acquisition system. The
voltages supplied to the diode, the fan and the differential pressure transducer readings
were recorded using a Fluke multimeter. The current through the diode was read directly
27
from the power supply and the current through the fan was measured using a Fluke
multimeter.
Once steady-state was reached, either the power supplied to the diode or the fan
speed was varied. Due to the fact that thermocouples could not be used to measure the
diode’s temperatures and that the RTD’s contact area was not negligible compared to the
total area of the diode, a preliminary series of runs was performed. In those tests, for each
diode - DBC assembly was tested, with one RTD attached on top of the diode and one on
the back of the DBC layer. This was done to determine the thermal resistance across the
diode. The relationship between the temperatures on the front and back sides of the diode
was found to be linear. While conducting the experiments reported in this work, the top
RTD was removed to expose the whole top surface of the diode to the jets.
The very small air flowrates, produced by the Flight II 80 DC fan (ComairRotron, 80x80x25 mm in size) could not be measured directly. To determine the flowrate,
the relationship between the fan voltage and the pressure drop across the fins was first
established. Thereafter, air from a compressor, at a known flow rate measured with a
Dwyer rotameter, was blown over the fins and the pressure drop was measured again.
Finally, the relationship between airflow rate and fan voltage was established.
The experimental uncertainty is discussed in appendix D.
28
2.3 Results
All the tests were conducted keeping the jet velocity approximately constant at
4.5 m/s. Figure 2.5 shows the heat flux at the diode surface as a function of the
temperature difference between the top surface of the diode (Tw) and the sprayed liquid
(Tjets). Single phase heat transfer prevailed for the curves described by the solid symbols,
while boiling was the dominant mode of heat transfer for those represented by the open
symbols.
In Figure 2.5, the highest heat fluxes that could be achieved were limited by the
high current flow through the diode, as in the 16 kPa data set, or by the fan speed
reaching a maximum, as for the 104 kPa, or by critical heat flux (CHF) conditions, as in
the 6.5 kPa case. Furthermore, the data obtained by Jiang [9] using 150 μm jets spaced 2
mm apart is also plotted along in Figure 2.5. A Good agreement is seen between the data
obtained by Jiang [9] and the data for a 97.5% mass fraction of noncondensable gas,
considering that the liquid flowrate in her case was lower than that tested for the module
case. The mass fraction of air was obtained from,
Pair
mair =
Pair
Pbox
M air +
M
Pbox air
( Pbox − Pair )
29
(2.1)
Pbox
M water
where Pair and Pbox are the air partial pressure and the total pressure in the
chamber, respectively, and Mair and Mwater are the molecular weights of air and water,
respectively.
The advantageous effect of reducing the pressure in the chamber is clearly
illustrated in Figure 2.5. Lowering the system pressure lowered the boiling inception
point. For the same Tw = 80 oC and Tjets = 47 oC, the heat flux increased from 130 W/cm2,
achieved with single-phase heat transfer, to 300 W/cm2, obtained with boiling, when the
pressure was reduced from 114 to 16 kPa. This can be seen by comparing the curves
represented by the open circles and solid stars, in Figure 2.5.
30
O
o
O
o
Pbox 16.0 kPa, mair 13.0%, Tliq 49 C, Tsat = 55.4 C *
O
o
O
o
Pbox 16.0 kPa, mair 79.2%, Tliq 33 C, Tsat = 54.8 C
O
o
O
o
350
2
Liquid flow rate 145.0 ml/min/cm for all of the above cases
* T chip > Tsat
325
300
275
O
o
Jiang and Dhir [9] T liq 25 C, T sat = 99.9 C, s = 2 mm,
dn = 150 μm Liquid flow rate 109.1 ml/min/cm
2
2
Heat Flux [W/cm ]
250
225
200
175
150
125
100
75
50
25
0
0
10
20
30
40
50
60
70
80
90
100 110
O
Tchip-Tliq [ C]
Figure 2.5 Cooling module test results ( 4 x 6 array of jets, dn = 140 μm, s = 2 mm ): heat
flux versus Tw - Tliq.
Figure 2.6 shows the heat flux as a function of the wall superheat. It can be seen that,
when fully developed boiling occurs on the chip surface, all the curves collapse into one.
The total pressure is the key parameter in this case. The last point (q = 122.2 W/cm2, Tw –
Tjets = 16.7 oC) of the 6.5 kPa curve represents the critical heat flux. A 5% increase in the
jet velocity and a vapor to liquid density ratio of 2.4 times higher than the 4.5 ⋅10−5 value
31
at 6.5 kPa, is attributed for critical heat flux exceeding at 300 W/cm2 for the 16 kPa
pressure.
1000
O
o
O
o
Pbox 16.0 kPa, mair 13.0%, Tliq 49 C, T sat = 55.4 C
O
o
O
o
O
o
2
Heat Flux [W/cm ]
100
2
Liquid flow rate 145.0 ml/min/cm for all of the above cases
10
0.1
1
10
100
o
Tchip - Tsat [ C]
Figure 2.6 Heat flux as a function of wall superheat.
Referring to Figure 2.7, two main thermal resistances, an internal and an external,
were defined as,
32
Rint =
Tw − Tvap
(2.2)
Q
and
Rext =
Tvap − Tair
(2.3)
Q
Vapor
Tvap
Rext
Rint
Air
Tair
Cooling
Module
Chip
Tchip
Figure 2.7 Equivalent thermal circuit for the cooling module.
The external resistance was found to be unaffected by the presence of air inside the
module, and depended only on the air flowrate indicating that the air side resistance
33
dominated the condensation resistance on the inner wall of the box (Figure 2.8). The
internal resistance did not account the sensible heat stored in the liquid which flowed
from the chip to the bottom of the module from where it was drained and recirculated. It
was expected for the internal resistance to decrease as the mass fraction of air in the
chamber is diminished, but not enough data are available to conclude anything.
The only useful data in that regard are those for which only single phase is the
dominant mode of heat transfer, namely the sets for which mair are 79%, 94%, and 97%.
For the remaining data either boiling is occurring on the surface of the chip or air bubbles
are likely to be present on the surface enhancing the heat transfer. The data shown in
Figure 2.9 shows a somewhat high scatter for mair = 94% - 97% which makes them
insufficient to draw any conclusion on the effect of mair.
34
1.0
0.9
0.8
0.6
0.5
O
Rext [ C/W]
0.7
0.4
0.3
0.2
0.1
0.0
0
5
10
15
20
25
30
35
3
Air flowrate [m /hr]
Figure 2.8 Cooling module test results: external resistance versus air flowrate.
35
1.00
o
Tliq = 32 - 33 C
o
Tliq = 46 C
0.50
O
Rint ( C/W)
0.75
0.25
0.00
0.00
0.25
0.50
0.75
1.00
mair
Figure 2.9 Cooling module test results: internal resistance versus mass fraction of air
contained in the module.
Another important aspect that must be considered is the ratio of the power
consumed (used for cooling the diode and operating the fan) to the power removed from
the chip. The pumping power varied between 3.8 - 5.1 W, while the fan power varied
from 0 to 2.2 W. Although the flowrate was kept constant during each run, slightly
different values of flowrates were used and the pumping power for each of them was also
different.
36
From Figure 2.10, it can be seen that spray cooling becomes more effective as the
heat removed from the diode increases. This means that it is not convenient to employ
this cooling technique if the power to be removed and the heat flux are low. For the most
efficient case, the ratio of the total power spent to the power removed was around 4.4%.
However this value is still a very conservative value since in several cases the power
input to the chip was limited by restriction imposed by the current rather than the critical
heat flux.
Power Used/ Power Removed
30.0%
25.0%
20.0%
15.0%
10.0%
5.0%
0.0%
0
20
40
60
80
100
120
Power Removed [W]
Figure 2.10 Cooling module test results: process efficiency.
37
140
2.4 Summary
The concept of using arrays of liquid micro-jets was successfully implemented.
The module has proved capable of dissipating 129 W to the surrounding environment,
while removing a heat flux of 300 W/cm2 at a surface temperature of 80 oC, which is a
considerable achievement at the present time.
Reducing the system pressure had the effect of lowering the boiling inception
temperature, thus allowing for higher heat removal rates at lower surface temperature.
The external resistance decreased with increasing air flowrate and seemes to be
unaffected by the mass fraction of air present in the module. The data were too limited to
make any judgment on the internal resistance behavior with respect to the mass fraction
of air. The lowest value for the ratio between power spent and power removed was about
4%.
38
C
CH
HA
AP
PT
TE
ER
R 33
MICROJET ARRAYS: HEAT TRANSFER IN AN
OPEN SYSTEM CONFIGURATION
The heat transfer under arrays of microjets is parametrically investigated in order
to quantify the effect of the various parameters such as jet diameter, spacing, flow
velocity, and liquid properties on the overall process. The results were correlated using
relevant nondimensional parameters. Given the pressure drop data, this correlation can be
used to find the optimal configuration of the geometrical parameters under various
operating conditions.
An experimental rig was designed and built to test ten different arrays of
microjets. Figure 3.1 shows a schematic of the experimental setup. The coolant is
circulated with two variable speed gear pumps, installed in parallel. Two rotameters and a
turbine flowmeter were installed in parallel to measure the flow rate of the liquid being
sprayed. The accuracy of these flowmeters is ±3%. Before entering the flowmeters, the
coolant passed through a heat exchanger, where it was cooled down to the specified spray
temperature. The liquid was then pushed through a 0.5 mm thick stainless steel orifice
plate to form jets. The holes in the plate were laser drilled and were arranged in a circular
39
pattern with a radial and circumferential pitch of 1 mm, 2 mm, and 3 mm. The number of
jets corresponding to 1, 2, and 3 mm pitch spacing were 397, 127, and 61 respectively.
Unfortunately, the laser drilling process was not very accurate when dealing with
such small dimensions. Visual inspection of the orifice plates under a microscope showed
that the holes in the plate are slightly tapered and not exactly circular. Based on
photographs of the orifice plates, taken using a camera attached to a microscope, the size
of the holes were determined. These values are listed in Table 3.1. The measurement of
the diameters on both sides of the plate confirms that the holes are tapered. The taper also
varied from hole to hole.
Figure 3.1 Schematic of the experimental setup.
40
Table 3.1 Orifice plate details.
Plate
s
Label mm
a
b
c
d
e
f
g
h
i
j
1
2
3
1
2
3
1
2
3
1
dn exit STD dn inlet STD Thickness
μm
μm
μm
μm
mm
69.3
76.4
122.6
118.7
113.8
116.3
182.1
178.5
173.6
250
1.5
3.3
6.0
4.7
3.9
5.4
8.3
5.8
5.1
n.a.
94.3
139.5
69.2
136.8
167.5
184.8
263.8
228
263
n.a.
2.9
6.3
4.5
9.7
6.3
6.3
10.0
9.6
8.7
n.a.
0.51
0.51
0.63
0.51
0.51
0.51
0.51
0.51
0.51
0.51
Figure 3.2 shows a 60° slice of the orifice plates used. The orifice plate was
attached with screws to a stainless steel adapter, which was in turn connected to the
flowmeters with a pipe. The pipe passed through a flange positioned on top of the heat
transfer surface. The pipe could be moved in the vertical direction such that the distance
between the orifice plate and the cooling surface could be adjusted to the desired value.
The jet pressure was measured upstream of the stainless steel adapter using an Omega
PX202-300AV absolute pressure transducer (0 – 2.07 MPa), which had been factory
calibrated. It had an accuracy of 0.25% and a zero balance within 1% of full scale.
41
Figure 3.2 60o slice of each orifice plate: details of the jet’s area of influence.
The jets impinged on the top surface of a 19.3 mm diameter copper cylinder,
which represented the backside of an electronic microchip. The cylindrical surface was
enclosed in a Teflon jacket that provided thermal insulation. The cylinder had a larger
cylindrical base (76.2 mm in diameter and 16.5 mm in length), which contained six 750
W cartridge heaters. The power to the heaters was controlled with a variac. Four K-type
thermocouples, soldered at different axial locations (5 mm apart starting from 1.8 mm
below the top surface) along the central axis of the cylinder were used to compute the
heat flux and to extrapolate the temperature of the heat transfer surface.
Figure 3.3 shows a schematic of the test chamber. The Teflon jacket – copper
block assembly was mounted on a stainless steel plate. The sprayed liquid was drained
back to reservoir installed below the test section. Thermocouples to measure the liquid
temperature were installed both upstream of the flow meters and downstream of the
orifice plate. Another thermocouple was used to measure the ambient temperature. All the
data were recorded using two IO-Tech 16-bit data acquisition boards.
It is important to note that the outer one or two rings of jets, depending on the
pitch used, did not directly hit the copper surface but instead impinged on the
42
surrounding Teflon surface. Thus, the actual number of jets impinging directly on the
copper surface was 37, 61, and 271 for 1, 2, and 3 mm pitch, respectively.
Figure 3.3 Details of the test section.
3.2 Experimental Procedure
The thermocouples were calibrated prior to installation, by submerging them in an
ice bath and in boiling water, and comparing the readings with those provided by a high
accuracy mercury thermometer (±0.1 oC). Prior to running the experiment the copper
surface was polished using a 600 grit sandpaper and then a copper polishing solution,
which made the surface very smooth and shiny. Thereafter, in order to guarantee the same
surface condition throughout the duration of the experiment, the surface was oxidized in
air for five hours at 320 oC.
After the pumps were started, and the liquid flow rate set to the desired value, the
cartridge heaters were energized. Once all the parameters reached steady state, values
were recorded for 100 s at a sampling rate of 1 Hz. The data acquisition system allowed
43
real time monitoring of all parameters in both numerical and graphical form so that it was
possible to assess when steady state had been reached. Thereafter, the power to the
copper block was increased and a new set of data recorded. The experiment was stopped
when either the surface temperature was above the boiling point or when the temperature
at the base of the copper block rose to above 350 oC, which could damage the Teflon
jacket and the electrical wires.
44
3.3 Data Reduction
For each data set recorded, the heat flux at the heat transfer surface was calculated
from the slope of the temperature profile obtained from the four thermocouples
embedded in the copper block. The same temperature profile, which was mostly linear,
also allowed the temperature at the heat transfer surface to be calculated (by
extrapolation). A sample calculation is shown in the appendix B
The average heat transfer coefficient, Nusselt number, and Reynolds number are
defined as,
h=
q
Tw − T jets
(3.1)
Nu =
hd n
k film
(3.2)
Re dn =
vn d n
(3.3)
4V
Nπ d n2
(3.4)
ν film
where,
vn =
45
All the physical properties are evaluated at the mean film temperature, Tfilm. The
uncertainty associated with each quantity is discussed in appendix B. Repeatability of the
data was explored by randomly repeating some of the cases already tested. Two examples
of the good repeatability are shown in Figure 3.4 and Figure 3.5, where the data for the
second and third series fall within the 95% confidence interval, proving that random error
is negligible.
100
s = 3 mm, dn = 122.6 μm
90
2
Pr = 6.1, Flowrate = 6.86 μl/mm s
±95% Confidence Band
±95% Confidence Prediction Band
80
70
60
2
q [W/cm ]
2
50
40
30
20
10
0
0
10
20
30
40
50
o
Tw - Tjets [ C]
Figure 3.4 Data repeatability.
46
60
70
80
200
2
q [W/cm ]
150
100
s = 2 mm, dn = 76.4 μm
2
50
2
2
0
±95% Confidence Band
±95% Confidence Prediction Band
0
20
40
60
o
Tw - Tjets [ C]
Figure 3.5 Data repeatability.
47
80
100
3.4 Results and Discussion
A comparison of the heat transfer data from the present work with the results
obtained by Oliphant et al. [8], is shown in Figure 3.6. It shows that the same heat
transfer rate is obtained at much lower coolant flowrates when arrays of microjets are
used instead of arrays containing a few large jets. The reduction in the flowrate is around
one order of magnitude.
2O
h [W/cm C]
10
Oliphant et al.
Jet arrays
N = 4, d n = 1.00 mm
N = 7, d n = 1.00 mm
N = 7, d n = 1.59 mm
1
Micro jets
s = 2 mm, dn
s = 1 mm, dn
s = 2 mm, dn
s = 3 mm, dn
s = 3 mm, dn
s = 2 mm, dn
0.1
10
100
1000
= 76.4 μm
= 69.3 μm
= 113.8 μm
= 116.3 μm
= 173.6 μm
= 178.5 μm
10000
Flow rate [ml/min]
Figure 3.6 Comparison between the heat transfer under arrays of microjets and the results
by Oliphant et al. [8].
48
Although cooling with impinging jets is quite a complicated phenomenon, where
many variables affect the heat transfer rate, in this work only three dimensionless
quantities are used to describe the time- and area-averaged heat transfer coefficients.
They are the jet Reynolds number (Redn), the liquid Prandtl number (Pr), and the ratio of
jet pitch and diameter at the nozzle exit (s/dn). The distance from the nozzle exit to the
heated surface was kept fixed at 10 mm and is not considered to be a parameter. All fluid
properties are evaluated at the mean film temperature. In the experiments it was noticed
that air bubbles existed in the liquid film covering the impinged surface, particularly
when the surface temperature approached the saturation value. This phenomenon,
resulting from air being trapped by the liquid jets, became more evident at higher liquid
velocities and closely spaced jets. It is possible that this lead to some enhancement of the
heat transfer from the surface to the liquid. Therefore, even though boiling usually is
initiated at a wall temperature higher than the saturation value, only data obtained for Tw
< Tsat are considered.
Pan and Webb’s study [4] also included the results obtained for a nozzle to heater
distance of 2 jet diameters, where the jets were changing from submerged to free surface
jets. Using only the data for higher nozzle to heater distance (only free jets) Pan and
Webb [4] reported a better fit to their experimental data. The data were correlated with
the expression,
⎛
s ⎞
0.4
Nu = 0.129 Re0.71
exp ⎜ −0.1 ⎟
d n Pr
dn ⎠
⎝
49
(3.5)
Different functions were tried to fit all the experimental data obtained but the best
correlation was achieved with the following expression,
⎛
s ⎞
0.48
Nu = 0.043Re0.78
exp ⎜ −0.069 ⎟
d n Pr
dn ⎠
⎝
(3.6)
A commercial software Datafit 7.1 by Oakdale Engineering was used to perform the
least-squares fitting process. The goodness of the fit for the 571 experimental data points
given by Eq. (3.6) is listed in Table 3.2. Figure 3.7 shows a comparison of prediction
from Eq. (3.6) with the data. Almost all of the experimental data are predicted to within
±25%. The correlation developed is strictly valid for the following range of parameters:
•
43 ≤ Re dn ≤ 3813
•
2.6 ≤ Pr ≤ 84
•
4≤
s
≤ 26.2
dn
Table 3.2 Prediction error on the experimental data.
% data points predicted by Eq. (3.6) 84.1 91.8 96.2
Standard Error %
50
20
25
30
20
18
16
14
+25%
Nupredicted
12
10
-25%
8
6
4
2
0
0
2
4
6
8
10
12
14
16
18
20
Nuexperimental
Figure 3.7 Comparison of the experimental and predicted Nusselt number.
Figure 3.8 gives a graph which shows the variation of the quantity
⎛
s ⎞
Nu 0.043Pr 0.48 exp ⎜ 0.069 ⎟ as a function of Redn. From Eq. (3.6) and Figure 3.8, it
dn ⎠
⎝
can be seen that Nu varies as Redn0.78, which is higher than the 2/3 power found by Pan
and Webb [4] and the 0.5 power obtained by Jiji and Dagan [3]. However, Eq. (3.5) gives
Nu ∝ Re0.71, which is close to the dependence found in the present study. It should
51
however be noted that none of the previous studies fully investigated the supposedly
laminar regime.
As has been reported by Webb and Ma [1], several researchers have found that Nu
varies as Redn0.5 for a single free surface liquid jet in the laminar regime. Only Elison and
Webb [2] found a stronger dependence of Nu on Redn (Nu ∝ Redn0.8), but they attributed
this enhancement to surface tension effects at the nozzle exit, which caused the jet
diameter to be bigger than the actual inner diameter of the nozzle. In the present study,
surface tension caused the jets to merge together at low jet velocities. All of the data
reported here are for velocities at which merger did not occur. Because the data for two
liquids, with widely different surface tensions, show the same dependence on the
Reynolds number, surface tension is not considered to be playing a role in causing a
stronger dependence on Redn. Entrained air may be the reason for enhanced heat transfer.
⎛
s ⎞
In Figure 3.9, the parameter Nu 0.043Re0.78
⎟ is plotted as a
d n exp ⎜ 0.069
dn ⎠
⎝
function of Pr. Consistent with correlation Eq. (3.6), Nusselt number is found to vary as
Pr0.48, which is slightly higher than that found by Womac et al. [5] (Nu ∝ Pr0.4). Figure
3.10 shows that Nu decreases exponentially with increasing s/dn.
52
1000
100
n
Nud /[0.043Pr
0.48
exp(-0.069s/dn)]
Water
FC40
Re
10
10
0.78
100
1000
Red
n
Figure 3.8 Variation of Nu with Redn for varying Pr and s/dn.
53
10000
100
10
0.48
Pr
1
n
Nud /[0.043Re
0.78
exp(-0.069s/dn)]
Water
FC40
0.1
1
10
Pr
Figure 3.9 Variation of Nu with Pr for varying Redn and s/dn.
54
100
10
]
Water
FC40
exp(-0.069s/dn)
0.1
n
Nud /[0.043Re
0.78
Pr
0.48
1
0.01
1
10
100
s/dn
Figure 3.10 Variation of Nu with s/dn for varying Redn and Pr.
Figure 3.11 - Figure 3.16 show the Nusselt number obtained from Eqs. (3.5), (1.4)
, (1.3), and (3.6) as a function of Redn for same Pr, but for s/dn of 26.1, 13.3 and 6.7,
respectively. . It is found that the predictions differ somewhat from each other. This
difference could be due to the fact that in most cases the magnitude of at least one of the
parameters lies outside the range of the correlations. A similar trend was found for higher
values of the Prandtl number.
55
2
10
1
10
0
Nud
n
10
10
Pan & Webb [4] 2 ≤ s/dn ≤ 8
Yonehara & Ito [7] 13.8 ≤ s/dn ≤ 330
Womac et al. [5] 5 ≤ s/dn ≤ 20
Present work 4 ≤ s/dn ≤ 26.2
s/dn = 26.1 Pr = 3.6
-1
10
1
10
2
3
10
10
4
10
5
Red
n
function of Redn for s/dn = 26.1 and Pr = 3.6.
Nud
n
10
3
10
2
10
1
10
0
10
Pan & Webb [4] 2 ≤ s/dn ≤ 8
Yonehara & Ito [7] 13.8 ≤ s/dn ≤ 330
s/dn = 13.3 Pr = 3.6
-1
10
1
10
2
3
10
10
4
10
5
Red
n
56
10
3
2
10
1
10
0
Nud
n
10
Pan & Webb [4] 2 ≤ s/dn ≤ 8
Yonehara & Ito [7] 13.8 ≤ s/dn ≤ 330
Present work
s/dn = 6.7 Pr = 3.6
1
10
10
2
10
3
10
4
5
10
Red
n
10
3
2
10
1
10
0
Nud
n
10
Pan & Webb [4] 2 ≤ s/dn ≤ 8
Yonehara & Ito [7] 13.8 ≤ s/dn ≤ 330
s/dn = 26.1 Pr = 30.5
1
10
10
2
10
3
10
4
5
10
Red
n
57
10
3
2
10
1
10
0
Nud
n
10
Pan & Webb [4] 2 ≤ s/dn ≤ 8
Yonehara & Ito [7] 13.8 ≤ s/dn ≤ 330
s/dn = 13.3 Pr = 30.5
1
10
10
2
10
3
10
4
5
10
Red
n
10
3
2
10
1
10
0
Nud
n
10
Pan & Webb [4] 2 ≤ s/dn ≤ 8
Yonehara & Ito [7] 13.8 ≤ s/dn ≤ 330
s/d n = 6.7 Pr = 30.5
1
10
10
2
10
3
10
4
5
10
Red
n
58
Figure 3.17 shows a comparison of predictions of various correlations as a
function of s/dn. It is found that for small s/dn values, the experimental results of Pan and
Webb [4] do not differ significantly from those predicted by extrapolating Eq. (3.6). For
5000 < Re < 20000 the three lines representing the work of Pan and Webb, Eq. (3.5),
Pr 0.48 from Eq. (3.6), fall very close to each other
normalized using the quantity Re0.78
d
n
and to the one representing the present work. At higher s/dn the present work matches
well with the work of Yonehara and Ito [7], Eq. (1.4). The data Yonehara and Ito used to
validate their theoretical work are also plotted. The data from the present work nicely fills
in the gap in the previous data with respect to s/dn (8 ≤ s/dn ≤ 13.8).
59
10
-1
Pan & Webb [4]
Eq. (3.5) 2 ≤ s/dn ≤ 8
5000 ≤ Red ≤ 20000
5000
n
Pr
0.48
]
10
0
Yonehara & Ito [7]
(Eq. 1.4) 13.8 ≤ s/dn ≤ 330
7100 ≤ Red ≤ 48000
10
-2
20000
n
Eq. (3.6)
n
Nud /[Re
0.78
10000
7100
10
28000
-3
48000
Pr = 7
10
Present work
Experimental data by Yonehara & Ito [7]
-4
1
10
100
500
s/dn
Figure 3.17 Comparison of the effect of s/dn on the Nusselt number in the present work
and those of Pan and Webb [4] and Yonehara and Ito [7].
60
3.5 Effect of the orifice plate to heater distance
A series of experiments was carried out to investigate the effect of the nozzle to
heater distance (z) on the heat transfer rate. With FC 40 as the test liquid, experiments
were conducted at flowrates of 240 ml/min [13.67 μl/mm2s] and 410 ml/min [23.36
μl/mm2s]. Only a single configuration of jets was tested. It had a jet pitch of 3 mm and a
jet diameter of 173.6 μm. The spray distance was parametrically varied from 10 mm to
2.1 mm, which corresponds to a range of z/dn between 12.1 and 57.6.
In order to establish a common reference point, all the results have been compared
with those predicted from Eq. (3.6), the data for which had been obtained for a z/dn value
of 57.6. Figure 3.18 shows the ratio between the Nu based on the observed heat trandfer
coefficient and that obtained from Eq. (3.6), as a function of the nondimensional nozzle
to heater distance. It can be seen that there is little effect of the spray distance on the heat
transfer as long as z/dn is greater than 12.1.
61
1.2
1.0
Nuz/d/Nu57.6
0.8
0.6
0.4
0.2
FC40, s = 3 mm, dn = 173.6 μm
0.0
0
10
20
30
40
50
60
z/dn
Figure 3.18 Effect of different spray distance on the heat transfer.
62
70
3.6 Optimal jet configuration
It is a matter of interest to know if there exists a particular combination of jet
parameters that yields optimal performance. To find an optimum, a cost function must be
defined and the constraints of the range of parameters must be taken into account. In the
design phase of an electronic cooling concept, the requirements are usually the maximum
power that must be removed from the component, the dimensions of such a device and
the maximum junction temperature that allows the component to work reliably.
The heat exchanger, which ultimately transfers the heat removed from the
electronic component to the environment, controls the coolant spraying temperature.
Once Tw – Tjets is fixed, the two quantities that can be minimized are the coolant flowrate
and the power needed to pump the liquid. The choice of one over the other depends on
the specific requirements of the application. For example, there might be constraints on
the volume or on the energy consumption.
The pumping power required to push the liquid through the orifice plate can be
calculated by multiplying the volumetric flowrate and the pressure drop, ΔP, across the
orifice plate. This can be expressed as,
Q pumping = V ΔP
(3.7)
In this study, the pressure drop data were recorded during each experiment.
Additional tests using water were also conducted to measure only the pressure drop
63
across the orifice plates. Based on the data, the friction factor was calculated using the
expression,
f =
ΔP
1 ρ v (t
plate / d n )
2
2
n
=
ΔP
2
⎞
⎛
1 ρ ⎜ 4V ⎟ (t / d )
2 ⎜ N π d 2 ⎟ plate n
⎝ jets n ⎠
(3.8)
The calculated friction factors are plotted in Figure 3.19 as function of Redn. A
least-squares fit of the data yields,
f = 0.507 +
189.9 μ N jetsπ d n
189.9
= 0.507 +
Re dn
4 ρV
(3.9)
where Redn is the jet Reynolds number calculated using fluid properties evaluated at the
jet temperature. The jet diameter used to calculate Redn is based on the smallest orifice
diameter.
64
100
10
f
1
0.1
0.01
10
Test s = 1, 2, 3 mm, dn = 182, 179, 174 μm
Test s = 1, 2, 3 mm, dn = 119, 114, 116 μm
Test s = 1, 2, 3 mm, dn = 69.3, 76.4, 69.2 μm
Experimental data
100
1000
10000
Red
n
Figure 3.19 Normalized pressure drop across the orifice plates.
Once s, dn, Qremoved, Tw – Tjets, and AH are specified, Eq. (3.6) can be used to
determine the flowrate necessary to remove the given power. That flowrate can be
expressed as,
⎡
⎢
Qremoved ⋅ d n
V =⎢
⎢
⎛
s ⎞
0.48
⎢ 0.043Pr exp ⎜ −0.069 ⎟ k (Tw − T jets ) AH
dn ⎠
⎢⎣
⎝
65
1
⎤ 0.78
⎥
N jetsπ d n μ
⎥
⎥
4ρ
⎥
⎥⎦
(3.10)
The pumping power can then be calculated by substituting V obtained from Eq.
(3.10) into Eqs. (3.7). The pumping power is finally only a function of dn, Qremoved /(Tw Tjets), s, and the fluid properties. The jets impinging on a given area is a discrete number.
Table 3.3 lists the number of jets impinging on a circular surface of 19.3 mm diameter
from a circular array with equal radial and circumferential pitch.
It is not possible to determine the minimum of Qpumping analytically (with respect
to dn, s, and Qremoved /(Tw - Tjets)) due to the nonlinearity of the function and the discrete
nature of Njets (s can only change discretely). As such, Qpumping is determined by
parametrically varying the independent parameters. For a given Qremoved, Tw - Tjets, Tjets,
and fluid, a graph like the one shown in Figure 3.20 can be easily obtained. The
extrapolated results for s = 0.5, 4, and 5 mm are plotted along with the 1, 2 and 3 mm
values of s studied in the present work. The value of Qpumping for fixed pitch, as a function
of dn is obtained by following the procedure described above. The largest value of dn is
equal to s/2 (where the jets would start merging) and the smallest value of dn is 25 μm
(where the jets are so small that the chances of clogging of the holes of the orifice plate
are considered to be too high). From Figure 3.20 it is seen that optimum jet diameter
increases with increase in pitch. In this particular case, the optimal configuration, yields a
pumping power of 2.53·10-2 W using a jet spacing of 2 mm and a jet diameter of 325 μm.
If the results of this study are extrapolated to jet spacings larger than those tested in this
study, the optimal configuration for the same case requires a jet spacing of 5 mm and jet
diameter of 775 μm, consuming 1.16·10-2 W.
66
Table 3.3 Number of jets impinging on a circular surface of 292.5 mm2.
s [mm]
0.5
1
2
3
4
5
Njets
1141
271
61
37
19
7
2
10
Water
o
Tjets = 18.6 C
o
Tw - Tjets = 60 C
Qremoved = 439 W
1
10
Qpumping [W]
2
q = 150 W/cm
DH = 19.3 mm
Lplate = 0.51 mm
s = 0.5 mm
s = 1.0 mm
s = 2.0 mm
s = 3.0 mm
s = 4.0 mm
s = 5.0 mm
0
10
10
-1
10
-2
10
-3
1
10
10
2
3
10
10
4
5
10
dn [μm]
Figure 3.20 Qpumping as a function of dn for a specific Qremoved/(Tw - Tjets).
The above procedure can be repeated for different Qremoved /(Tw - Tjets) and the
minimum value of each curve can be used to develop a graph like that shown in Figure
3.21 that includes the effect of all the main parameters. It is seen from Figure 3.21 that
67
for a fixed s, the optimum pumping power increases with Qremoved / (Tw - Tjets), but the
corresponding optimum jet diameter is weakly dependent on Qremoved / (Tw - Tjets). The
pumping power for a fixed s increases with Qremoved / (Tw - Tjets) because a larger flowrate
is needed for the cooling process.
There are also some constraints that must be satisfied. For the chosen combination
of geometrical parameters, flowrate and coolant it must be possible to form jets, and that
the jet velocity or the pressure drop must not attain unrealistic or impractical values.
10
1
10
0
s = 0.5 mm
1
2 34
Fluid: Water
o
Tjets = 18.6 C
Lplate = 0.51 mm
DH = 19.3 mm
Qremoved/(Tw - Tjets)
o
[W/ C]
0.6
1.2
2.4
4.9
7.3
9.8
12.2
14.6
17.1
19.5
5
-1
Qpumping [W]
10
-2
10
-3
10
-4
10
-5
10
-6
10
10
1
10
2
10
3
10
4
10
5
dn [μm]
Figure 3.21 Variation of the optimal Qpumping as a function of dn for different Qremoved/(Tw Tjets) and s.
68
If the flowrate is the parameter that must be minimized then the minimum value
for Eq. (3.10) must be found. It is easy to find for the given values of Qremoved / (Tw - Tjets),
AH, and fluid properties the volumetric flowrate versus dn for different values of s, as
shown in Figure 3.22.
s =0.5 mm, dn min = 19.4 μm
s = 1 mm, dn min = 38.8 μm
s = 2 mm, dn min = 77.5 μm
s = 3 mm, dn min = 116.3 μm
s = 4 mm, dn min = 155.0 μm
s = 5 mm, dn min = 193.8 μm
3
2
Flowrate [μl/mm s]
100
4
10
0.5
2
1
5
o
Water, Tjets = 18.6 C, Qremo ved = 438.9 W
o
1
2
Tw-T jets = 60 C, Area = 292 mm
1
10
100
1000
dn [μm]
Figure 3.22 Flowrate versus dn for different s.
Alternatively, setting the first derivative of Eq. (3.10) with respect to dn to zero,
the value of dn can be obtained as,
69
d n = 3.876 ⋅10−2 s
(3.11)
The minimum flowrate is then obtained by substituting Eq. (3.11) into Eq. (3.10). This
yields,
1
⎡
⎤ 0.78 0.365 N jetsπμ s 2.282
Qremoved
V = ⎢ 0.48
⎥
ρ
⎢⎣ Pr k (Tw − T jets ) Aheater ⎥⎦
(3.12)
The smallest feasible value of s will yield the minimum flowrate. After the minimization
of Qpumping, it must be checked that jet velocity and pressure drop have acceptable values.
As a final consideration, it is interesting to see which combination of jet diameter
and jet pitch gives the highest heat removal rate for the same flowrate. Table 3.4 shows
an example for a water flowrate of 2·10-6 m3/s impinging on an area of 292 mm2 (6.84
μl/mm2s), with a jet temperature of 18.6 oC, Tw - Tjets = 60 oC, and an orifice plate
thickness of 0.51 mm. The best performing configuration is the one having the largest
number of the smallest diameter jets. When the jet number is decreased the best
configuration has a dn = 100 μm. At smaller values of dn, the jets are too far apart, and the
increase in vjet cannot compensate for the effect of large jet spacing. At a higher dn, the jet
velocity is too low and the increased s/dn does not make up for it.
The numbers in italics indicate parameters that are not acceptable. For those jet
diameters and velocities below 2 m/s (using water), jets start to merge at the exit of the
orifice plate. A pressure drop above 0.5 MPa is not acceptable for electronic applications.
70
It should be noted that the pumping power given here does not include pump efficiency
and the pressure losses in the piping forming the loop. For implementing the concept in a
closed system a fan must also be used to dissipate heat to the environment. Such fan
losses will also be in addition to the pumping power calculated here.
A few final words must be spent on the fact that usually the pumping power
utilized for the cooling process is only a few percent of the total power removed from the
system, thus rendering the optimization of the jet parameters not so critical for the
cooling system.
Table 3.4 Qremoved, vjets, ΔP for a flowrate of 2·10-6 m3/s of water. Tw-Tjets = 60 oC, Tjets =18.6
o
C, Area = 292 mm2 (6.84 μl/mm2s), tplate = 0.51 mm.
s [mm]
1
2
3
dn
Qremoved
vjets
ΔP
Qremoved
vjets
ΔP
Qremoved
vjets
ΔP
[μm]
[W]
[m/s]
[Pa]
[W]
[m/s]
[Pa]
[W]
[m/s]
[Pa]
50
418.7
3.76
76899
337.1
16.70
894007
125.3
27.53
2236197
100
243.1
0.94
3678
390.2
4.17
33600
289.0
6.88
79216
150
148.7
0.42
652
300.3
1.86
5170
280.0
3.06
11661
71
3.7 Summary
Single phase heat transfer under circular free surface microjet arrays using water
and FC 40 as tests liquids has been experimentally studied. It was found that Nu
improves with increasing Redn, and Pr, and decreasing s/dn. The Nusselt number was
found to have stronger dependence on the Reynolds number than that reported by
previous researchers. However, the previous studies did not consider arrays with as many
jets as those used in the present study, and also never used jet diameters smaller than 500
μm.
An empirical correlation containing only three dimensionless parameters has been
developed. It was used in conjunction with the pressure drop data to find an optimal
configuration which depends on the heat flux and the cooling requirements. For the 150
W/cm2 sample case, the optimal configuration, yields a pumping power of 2.53·10-2 W
using a jet spacing of 2 mm and a jet diameter of 325 μm. If the results of this study are
extrapolated to larger jet spacing, the optimal configuration for the same case will require
a jet spacing of 5 mm and jet diameter of 775 μm, consuming 1.16·10-2 W.
If the flowrate has to be minimized, it was found that d n = 3.876 ⋅ 10 −2 s . In
employing this approach, one must always verify that the jet velocity and the pressure
drop have acceptable values. If the flowrate is kept constant, the configuration that has
the highest heat removal rate has a large number of small diameter jets. For example, 418
W could be removed using a jet spacing of 1 mm and a jet diameter of 50 μm.
72
It has also been pointed out how the minimization of the pumping power is not
very critical since it amounts in any case to only a few percent of the total power
removed.
73
C
CH
HA
AP
PT
TE
ER
R 44
MICROJET ARRAYS: HEAT TRANSFER IN A
CLOSED SYSTEM CONFIGURATION
A set of experiments in a closed system configuration has been carried out to
investigate the effect of the presence of noncondensable gases in the environment
surrounding the jets. The experimental apparatus has also been modified to perform
experiments at higher heat fluxes than those possible using cartridge heaters inserted in a
copper block. Two phase data are presented and discussed.
The experimental rig used for the experiments in the open system configuration
was modified to allow the control of the noncondensable gases content in the ambient
surrounding the jets. A stainless steel chamber 190 mm x 190 mm x 205 mm was built
and a flange was mounted at the bottom, matching the size of the stainless steel plate on
which the copper block assembly, described in Chapter 3, was installed. Two K - type
thermocouples were inserted through the top to measure the temperature inside the
chamber. A factory calibrated absolute pressure transducer, PX202-030AV model
manufactured by Omega (0.25% accurate, with a zero balance of 1% of full scale), was
installed also at the top of the chamber to provide the pressure in the system. The pipe on
74
which the adapter carrying the orifice plate was mounted passed through an o-ring fitting
installed in the center of the top plate of the chamber. When the bottom plate, in which an
o-ring was installed, was screwed on the chamber flange, providing a vacuum tight
sealing, the copper block was exactly centered under the orifice plate. A vacuum pump,
connected to the top of the chamber was used to remove the noncondensable gases.
Alternatively, instead of the vacuum pump, a compressed air supply could be attached to
the top of the chamber.
The chamber was insulated using a fiberglass blanket 2.5 cm thick to reduce the
heat losses. Also two electric plate heaters were installed on two opposite sides of the
chamber. They were used to compensate for heat losses during the experiments. The
copper block base was also insulated using the same fiberglass blanket. The schematic of
the modified set-up and of the test chamber are shown in Figure 4.1 and Figure 4.2.
75
Figure 4.1 Schematic of the experimental rig for the closed system tests.
76
Figure 4.2 Test chamber for the closed system configuration experiments.
A finned copper coil, 9.52 mm O.D., was inserted into the chamber through two
fittings mounted on the top plate, and it was connected to a chilled water line. A needle
valve and a solenoid valve were installed in series on the coil line to control the flow. An
extra heat exchanger was installed on the jet pipeline to heat up the spray liquid to the
desired temperature. The cartridge heaters in the copper block, the liquid heater, and the
two plate heaters were controlled manually using a Variac. The water flow in the finned
cooling coil inside the chamber was controlled by a solenoid valve which received the
77
opening signal from the data acquisition system, based on the pressure readings acquired
in real time.
78
4.2 Experimental Procedure
Before installation, the thermocouples were calibrated by submerging them in an
ice bath and in a pool of boiling water. A very accurate mercury thermometer (±0.1 oC)
provided the reference temperature values during calibration. The pressure transducers
were also checked against the saturation pressure at the boiling point of water.
Before starting the experiment, the chamber was evacuated to the desired
pressure. The pump was started and the liquid flowrate was set at the desired value. Once
the temperatures were steady, the pressure in the chamber was checked, and adjustments
were made if necessary. Thereafter, the liquid was brought to the desired temperature by
using the heater installed after the flowmeters. The liquid temperature was chosen such
that the vapor pressure at that temperature added to the initial chamber pressure would
give 101 kPa. The two electric plate heaters were also switched on and helped in
maintaining the temperature in the chamber constant at the set value. At the bottom of the
chamber a heat gun blowing hot air on the stainless steel plate reduced the heat loss.
Once the pressure reached the set value, the cartridge heaters in the copper block were
powered. Once all the temperatures were steady, the data were recorded by using the data
acquisition system for 100 s with a sampling rate of 1 Hz. The maximum flow of coolant
through the copper coil could be controlled using a needle valve installed before the
solenoid valve. The solenoid valve opened when the chamber pressure went above the set
value. The pressure oscillations in the chamber were in most of the cases less than 1.5
kPa.
79
The experiment was stopped when the temperatures in the base of the copper
block were around 350 oC, in order to protect the Teflon jacket and the cartridge heaters
wires from being damaged.
80
4.3 Data Reduction
The data reduction follows the same procedure as described in Chapter 3 for the open
system. In addition to that, the chamber temperature was taken as the arithmetic average of
the two thermocouple measurements. The vapor partial pressure was calculated for each data
point by assuming 100% relative humidity in the chamber, and using the average chamber
temperature as,
Pvap = Psat (Tbox )
(4.1)
The air fraction in the chamber was calculated as
X air = 1 −
81
Pvap
Ptot
(4.2)
4.4 Results and Discussion
Three orifice plates have been tested in a closed system configuration using water
as test fluid. The exact test configurations are shown in Table 4.1.
Table 4.1 Test configurations.
Plate
Label
s [mm] dn [μm] V [ml/min] [μl/mm2s]
d
1
118.7
516
29.4
f
3
116.3
233
13.27
f
3
116.3
350
19.94
i
3
173.6
230
13.10
i
3
173.6
360
20.51
4.4.1 Single phase data
Figure 4.3 - Figure 4.7 show the heat flux versus Tw - Tjets data for test cases with
different noncondensable gas content in the chamber. The predictions obtained using Eq.
(3.6) are also plotted along. It can be noticed how the experimental data for different
values of Xair are well the predicted by Eq. (3.6). This clearly indicates that the effect of
the presence of noncondesible in the chamber is negligible or none at all for the range of
flowrates tested.
82
No data useful could be obtained running the same type of experiment for cases
having a lower Xair, because the jet temperature was close to the saturation value
corresponding to the total pressure in the chamber, and even at low heat flux the wall
temperature was greater than Tsat, indicating that boiling might occur on the surface.
It has also been reported that air entrained or dissolved in the liquid jets tends to
form bubbles on the impinging surface even when boiling has not yet started. This
phenomenon enhances the heat transfer and it is hard to quantify.
2
q [W/cm ]
100
s = 1 mm, dn = 118.7 μm, water
10
o
Psystem = 101 kPa, T sat = 99.9 C
2
Flowrate = 29.4 μl/mm s
o
Tjets 91.3 C, Xair = 24.4%
Prediction Eq. (3.6)
o
Tjets 81.6 C, Xair = 50.1%
o
Tjets 61.4 C, Xair = 79.7%
1
1
10
100
o
Tw-Tjets [ C]
Figure 4.3 Heat flux versus Tw – Tjets for different Xair. s = 1 mm, dn = 118μm, V = 516
ml/min [29.4 μl/mm2s].
83
300
o
Tjets 82.9 C, Xair = 46.5%
o
Tjets 20.3 C, Xair = 97.4%
s = 3 mm, dn = 116.3μm, water
100
o
Psystem = 101 kPa, Tsat = 99.9 C
2
2
q [W/cm ]
10
1
1
10
100
o
Tw - Tjets [ C]
200
100
2
q [W/cm ]
o
Tjets 92.8 C, Xair = 23.9%
o
Tjets 81.7 C, Xair = 49.2%
o
Tjets 65.9 C, Xair = 74.9%
o
Tjets 17.9 C, Xair = 97.9%
10
o
2
1
1
10
100
o
Tw - Tjets [ C]
84
100
o
2
o
2
q [W/cm ]
T jets 66.1 C, Xair = 75.1%
10
1
1
10
100
o
Tw-Tjets [ C]
400
o
2
q [W/cm ]
100
10
1
0.1
0.1
2
o
Tjets 96.2 C, Xair = 10.2%
o
Tjets 91.2 C, Xair = 23.2%
o
Tjets 92.3 C, Xair = 25.3%
o
Tjets 81.8 C, Xair = 51.1%
o
Tjets 19.9 C, Xair = 97.6%
1
10
100
o
Tw-Tjets [ C]
85
4.4.2 Two phase data
In Figure 4.8 - Figure 4.17 the wall heat flux is plotted as a function of the wall
superheat for different volume fractions of air contained in the chamber. It is shown that
the air content has no effect in the boiling region. Once boiling starts, all the curves
merge into one. The negative percentage in the air fraction, which does not have any
physical meaning, for the cases with Tjets very close to the saturation value falls within
the experimental uncertainty (3%). When the air fraction is close to zero, a variation of a
fraction of a degree in the temperature of the chamber is enough to cause the value of Xair
to change from positive to negative. This is also due in part to the rough control of the
chamber’s temperature using the two plate heaters and the cooling coil.
The effect of the degree of liquid subcooling is apparent at low wall superheats;
the boiling curve shifts to the right as it can be seen in Figure 4.8 - Figure 4.17. In Figure
4.18 and Figure 4.19 the heat flux is plotted as a function of the wall superheat for same
degree of subcooling, two different flowrates and two different jet diameters. The effect
of higher flowrate or higher jet velocity is to move each curve upward, shrinking the
boiling region independently of the degree of subcooling of the jet diameters.
86
1000
2
q [W/cm ]
100
10
o
Psystem = 101 kPa, Tsa t = 99.9 C, Flowrate = 516 ml/min
o
o
Tjets 100.7 C, Xair = -2%
T jets 96.7 C, Xair = 10.8%
o
o
Tjets 91.3 C, Xair = 24.4%
o
Tjets 61.4 C, Xair = 79.7%
1
0.1
Tjets 81.6 C, Xair = 50.1%
1
10
100
o
Tw-Tsat [ C]
118.7 μm, V = 516 ml/min [29.4 μl/mm2s].
1000
o
Tjets 100.7 C, Xair = -2%
Tjets 96.7 C, Xair = 10.8%
o
o
2
o
Tjets 91.3 C, Xair = 24.4%
o
o
Tjets 81.6 C, Xair = 50.1%
Tjets 61.4 C, Xair = 79.7%
2
q [W/cm ]
100
10
1
-40
-20
0
20
40
o
Tw-Tsat [ C]
118.7 μm, V = 516 ml/min [29.4 μl/mm2s]
87
1000
o
o
Tje ts 99.1 C, Xair = -2.4%
T je ts 100.7 C, Xair = -2.8%
o
o
Tje ts 100.8 C, Xair = -2.5%
o
Tje ts 93.4 C, Xair = 19.4%
T je ts 96.8 C, Xair = 9.6%
o
Tjets 82.9 C, Xair = 46.5%
o
2
2
q [W/cm ]
100
10
1
0.01
0.1
1
10
100
o
Tw-Tsat [ C]
Figure 4.10 Heat flux versus Tw – Tsat for different Xair or liquid subcooling s = 3 mm, dn =
116.3 μm, V = 233 ml/min [13.27 μl/mm2s].
1000
o
o
Tjets 99.1 C, Xair = -2.4%
Tjets 96.8 C, Xair = 9.6%
Tjets 93.4 C, Xair = 19.4%
Tjets 82.9 C, Xair = 46.5%
Tjets 20.3 C, Xair = 97.4%
Tjets 100.7 C, Xair = -2.8%
o
o
o
o
o
Tjets 100.8 C, Xair = -2.5%
2
q [W/cm ]
100
10
o
2
1
-80
-60
-40
-20
0
20
40
o
Tw - Tsat [ C]
116.3 μm, V = 233 ml/min [13.27 μl/mm2s].
88
1000
o
o
Tjets 100.6 C, Xair = -2.0%
o
Tjets 92.8 C, Xair = 23.9%
o
Tjets 81.7 C, Xair = 49.2%
o
Tjets 65.9 C, Xair = 74.9%
o
2
q [W/cm ]
Flowrate = 350 ml/min
100
10
0.1
1
10
100
o
Tw-Tsat [ C]
116.3 μm, V = 350 ml/min [19.94 μl/mm2s].
1000
o
o
Tjets 100.6 C, Xair = -2.0%
Tjets 92.8 C, Xair = 23.9%
Tjets 81.7 C, Xair = 49.2%
Tjets 65.9 C, Xair = 74.9%
Tjets 17.9 C, Xair = 97.9%
o
o
o
o
o
2
q [W/cm ]
100
2
10
1
-80
-60
-40
-20
0
20
o
Tw - Tsat [ C]
116.3 μm, V = 350 ml/min [19.94 μl/mm2s].
89
1000
2
q [W/cm ]
100
o
2
10
o
Tjets 99.8 C, Xair = -5.2%
o
Tjets 92.4 C, Xair = 22.8%
o
Tjets 66.1 C, Xair = 75.1%
o
Tjets 99.2 C, Xair = -2.0%
o
1
Tjets 99.4 C, Xair = -2.4%
1
10
100
o
Tw-Tjets [ C]
Figure 4.14 Heat flux versus Tw – Tjets for different Xair or liquid subcooling s = 3 mm, dn =
173.6 μm, V = 230 ml/min [13.1 μl/mm2s].
1000
o
Tjets 99.8 C, Xair = -5.2%
Tjets 92.4 C, Xair = 22.8%
o
o
2
o
Tjets 66.1 C, Xair = 75.1%
o
Tjets 99.2 C, Xair = -2.0%
o
Tjets 99.4 C, Xair = -2.4%
2
q [W/cm ]
100
10
1
-40
-30
-20
-10
0
10
20
30
o
Tw-Tjets [ C]
Figure 4.15 Heat flux versus Tw – Tjets for different Xair or liquid subcooling s = 3 mm, dn =
173.6 μm,
V = 230 ml/min [13.1 μl/mm2s].
90
1000
o
2
o
Tjets 99.7 C, Xair = -2.0%
o
Tjets 96.2 C, Xair = 10.2%
o
Tjets 91.2 C, Xair = 23.2%
o
Tjets 92.3 C, Xair = 25.3%
o
Tjets 81.8 C, Xair = 51.1%
2
q [W/cm ]
100
10
1
0.1
1
10
100
o
Tw-Tsat [ C]
173.6 μm, V = 360 ml/min [20.51 μl/mm2s].
1000
o
2
2
q [W/cm ]
100
o
Tjets 99.7 C, Xair = -2.0%
10
o
Tjets 96.2 C, Xair = 10.2%
o
Tjets 91.2 C, Xair = 23.2%
o
Tjets 92.3 C, Xair = 25.3%
o
Tjets 81.8 C, Xair = 51.1%
o
1
-80
Tjets 19.9 C, Xair = 97.6%
-60
-40
-20
0
20
o
Tw-Tjets [ C]
173.6 μm, V = 360 ml/min [20.51 μl/mm2s].
91
1000
o
o
2
o
2
Tjets = 100.8 C, Flowrate = 13.27 μl/mm s
2
q [W/cm ]
100
10
o
o
2
o
1
2
1
10
100
o
Tw - Tsat [ C]
Figure 4.18 Heat flux versus Tw – Tsat for two different flowrates, and jet diameters (Tjets ≈
100 oC).
1000
o
o
2
o
2
o
2
q [W/cm ]
o
100
10
0.1
2
Tje ts = 93.4 C, Flowrate = 13.27 μl/mm s
o
2
Tje ts = 92.8 C, Flowrate = 19.94 μl/mm s
1
10
100
o
Tw - Tsat [ C]
Figure 4.19 Heat flux versus Tw – Tsat for two different flowrates, and jet diameters (Tjets ≈
93 oC).
92
4.4.3 High heat flux data
In an attempt to be able to perform the experiments at higher heat fluxes than
those provided by the copper block, the lower part of the experimental set up was
modified. A copper slug 21.5 mm long and 19.02 mm in diameter was mounted on a
stainless steel disc 25.4 mm thick and 76.2 mm in diameter. The details of the modified
test section are shown in Figure 4.20.
Figure 4.20 Details of the test section modified to accommodate high heat fluxes.
93
The copper slug was shrink-fitted in the hole made in the stainless steel disc by
first submerging the copper into liquid nitrogen and then heating the disc with a torch
until the step made in the copper hit the disc. Four K-type thermocouples were silversoldered in the four holes drilled in the side and solder was also used to seal the joint with
the copper.
The stainless steel disc was welded onto the stainless steel plate used in the
previous experimental set-up. In order to insulate the copper slug, a machinable ceramic
ring was manufactured, fired, and mounted onto the copper piece.
An arc welder torch was used to provide the heating. The tip of the electrode of a
Miller 330 A/B/SP welder was positioned a few millimeters below the end of the copper
slug. The ground was attached to the stainless steel plate holding the copper slug. The
power was controlled by a rheostat in the welding machine. The test fluid was deionized
water.
Unfortunately, this new set-up presented some sealing problems which eventually
led to it being discarded. The expansions and contractions generated by the heating cycles
caused the seal between the copper and the steel to fail. Not only was the chamber not
vacuum proof any longer, but cooling water was leaking through the cracks and dripping
onto the arc, which produced large flames.
However, a few data sets could be recorded and are presented below. Four
different orifice plates have been tested and the details are reported in Table 4.2. The
arrays have a circular pattern and the outer ring of jets does not hit directly the heated
94
surface. The number of jets directly impinging on the target surface (Njets target) is reported
in the last column of Table 4.2.
Table 4.2 List of orifice plate tested.
s
dn exit STD dn inlet STD Thickness Njets Njets target
mm
μm
μm
μm
μm
mm
1
1
1
3
69.3
118.7
182.1
263
1.5
4.7
8.3
8.7
94.3
136.8
263.8
173.6
2.9
9.7
10.0
5.1
0.51
0.51
0.51
0.51
397
397
397
61
291
291
291
37
The four jets arrays were tested for different water flowrates. Figure 4.21 - Figure
4.23 show the results of tests performed on two arrays with s = 1 mm and jet diameter of
69.3, 118.7, and 182.1 μm respectively. Figure 4.24 shows the heat flux as a function of
Tw - Tjets for a case with s = 3 mm and dn = 263 μm. The lines in the figures represent the
predictions obtained from Eq. (3.6) for single-phase heat transfer. The agreement is very
good even at remarkably high heat fluxes where evaporation from the liquid film can
enhance the heat transfer. Only for one case in Figure 4.24, where the flowrate was the
lowest, the predictions failed to fall close to the experimental data. At such flowrate the
jet velocity is also low, about 1 m/s and it was noticed that some jets did not form
properly. This was attributed to surface tension effects that pulled the liquid up against
the orifice plate causing it to form big droplets or to flow along the plate to the mounting
screws and the drip down off the target surface.
The predictions are not used beyond the saturation temperature because even if
boiling has not started, air bubbles are usually present in the liquid film deposited on the
95
cooling surface and the flow can no longer be considered single phase. From the figures it
can be seen that the heat transfer improves as the liquid flowrate is increased. A
maximum heat flux of 840 W/cm2 at a surface temperature of 118 oC was removed from
the target surface of 283.5 mm2 using a jet pitch of 1 mm, jet diameter of 118.7 μm, and a
water flowrate of 1742 ml/min [102.4 μl/mm2s]. The liquid temperature was 16.5 oC. A
remarkable 680 W/cm2 could be removed by convection only at a surface temperature of
100 oC using a jet pitch of 1 mm, jet diameter of 69.3 μm, and a water flowrate of 920
1000
Prediction Eq.(3.6)
2
Flowrate: 17.63 μl/mm s
2
2
2
2
2
q [W/cm ]
2
100
o
s = 1 mm, dn = 69.3 μm, water, Tjets = 16.8 C
o
Psyst = 100 kPa, Xair = 97.8%, Tsat = 99.6 C
2
2
2
2
2
2
10
10
100
1000
o
Tw-Tjets [ C]
96
1000
2
35.8 μl/mm s
2
59.37 μl/mm s
2
59.96 μl/mm s
2
102.4 μl/mm s
2
2
104.04 μl/mm s
2
q [W/cm ]
103.75 μl/mm s
100
o
o
Psyst = 101 kPa, Xair = 97.8%, Tsat = 99.9 C
2
2
2
2
2
2
10
10
100
1000
o
Tw-Tjets [ C]
2
q [W/cm ]
1000
100
o
o
Psyst = 100.4 kPa, Xair = 97.7%, Tsat = 99.7 C
2
Eq. (3.6) 63.49 μl/mm s
2
Eq. (3.6) 91.99 μl/mm s
2
10
10
2
100
1000
o
Tw-Tjets [ C]
97
1000
o
s = 3 mm, dn = 263 μm, water, Tjets = 20.7 C
o
Psyst = 119.5 kPa, Xair = 94%, Tsat = 104.6 C
Exp. Data
2
12.64 μl/mm s
2
20.16 μl/mm s
100
2
32.92 μl/mm s
2
2
66.42 μl/mm s
2
q [W/cm ]
51.14 μl/mm s
2
12.64 μl/mm s
10
2
20.16 μl/mm s
2
32.92 μl/mm s
2
51.14 μl/mm s
2
66.42 μl/mm s
1
1
10
100
1000
o
Tw-Tjets [ C]
Figure 4.24 Heat flux versus Tw – Tjet for different flowrates, s = 3 mm, dn = 173.6 μm.
The effect of jet velocity on the heat transfer in single-phase is illustrated in
Figure 4.25. It is appears clearly that for similar liquid flowrate and pitch (number of jets)
higher heat fluxes for same wall temperatures can be accommodate by using smaller
higher velocity jets. At approximately Tw = 69 oC (Tw – Tjets = 52.4 oC) the heat flux
removed from the surface is 98 W/cm2 with an array containing 182.1 μm diameter jets,
293 W/cm2 with 118.7 μm diameter jets, and 407 W/cm2 with 69.3 μm diameter jets.
Unfortunately, 69.3 μm holes are easily plugged by any small particle that might be
entrained in the liquid. As such, the use of holes smaller than 100 μm for electronic
cooling applications is not recommended.
Figure 4.26 shows the effect of different jet velocities for s = 3 mm and dn = 263
μm. It can be noticed that the slope of each curve starts changing after a wall superheat of
10 oC indicating the onset of boiling (ONB), marked by a dashed line in Figure 4.26.The
98
ONB point seems to be weakly dependent on the wall superheat, but a stronger function
of the jet velocity. Fully developed nucleate boiling (FNDB) conditions occur at higher
wall superheats, which increase with increasing velocity. During fully developed nucleate
boiling all the data fall on the same curve and the effect of velocity disappears.
In agreement with the results of other researchers, the subcooling did not affect
the heat transfer during fully developed boiling, as shown in Figure 4.27. Some small
difference seemed to appear at low wall superheats, but the data showed enough scatter to
prevent any definitive conclusions on the matter.
2
q [W/cm ]
1000
100
10
10
s = 1 mm
Tjets
Flowrate
vjets
o
2
C
μl/mm s
m/s
16.8
54.63
10.33
16.5
59.73
3.85
16.3
63.50
1.74
dn
μm
69.3
118.7
182.1
100
1000
o
Tw-Tjets [ C]
Figure 4.25 Effect of jet velocity on single-phase heat transfer.
99
ONB = Onset of Nucleate Boiling
FDNB = Fully Developed Nucleate Boiling
Single-Phase Region
2
q [W/cm ]
1000
100
FDNB
ONB
o
s = 3 mm, dn = 263 μm, water, Tjets = 20.7 C
o
Psyst = 119.5 kPa, Xair = 94%, Tsat = 104.6 C
2
2
12.64 μl/mm s
20.16 μl/mm s
2
2
32.92 μl/mm s
51.14 μl/mm s
2
10
0.1
66.42 μl/mm s
1
10
100
o
Tw-Tsat [ C]
Figure 4.26 Effect of jet velocity on two-phase heat transfer.
Figure 4.28 shows the heat flux as a function of Tw – Tliq for different system
pressures. The heat transfer was unaffected by a change in system pressure in the singlephase region, as shown by the overlapping of the curves for different pressures. Due to
different saturation temperatures, the onset of boiling occured at Tw – Tliq = 76 oC when
Psyst = 84.5 kPa, which was 20 oC lower than the Tw – Tliq = 96 oC at Psyst =119 kPa. This
could be a favorable effect when electronic cooling is considered, because it would allow
100
the high heat transfer rates characteristic of boiling to occurs at surface temperatures
lower than the water saturation temperature of approximately 100 oC at ambient pressure.
2
q [W/cm ]
1000
100
10
s = 3 mm, dn = 263 μm, water
Exp. Data
o
o
vjets [m/s] Tjets [ C] Tsat [ C]
0.97
25.6
95.0
0.98
46.7
95.0
1
Psyst [kPa]
84.5
84.5
10
100
o
Tw - Tsat [ C]
Figure 4.27 Effect of liquid subcooling on boiling.
101
o
ΔTsub [ C]
69.4
48.3
600
Exp. Data
Flowrate
vjets
Tjets
500
2
μl/mm s
12.64
11.75
11.75
C
20.7
23.0
24.2
Psyst
kPa
119.5
84.5
84.5
Tsat
o
C
104.6
94.9
94.9
2
q [W/cm ]
400
m/s
1.1
1.0
1.0
o
300
200
ONB
100
0
FDNB
0
25
50
75
100
125
150
o
Tw - Tjets [ C]
Figure 4.28 Effect of change in system pressure
The ONB points for the two set of data coincidentally occur at the same wall
superheat and heat flux, since the liquid subcooling is higher for the data at higher
pressure. In general a lower system pressure corresponds to a higher heat flux at ONB. In
the fully developed nucleate boiling region the higher pressure data showed a steeper
slope than the low pressure one, as illustrated in Figure 4.29. The jet velocity is the same
both curves, but the subcooling is different, about 69 oC at 84 kPa and 84 oC at 120 kPa.
A better example is shown in Figure 4.30, where the heat flux as a function of wall
102
superheat is plotted for data at high and low pressure for different jet velocities. The
different slopes of the data for high and low pressure are probably caused by a change in
the physical properties. The liquid to vapor density ratio at 120 kPa is 71.5% of that at 84
kPa. It has been shown [25] [26] that the critical heat flux (CHF) is higher at lower
pressures.
Exp. Data
Tjets
Psyst
Flowrate
vjets
2
o
μl/mm s
m/s
C
kPa
12.64
1.1
20.7
119.5
11.75
1.0
23.0
84.5
11.75
1.0
24.2
84.5
Tsat
C
104.6
94.9
94.9
o
2
q [W/cm ]
1000
100
FDNB
ONB
10
0.1
1
10
o
Tw - Tsat [ C]
Figure 4.29 Effect of system pressure in on two-phase heat transfer
103
100
1000
2
q [W/cm ]
100
10
1
10
Exp. Data
o
vjets [m/s]
Tjets [ C]
1.1
20.2
1.7
20.6
2.8
20.6
4.4
21.7
1.0
23.0
1.0
24.0
0.97
25.6
o
Tsat [ C]
104.8
104.8
104.8
104.8
95.0
95.0
95.0
Psyst [kPa]
120
120
120
120
84.5
84.5
84.5
100
o
Tw - Tsat [ C]
Figure 4.30 Effect of system pressure
The sets of data at high and low pressure can be fitted using the same functional
dependence as that used in Table 1.1. A least-squares fit of the data yields values of C of
5.6 and 11323, and of n of 3.6 and 1.45, for high and low pressure respectively. A
comparison of the present data for fully developed boiling with the correlations reported
in Table 1.1 is illustrated in Figure 4.31. The data for 120 kPa exhibits a trend similar to
those presented by Copeland [13], but it yields a lower heat flux in the overlapping range
of wall superheat. The data for R-113 yield lower heat fluxes due to the significant
differences in the physical properties.
104
2000
1
2
3
4
5
6
7
8
2
q [W/cm ]
1000
100
4
Copeland [13] - water
Katsuta & Kurose [17] - R-113
Katto & Kunihiro [18] - water
Katto & Monde [19,24,22] - water
Monde & Katto [23] - R-113
Ruch & Holman [20] - R-113
Present work - 120 kPa - water
Present work - 84.5 kPa - water
3 7
8
6
5
10
1
2
1
1
10
100
o
Tw - Tsat [ C]
Figure 4.31 Fully developed boiling data and prediction from other correlations.
Only in a few cases at low flowrates was it possible to reach the critical heat flux.
Most of the times, the temperatures in the copper slug, when the last point of each curve
was recorded were higher than the melting point of the silver solder used to seal. That
caused the seal to fail and the water to leak thourgh and to drip onto the electric arc. The
experiment had to be stopped and the seal had to be repaired. A list of the CHF points
measured during the experiments is reported in Table 4.3. The CHF values obtained from
Eqs. (1.5) - (1.10) are also listed. The characteristic length, L, used in Eqs. (1.5) and
(1.10) was the distance between the center of a jet and the farthest away point in the area
105
of influence, as shown in Figure 4.32. In the other equations., the heater diameter, D, has
been replaced by 2L. The characteristic lengths were 0.74 mm, 1.51 mm and 2.31 mm for
configurations with s = 1 mm, 2 mm, and 3 mm, respectively.
Table 4.3 Comparison of CHF data (s = 3, dn = 263μm) with predictions from other
correlations.
Psyst
[kPa]
84.5
84.5
84.5
84.5
84.5
120
120
120
Tsat
[oC]
95
95
95
95
95
104.8
104.8
104.8
ΔTsat
[oC]
51.6
50.7
49.3
47.6
50.7
36.9
41.8
43.2
ΔTsub
[oC]
61.5
60.5
58.9
30.1
37.8
84.6
84.2
84.2
vn
[m/s]
1.0
1.0
0.97
0.58
0.98
1.1
1.7
2.8
qCHF
[W/cm2]
358
359
313
255
332.5
267.5
403
523
Lee et al.
[12]
[W/cm2]
Katto &
Yokoya
[27]
[W/cm2]
Eq. (1.5)
820
818
809
658
771
914
1026
1175
Eq. (1.6)
372
372
368
308
368
384
444
524
Monde
[22]
[W/cm2]
Sharan &
Lienhard
[28]
[W/cm2]
Monde
& Katto
[24]
[W/cm2]
Eq. (1.7)
341
341
337
286
338
386
442
517
Eq. (1.8)
377
377
373
319
375
358
421
507
Eq. (1.9)
598
595
586
436
534
685
790
933
Figure 4.32 Area of influence of a jet and characteristic length.
106
Monde
et al.
[21]
[W/cm2]
Eq.
(1.10)
398
398
394
332
395
455
526
621
Equation (1.10), the only one obtained using multiple jets, while not accounting
for subcooling overpredicts the experimental data, particularly those for 120 kPa. At
84kPa Eq. (1.10) overpredicts by at most 30%. Equations (1.5) and (1.9) overpredict by
as much as 341%. The other three correlations seem to predict well the present data, but
again they do not account for subcooling effects.
107
4.5 Summary
Experiments were carried out in a closed system configuration and the air fraction
in the environment surrounding the jets was varied to investigate if there was an extra
evaporative contribution to the convective heat removal by arrays of microjets. It was
found that the presence of noncondensable gas in the environment surrounding the jets
does not affect the heat transfer in either single or two phase conditions. The single phase
data are in general well predicted by the correlation developed for the open system.
The data showed that, as expected, the noncondensables gas content has no effect
when boiling occurs on the heated surface, and all the data obtained for different
noncondensable fractions merge into one curve. At low heat flux and wall superheat, the
effect of higher liquid subcooling is to shift the boiling curve to the left. Such effect
disappears in fully developed boiling. The effect of higher flowrate is to shift the boiling
curve to the left and to increase the boiling inception point.
It was shown that in fully developed boiling the heat transfer is independent of
velocity and all the data fall on the same curve. For the same flowrate, even at high
surface temperatures, the best heat transfer is obtained when a large number of small
diameter jets is employed instead of fewer larger jets.
It was also demonstrated that at lower system pressure the boiling inception
occurs at lower surface temperatures, thus allowing high heat transfer rates at low surface
temperature.
108
A few data sets were obtained where the heat flux ranged from zero to the critical
heat flux limit. It was also shown how as the flowrate increases, the boiling region
shrinks, and the CHF value increases. The experimental values have been compared to
the predictions from some of the available correlations. Some correlations valid for
saturated jets coincidentally predicted well the experimental values which, on the other
hand, were highly subcooled.
A maximum heat flux of 840 W/cm2 at a surface temperature of 118 oC was
removed from the target surface of 283.5 mm2 using a jet pitch of 1 mm, jet diameter of
118.7 μm, and a water flowrate of 1742 ml/min [102.4 μl/mm2s]. The liquid temperature
was 16.5 oC. A remarkable 680 W/cm2 could be removed by convection only at a surface
temperature of 100 oC using a jet pitch of 1 mm, jet diameter of 69.3 μm, and a water
flowrate of 920 ml/min [54.08.4 μl/mm2s].
109
C
CH
HA
AP
PT
TE
ER
R 55
COMPARISON BETWEEN JET ARRAYS AND
DROPLET SPRAYS
Direct cooling by means of jets or sprays has been considered a solution to the
problem of cooling high power density electronic devices. Although both methods are
capable of very high heat removal rates it is necessary to be able to decide which one is
more convenient than the other when designing a cooling system for electronic
applications. In this chapter a comparison between the results of experimental
investigations of the performances of sprays and of arrays micro jets is presented.
5.1 Introduction
Liquid droplets spray cooling has been widely used in the metal manufacturing
industry and has been shown capable of high heat removal rates. Researchers have
investigated the possibility of applying such technique to the cooling of electronic
components.
The droplet sprays can have the form of a mist, and impinge on the surface with a
random pattern or they can be formed by one or more streams of droplets which impinge
upon the surface with a fixed pattern. If the frequency of the streams is high enough, the
droplets merge forming continuous liquid jets. After hitting the surface, the liquid
110
droplets spread and, if the spreading area is small enough a continuous thin liquid film
covering the surface is formed. If the wall superheat is high, a thin vapor layer can be
present underneath the droplets or the thin liquid film. The heat transfer process is
transient and it involves liquid and vapor convection, thin film evaporation, and air
convection. The areas not covered by the film dry out.
When continuous liquid jets are employed, the liquid film covering the surface is
continuous and the heat is removed mainly by convection. Evaporation from the thin film
may occur at high heat fluxes or low flow rates.
The physics governing the heat removal process by droplet sprays is very
complex and still is not completely understood, and few theoretical models are available
in the literature. Hence, it has turned out to be easier to investigate the various aspects of
the problem by performing experimental work. Several studies have been conducted in
the past on sprays, but most of them deal with the boiling regime, which was not
considered in the present work. Air driven sprays obtained using atomizer nozzles are not
considered in this study either because they would be impractical to use in a closed
system for electronic cooling.
Bonacina et al. [29] presented a study in which they developed a one-dimensional
conduction model for multi drop evaporation. They compared the predictions from the
model to the experimental results they obtained using water droplets impinging on an
aluminum surface, at low wall superheats. The average droplet size was approximately
400 μm and the impinging velocity was between 1 and 2 m/s. They used cameras (both
still and video) to obtain information about the fraction of the heater area covered by the
111
droplets. The highest heat transfer coefficient achieved in the experiments was 150
kW/m2K, and the maximum heat flux was 220 W/cm2. The experimental data matched
well with their prediction.
Both Ghodbane and Holman [30], and Holman and Kendall [31] studied spray
cooling on constant heat flux vertical surfaces. They tested full-cone circular and square
hydraulic nozzles with Freon-113 as test liquid. Two square heat transfer surfaces were
studied (7.62 x 7.62 cm2 and 15.24 x 15.24 cm2) and from that they concluded that the
heat transfer is independent of the impinged area as long as the spray is uniform. They
also found that the heat transfer increases almost linearly with the droplet mass flux, and
that a high degree of subcooling causes higher superheat for the onset of nucleate boiling
and CHF. They correlated all the data obtained in [30] and [31] by the expression,
⎛ c p _ liq (Tw − Tliq ) ⎞
qz
⎟
= 9.5We0.6 ⎜
⎟
⎜
μliq h fg
h fg
⎝
⎠
1.5
(5.1)
where We is the droplet Weber number and it was defined as,
We = ρliq vbr2 d d σ −1
(5.2)
and vbr is the droplet breakup velocity given by
⎛
⎞
vbr = ⎜ v12 + 2 ΔP
− 12 σ
⎟
d
ρ
ρ
liq
liq d ⎠
⎝
112
0.5
(5.3)
They opted to calculate the droplet mean Sauter diameter according to the
correlation developed by Bonacina et al. [32], since it had the best agreement with the
nozzle manufacturer’s specifications. That equation was given as,
dd =
9.5d n
ΔP sin ( 0.5 β )
(5.4)
0.37
In Eq. (5.4) all properties except for hfg were evaluated at the mean film temperature. The
range of parameters for their experiments is given in Table 5.1.
Table 5.1 Range of parameters for the experimental work of Ghodbane et al. [30] and
Holman et al. [31]
Variable
V
dn (max free passage)
z
vbr
dd
Tw
Tliq
q
We = ρliqvbr2dd /μliq
Re = ρliqvbrdd /μliq
Pr
Range [2]
5 - 126
0.63 – 2.38
180 – 350
5.4 – 28
210 – 980
20 – 90
5 – 10
0.12 – 50
2200 – 13750
2557 – 61878
7.5 – 10.5
Range [3]
6.3 - 56.8
0.635 - 1.27
184.2 - 193.7
11.4 - 28.5
96 - 343
20 - 80
4 - 10
0.28 - 25.2
2400 - 11775
4875 - 12850
6.0 - 10.7
Units
ml/s
mm
mm
m/s
μm
o
C
o
C
W/cm2
Cho and Ponzel [33] experimentally investigated spray cooling of a heated solid
surface using subcooled and saturated water. They tested three full-cone nozzles having
113
orifice diameters of 0.51, 0.61, and 0.76 mm, respectively. The distance between the
nozzle and the 50 mm diameter copper heated surface was 30 mm. Three liquid flowrates
were tested (8.7, 5.4, and 3.7 ml/s). From the analysis of their data, Cho and Ponzel
concluded that the droplet size was important only when evaporation occurred on the
liquid film deposited on the impinged surface. Even though most of the data showed that
the liquid flow rate had negligible effect on the heat transfer in single-phase, for the case
of the 0.51 mm diameter nozzle, where a flowrate of 1.8 ml/s was also tested, the heat
transfer improved as the flowrate increased. They correlated the single-phase heat
transfer data as a function of Reynolds and Prandtl number as,
Nu = 2.531Re0.667 Pr 0.309
where Re =
(5.5)
ρliq V A d d
hd
, and Nu = d .
kliq
μliq
H
They used the empirical formula developed by Mudawar et al. [34] given in Eq.(5.6) to
calculate the droplet diameter. The fluid properties were evaluated at the mean film
temperature.
d d = 3.67 d n [Wed0.5n Re dn ]−0.259
(5.6)
Jiang [9] at UCLA carried out an experimental investigation on droplet sprays.
The experimental rig used for the testing of droplets spray was similar to the one used for
the study of microjets described in Chapter 3, but instead of orifice plates a HAGO
nozzle was installed above the copper heat transfer surface. The minimum operating
pressure was 274.8 kPa gage pressure but increasingly finer droplets resulted from higher
operating pressures. Each nozzle was individually spray tested for flow rate, spray angle,
114
and spray quality. The standard spray angle was 70o. It employed two sintered bronze
filters, which gave more surface filtration. The specific type of the nozzle used in that
study was “DFN” B100. The mean Sauter diameter of droplet for DFN-B100 nozzle at
274.8 kPa gage pressure is 44 μm according to the manufacturer. The orifice’s diameter
of the spray nozzle is 356 μm. The results of the investigation by Jiang are compared to
those presented in Chapter 3 for the microjet arrays.
115
5.2 Results and discussion
Many different criteria can be used to evaluate the cooling performance of
different systems. In this study, the heat transfer performance of droplet sprays and arrays
of micro jets are evaluated by comparing results for test cases having either the same
water flow rate or same heat transfer rate or same amount of power spent for the heat
removal process. A suitable parameter used in this evaluation is the ratio between the
power removed from the copper surface (which represents an electronic device), and the
power necessary for accomplishing this task. The power consumed for the cooling
process corresponds to the pumping power necessary to push the liquid through the
HAGO nozzle or the orifice plate. The losses through pipes and fittings are not included.
It is this parasitic power which can be of concern in some applications.
The water flowrates tested using the HAGO nozzle were 50.56 ml/min (2.87
μl/mm2s) and 81.56 ml/min (4.63 μl/mm2s), respectively. The major drawback of the
HAGO nozzle is the high flow coefficient, which causes the pressure drop to increase
rapidly with increasing flowrate. At a flowrate of 2.87 μl/mm2s the pressure drop is 283
kPa, whereas at a flowrate of 4.63 μl/mm2s it becomes 843 kPa.
In Figure 5.1 (a) and (b) the heat transfer coefficients obtained in the experiments
(further details are available in the work of Jiang [9]) with the HAGO nozzle are
compared to those predicted from Eqs. (5.1) and (5.4). The experimental data obtained in
this study shows the heat transfer coefficient to be independent of the wall to liquid
temperature difference. It can be seen the experimental data are overpredicted by both
116
correlations. The differences can probably be attributed to the fact that the droplet size
generated with the HAGO nozzle (smaller than 44 μm) is different than that in the
experiments of Ghodbane et al. [30], Holman et al. [31] (between 210 – 980 μm), and
Cho et al. [33]. The Wedd for the results of this work is between 317 and 1080 and it is
out of the range for which Eq. (5.1) was originally developed.
The area-averaged heat transfer coefficients obtained using the HAGO nozzle are
shown in Figure 5.2 (a) and (b) along with those obtained using micro jets for similar
values of liquid flowrate. The flowrate accounts only for those jets directly impinging on
the heated area, which had a diameter of 19.2 mm. Figure 5.2 (a) shows that at a liquid
flow rate of about 2.87 μl/mm2s, the spray performs better than the micro jets, while a
liquid flow rate of about 4.63 μl/mm2s (Figure 5.2 (b)), the droplets and the micro jets
have almost the same heat transfer rate. The heat transfer coefficient is found to be
independent of Tw-Tliq for the droplets spray and to increase weakly with Tw-Tliq for the
microjet arrays. In both cases the ratio of pumping power to power removed for the
droplet spray is much higher than for most of the jet arrays (Figure 5.3 (a) and (b)).
117
4.0
2
Flowrate = 2.87 μl/mm s, dd = 41.5 μm
Predict. of Cho et al. [33]
3.5
Present work
Predict. of Holman et al. [30, 31]
2 0
h [W/cm C]
3.0
2.5
2.0
1.5
1.0
0.5
0.0
(a)
4.0
3.5
2 0
h [W/cm C]
3.0
2.5
2.0
1.5
1.0
0.5
0.0
2
Flowrate = 4.63 μl/mm s, dd = 30.0 μm
Predict. of Cho et al. [33]
0
20
40
Present work
Predict. of Holman et al. [30, 31]
o
60
Tw - Tliq [ C]
80
100
(b)
Figure 5.1 Comparison of spray data for two flowrates (a) 50.56 ml/min [2.87μl/mm2s] and
(b) 81.56 ml/min [4.63μl/mm2s], with the predictions of Holman et al. [30,31] and Cho et al.
[33].
118
2.0
o
Micro jets: Tliq = 19 C
2
dn = 122.6 μm, s = 3 mm, Flowrate = 2.65 μl/mm s
2
20
h [W/cm C]
1.5
2
1.0
0.5
2
o
HAGO nozzle, Flowrate = 2.87 μl/mm s Tliq = 23 C
0.0
(a)
2.0
20
h [W/cm C]
1.5
1.0
2
O
HAGO nozzle, Flowrate = 4.63 μl/mm s, Tliq = 23 C
O
Micro jets, Tliq = 19 C:
2
0.5
2
2
2
0.0
0
20
40
o
60
Tw - Tliq [ C]
80
100
(b)
Figure 5.2 Comparison between spray and micro jets performance for two flowrates (a)
50.56 ml/min [2.87μl/mm2s] and (b) 81.56 ml/min [4.63 μl/mm2s].
119
-1
10
-2
Qpumping/Qremoved
10
-3
10
-4
10
2
o
HAGO nozzle, Flowrate = 2.87 μl/mm s Tliq = 23 C
o
Micro jets: Tliq =19 C
-5
2
10
2
2
-6
10
(a)
-1
10
-2
Qpumping/Qremoved
10
-3
10
2
-4
O
HAGO nozzle, Flowrate = 4.63 μl/mm s, Tliq = 23 C
10
O
2
-5
10
2
2
2
-6
10
1
10
o
Tw - Tliq [ C]
100
(b)
Figure 5.3 Comparison of process efficiency between spray and micro jets for two
flowrates (a) 50.56 ml/min [2.87μl/mm2s] and (b) 81.56 ml/min [4.63 μl/mm2s]
120
Referring to Figure 5.3 (a) and (b), it can be seen that for the spray the ratio of
power consumed to power removed is higher than that for most jet configurations. For
the microjets arrays it can also be inferred that the pumping power is less for higher flow
rate and larger jet diameters than for small high velocity jets. A similar conclusion can
also be drawn by comparing the heat transfer coefficients on a constant pumping power
basis. As Figure 5.4 illustrates, most of the micro jets configurations outperform the
sprays. Micro jets of 173.6 μm diameter spaced 3 mm apart yield a heat transfer rate
almost three times higher than a spray for the same Tw-Tliq and using the same pumping
power.
The data obtained by Oliphant et al. [8] for spray and jets are plotted together
with the present data in Figure 5.5. It can be seen that the two different types of sprays
have similar heat transfer coefficients with a small edge in favor of the HAGO nozzle. On
the other hand, the highly populated micro jet arrays used in this study are preferable than
the arrays with few large jets, because they require a much lower flowrate to obtain the
same heat transfer rates. Better performance is obtained with microjets because of the
presence of a thinner liquid film and of the presence of many more stagnation points on
the heater surface. Lastly, the microjet arrays can give same or better performance than
the sprays using same flowrate, however because of the much lower pressure drop with
the microjets than with the sprays, the pumping power is also smaller.
121
6
2
HAGO nozzle, Flowrate = 2.87 μl/mm s,
O
Tliq = 23 C, Qpumping = 0.24 W
5
O
2
dn = 122.6 μ m, s = 3 mm, Flowrate = 4.1 μl/mm s, Qpumping = 0.2 W
2
dn = 76.4 μm, s = 2 mm, Flowrate = 7.09 μl/mm s, Qpumping = 0.24 W
2o
h [W/cm C]
4
2
2
3
2
1
0
0
10
20
30
40
50
60
70
80
90
100
O
Tw-Tliq [ C]
Figure 5.4 Comparison between spray and micro jets performance for the same pumping
power.
122
2O
h [W/cm C]
10
Oliphant et al. [8]
Delavan Airo type B Nozzle
Jet arrays
N = 4, dn = 1.00 mm
N = 7, dn = 1.00 mm
N = 7, dn = 1.59 mm
1
0.1
1
10
HAGO Nozzle
Microjets
s = 3 mm, dn = 122.6 μm
s = 2 mm, dn = 76.4 μm
s = 1 mm, dn = 69.3 μm
s = 2 mm, dn = 113.8 μm
s = 3 mm, dn = 116.3 μm
s = 3 mm, dn = 173.6 μm
s = 2 mm, dn = 178.5 μm
2
3
10
10
4
10
Flowrate [ml/min]
Figure 5.5 Comparison of the present data with the results by Oliphant et al.[8].
123
5.3 Summary
The heat transfer rates using droplets sprays and arrays of micro jets have been
compared. It is found that at a flowrate of 2.87 μl/mm2s the spray has a higher heat
transfer rate than any jet configuration, while at a higher flowrate of 4.63 μl/mm2s jet
arrays can perform as well as the spray.
The micro jets arrays have usually lower energy consumption than the spray for
the same flow rate. For equal pumping power and Tw – Tliq = 76 oC, the jets can remove
heat fluxes as high as 240 W/cm2, while the spray can only handle 93 W/cm2.
The pressure drop for the HAGO nozzle quickly reaches values that are not
practical. In practice, there is always a combination of jet diameter and jet spacing that
yields the same heat transfer coefficient as that of the spray, but at a much lower energy
cost.
124
C
CH
HA
AP
PT
TE
ER
R 66
CONCLUSIONS AND FUTURE WORK
6.1 Conclusions
This work has shed light on several issues concerning electronic cooling by means
of arrays of microjets.
The idea of using arrays of liquid micro-jets has been successfully implemented.
A prototype of a cooling module was built and it has been capable of dissipating 129 W
to the surrounding environment, while removing a heat flux of 300 W/cm2 at a surface
temperature of 80 oC using water, which is a significant achievement at the present time.
The external resistance decreased with increasing air flowrate and seemed to be
unaffected by the mass fraction of air present in the module. Reducing the system
pressure had the effect of lowering the boiling inception temperature, thus allowing for
higher heat removal rates at lower surface temperature.
The data were too limited to make any judgment on the internal resistance
behavior with respect to the mass fraction of air. The minimum value achieved for the
ratio of pumping power to the power removed was 4%.
Once the feasibility of the idea of cooling electronic components using liquid jets
was proven, the focus shifted to the study of the heat transfer under arrays of microjets.
Single phase heat transfer under circular free surface jet arrays of water and FC 40 has
125
been experimentally studied. It was found that Nu improves with increasing Redn, Pr, and
decreasing s/dn. The Nusselt number was found to be more strongly dependent on the
Reynolds number than that reported by previous researchers. However, the previous
studies did not consider arrays as highly populated jets as those used in the present study,
and also never used jets diameters smaller than 500 μm. In the range explored, Nu was
found to vary as Pr0.48. A third parameter, s/dn was used to correlate the experimental
data. It is believed that the results obtained in the present work can be extrapolated to
higher and lower values of s/dn.
The empirical correlation developed in conjunction with the pressure drop data
was used to find an optimal configuration which minimizes the pumping power, even
though it has been shown that the optimization is not critical being the pumping power
only a few percent of the power removed. If the flowrate has to be minimized, it was
found that d n = 3.876 ⋅ 10 −2 s . It must be always verified that the jet velocity and the
pressure drop have acceptable values. If the flowrate is kept constant, the configuration
that has the highest heat removal rate has a large number of small diameter jets.
Experiments were carried out in a closed system configuration and the air fraction
in the environment surrounding the jets was varied to investigate if there was an extra
evaporative contribution to the convective heat removal by arrays of microjets. It was
found that the presence of noncondensable gas in the environment surrounding the jets
does not affect the heat transfer in either single or two phase conditions. The data in
general are well predicted by the correlation developed for the open system.
126
The data showed that, as expected, the noncondensables gas content has no effect
when boiling occurs on the heated surface, and all the data obtained for different
noncondensable fractions merge into one curve. The effect of higher liquid subcooling is
to shift the boiling curve to the right. The effect of higher flowrate is also to shift the
boiling curve to the left and to increase the boiling inception point.
Few data sets were obtained where the heat flux ranged from zero to the critical
heat flux limit. It was also shown how as the flowrate increases, the boiling region
shrinks, and the CHF value increases. For the same flowrate, even at high surface
temperatures, the best heat transfer is obtained when a large number of small diameter
jets is employed instead of fewer larger jets.
A maximum heat flux of 840 W/cm2 at a surface temperature of 118 oC was removed
from the target surface of 283.5 mm2 using a jet pitch of 1 mm, jet diameter of 118.7 μm,
and a water flowrate of 1742 ml/min [102.4 μl/mm2s]. The liquid temperature was 16.5
o
C. A remarkable 680 W/cm2 could be removed by convection only at a surface
temperature of 100 oC using a jet pitch of 1 mm, jet diameter of 69.3 μm, and a water
flowrate of 920 ml/min [54.08.4 μl/mm2s].
Lastly, the heat transfer using droplets sprays and arrays of micro jets has been compared.
It was showed that at a flow rate of 2.87 μl/mm2s the spray has a higher heat transfer rate
than any jet configuration, but that at a flow rate of 4.63 μl/mm2s, jet arrays with different
number of jets can perform as well as the spray. The micro jets arrays usually have lower
energy consumption than the spray for the same flow rate. For equal pumping power and
at a wall to liquid temperature difference of 76 ºC, the jets can remove heat fluxes as high
127
as 240 W/cm2, while the spray can only handle 93 W/cm2. Furthermore, the pressure drop
for the HAGO nozzle quickly reaches values that are not practical, and which would
require more sophisticated pumps. In practice, there is always a combination of jet
diameter and jet spacing that yields the same heat transfer coefficient as that of the spray,
but at a much lower energy cost.
128
6.2 Future work
Single phase heat transfer under arrays of free jets has been investigated
experimentally in a few studies. With this latest addition, the range of parameters covered
is almost complete, even though the physics remains largely unknown and only one
rather complicated theoretical model is available. There are no data available about the
the liquid film thickness or the temperature at the liquid air film interface.
The evaporative contribution to the cooling process, which seemed higher at low
liquid flowrates, has not yet been determined. Careful experimental studies are needed in
that direction. Data of the the liquid film thickness and the temperature at the liquid air
film interface would prove useful to quantify theevaporative contribution..
Two phase heat transfer under arrays of free jets has been investigated on a very
limited basis, but it has shown great potential. Careful experimental studies are needed to
establish the full capabilities and limitation of boiling heat transfer.
Water has demonstrated capable of removing extremely high heat fluxes at
relatively low surface temperatures, which are allowable for the new chips generation
built with wide band gap semiconductors. Unfortunately, water is electrically conductive.
To solve the problem, some researchers have successfully coated all the wetted surfaces
with Perylene, but no tests were performed at high temperatures or for repeated thermal
cycles for long times. Efforts should be made to find a fluid with similar thermophysical
properties to those of water, but with a high dielectric constant.
129
A
AP
PP
PE
EN
ND
DIIX
XA
A
In this section all the data relative to the cooling module experiments as described
in Chapter 2 are listed.
130
Table A.1
Tbox
o
Tjets
Tair out Tchip back Tair in
o
o
o
Tw
o
qw
Vflow vjets
h
2
Pbox
Pvap Pair init
Pair fin
2o
Xair
VflowAir Fan pwr Pump pwr
C
32.8
32.5
32.8
32.7
C
28.9
30.0
29.1
28.3
C
43.5
47.6
50.7
54.4
C
23.4
23.5
23.4
23.5
C
37.9
40.8
43.0
45.5
W/cm ml/min m/s W/cm C Pa
Pa
Pa
28.75 99.2 4.5
5.66
6413 3271 1250
45.39 99.2 4.5
5.49
6407 3271 1250
63.11 99.2 4.5
6.18
6414 3271 1250
81.79 99.2 4.5
6.35
6404 3271 1250
Pa
1283
1283
1286
1285
m3/hr
0.00
3.33
8.65
15.10
W
0.00
0.08
0.21
0.53
W
4.74
4.74
4.74
4.74
33.8 32.3
34.1 32.3
27.0
26.2
58.1
59.4
22.5
22.2
48.1
49.0
101.41 99.2 4.5
122.21 104.2 4.7
1285 20.1% 22.16
1286 19.8% 32.51
1.08
2.23
4.74
5.00
C
33.4
33.4
34.0
33.9
o
6.43
7.32
6385 3271 1250
6493 3271 1250
20.0%
20.0%
20.0%
20.1%
Table A.2
131
Tbox
o
C
54.1
54.0
53.8
53.7
53.6
53.8
Tjets
o
C
49.4
49.0
48.8
48.7
48.5
48.4
o
C
44.4
46.1
43.5
41.9
40.4
39.3
o
C
78.5
85.6
89.8
94.5
98.8
104.4
o
C
22.3
22.0
22.0
22.2
22.0
22.2
Tw
o
C
62.0
66.7
69.5
72.7
75.6
79.5
qw
Vflow vjets
2
W/cm
121.48
170.01
203.95
240.67
272.32
298.97
h
Pbox
2o
ml/min m/s W/cm C
106.7 4.8
9.67
106.5 4.8
9.64
106.4 4.8
9.86
106.4 4.8 10.04
106.4 4.8 10.03
106.4 4.8
9.61
Pa
16010
16126
16090
16113
15972
16076
Pvap Pair init
Pair fin
Pa
3271
3271
3271
3271
3271
3271
Pa
1370
1369
1369
1368
1368
1369
Pa
1250
1250
1250
1250
1250
1250
Xair
8.6%
8.5%
8.5%
8.5%
8.6%
8.5%
m3/hr
0.00
2.83
5.98
9.51
12.40
14.87
W
0.00
0.08
0.13
0.25
0.38
0.52
W
5.13
5.12
5.12
5.12
5.12
5.12
Table A.3
Tbox
o
C
32.5
32.6
32.4
34.0
32.7
Tjets
o
C
32.3
32.6
33.3
33.7
33.7
o
C
28.7
28.6
27.7
26.6
25.0
o
C
45.0
52.5
57.7
64.0
68.4
o
C
23.0
23.0
23.1
22.5
21.8
Tw
o
C
39.0
44.2
47.8
52.2
55.2
qw
Vflow vjets
2
W/cm
28.75
45.21
62.97
83.70
101.73
h
Pbox
Pvap Pair init
Pair fin
Xair
2o
ml/min m/s W/cm C Pa
Pa
Pa
Pa
90.0 4.1
4.31
15596 3094 10707 10991 70.5%
91.9 4.1
3.90
15585 3094 10707 10993 70.5%
90.6 4.1
4.33
15608 3094 10707 10985 70.4%
80.3 3.6
4.52
15713 3094 10707 11043 70.3%
87.3 3.9
4.75
15735 3094 10707 10996 69.9%
m3/hr
0.00
4.37
10.08
18.32
31.20
W
0.00
0.10
0.27
0.76
2.06
W
4.26
4.36
4.29
3.75
4.12
Table A.4
132
Tbox Twaterin Tair out Tchip back Tair in
o
C
52.7
52.5
54.9
55.1
o
C
47.1
47.0
46.8
46.6
o
C
41.8
41.8
37.1
35.2
o
C
79.6
90.1
103.2
109.5
o
C
21.5
21.5
21.6
21.6
Tw
o
C
62.7
69.7
78.7
83.2
qw
Vflow vjets
2
W/cm
107.12
150.01
209.14
243.34
h
Pbox
Pvap Pair init
Pair fin
Xair
2o
ml/min m/s W/cm C Pa
Pa
Pa
Pa
87.3 3.9
6.85
23575 3094 10707 11716
90.9 4.1
6.59
23496 3094 10707 11710
90.9 4.1
6.55
23566 3094 10707 11797
90.9 4.1
6.65
23506 3094 10707 11803
49.7%
49.8%
50.1%
50.2%
m3/hr
0.00
3.23
10.61
15.02
W
0.00
0.08
0.29
0.53
W
4.12
4.31
4.31
4.31
Table A.5
Tbox
o
C
33.3
34.0
33.6
31.2
Tjets
o
C
32.3
33.0
33.8
33.9
o
C
28.1
27.6
27.2
26.2
o
C
51.5
61.5
73.9
86.4
o
C
23.1
23.4
23.2
23.4
Tw
o
C
43.5
50.4
58.9
67.2
qw
Vflow vjets
2
h
Pbox
Pvap Pair init
Pair fin
Xair
2o
Pa
Pa
Pa
30.07 93.5 4.2
2.68 104791 2918 97262 100440
47.79 83.4 3.8
2.74 104767 2918 97262 100660
67.84 82.1 3.7
2.70 104668 2918 97262 100527
89.32 83.9 3.8
2.68 104604 2918 97262 99731
95.8%
96.1%
96.0%
95.3%
m3/hr
0.00
4.34
9.97
22.01
W
0.00
0.10
0.27
1.07
W
4.44
3.92
3.85
3.94
Table A.6
Tbox
o
Tjets
o
C
C
48.6 46.1
50.4 46.5
51.9 45.6
o
C
36.9
35.9
29.9
o
C
85.8
105.0
142.5
o
Tw
o
qw
Vflow vjets
2
h
Pbox
2o
Pvap Pair init
Pair fin
Xair
C
C
Pa
Pa
Pa
m3/hr
24.1 66.8 93.03 106.9 4.8
4.49 113613 2868 95893 104053 91.6% 0.00
24.2 80.0 130.25 94.3 4.3
3.89 113630 2868 95893 104636 92.1% 3.29
22.4 112.4 203.95 90.2 4.1
3.05 113566 2868 95893 105135 92.6% 18.33
W
0.00
0.08
0.76
W
5.14
4.49
4.27
133
A
AP
PP
PE
EN
ND
DIIX
XB
B
In this section all the experimental data obtained in an open system configuration
as described in Chapter 3 are listed.
134
Table B.1
z
s Fluid Tjets Tamb Pjets
Tw
qw
Vflow
dn
o
o
μm mm mm
C
C kPa oC W/cm2 ml/min
69.3 10 1 water 21.13 21.39 141 24.74 6.81 278.5
69.3 10 1 water 21.14 21.26 142 28.86 14.70 278.5
69.3 10 1 water 21.18 21.14 142 35.04 27.12 278.5
69.3 10 1 water 21.21 21.30 142 43.36 45.07 276.7
69.3 10 1 water 21.27 21.41 141 53.10 67.16 275.0
69.3 10 1 water 21.44 21.87 142 64.42 96.03 278.1
69.3 10 1 water 21.54 22.66 141 76.17 126.07 275.0
69.3 10 1 water 21.73 24.72 141 90.02 161.53 274.3
69.3 10 1 water 21.83 25.06 141 96.37 177.74 272.9
vjets
m/s
3.10
3.10
3.10
3.08
3.06
3.09
3.06
3.05
3.04
Pr
6.46
6.13
5.67
5.14
4.61
4.09
3.65
3.22
3.05
h
W/cm2 oC
1.89
1.90
1.96
2.04
2.11
2.23
2.31
2.37
2.38
135
Xair
Nu
Re
s/dn
z/dn
97.5%
97.5%
97.5%
97.5%
97.5%
97.4%
97.4%
96.7%
96.9%
2.17
2.17
2.22
2.28
2.34
2.45
2.50
2.54
2.54
229.3
240.4
257.4
279.2
305.6
343.5
375.9
418.9
437.4
14.4
14.4
14.4
14.4
14.4
14.4
14.4
14.4
14.4
144.2
144.2
144.2
144.2
144.2
144.2
144.2
144.2
144.2
Xair
Nu
Re
s/dn
z/dn
97.4%
97.4%
97.4%
97.4%
97.4%
97.3%
97.3%
97.2%
97.2%
97.1%
3.43
3.31
3.28
3.34
3.38
3.44
3.49
3.57
3.59
3.65
372.2
382.0
394.7
423.5
451.5
484.7
524.3
576.9
626.0
675.8
14.4
14.4
14.4
14.4
14.4
14.4
14.4
14.4
14.4
14.4
144.2
144.2
144.2
144.2
144.2
144.2
144.2
144.2
144.2
144.2
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.2
z
Tw
qw
Vflow
dn
o
o
o
2
μm mm mm
C
C kPa
C W/cm ml/min
69.3 10 1 water 21.22 22.01 190 22.95 5.14 461.1
69.3 10 1 water 21.25 22.10 189 25.47 12.19 459.4
69.3 10 1 water 21.29 21.87 192 28.62 21.04 457.7
69.3 10 1 water 21.37 22.12 191 33.88 36.83 462.9
69.3 10 1 water 21.46 22.05 192 40.54 57.25 459.4
69.3 10 1 water 21.59 22.57 192 48.11 81.91 456.3
69.3 10 1 water 21.74 23.03 191 56.65 110.16 454.2
69.3 10 1 water 21.96 23.68 193 66.21 144.28 457.7
69.3 10 1 water 22.13 23.82 192 75.86 178.12 457.0
69.3 10 1 water 22.20 24.45 192 86.14 216.99 454.2
vjets
m/s
5.13
5.11
5.09
5.15
5.11
5.07
5.05
5.09
5.08
5.05
Pr
6.61
6.39
6.13
5.74
5.29
4.85
4.41
4.00
3.64
3.31
h
W/cm2 oC
2.98
2.89
2.87
2.94
3.00
3.09
3.16
3.26
3.32
3.39
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.3
z
Tw
qw
Vflow
vjets
dn
o
o
μm mm mm
C
C kPa oC W/cm2 ml/min m/s
69.3 10 1 water 25.27 23.42 467 26.28 8.27 990.8 11.02
69.3 10 1 water 25.30 23.79 468 28.27 18.60 996.4 11.08
69.3 10 1 water 25.29 24.30 469 30.57 33.72 998.7 11.11
69.3 10 1 water 25.54 24.79 469 33.44 53.50 1000.7 11.13
69.3 10 1 water 25.74 25.26 470 36.89 76.35 996.7 11.09
69.3 10 1 water 26.52 24.49 469 45.29 134.31 987.9 10.99
69.3 10 1 water 26.90 24.69 465 55.75 211.39 980.3 10.90
69.3 10 1 water 26.26 24.55 461 69.98 299.66 969.7 10.79
Pr
6.01
5.86
5.70
5.48
5.25
4.74
4.22
3.70
h
W/cm2 oC
8.19
6.26
6.38
6.77
6.84
7.16
7.33
6.86
Xair
97.1%
97.1%
97.0%
96.9%
96.8%
97.0%
97.0%
97.0%
Nu
Re
s/dn
z/dn
9.33 870.4 14.4 144.2
7.11 894.9 14.4 144.2
7.23 919.8 14.4 144.2
7.64 952.9 14.4 144.2
7.69 986.0 14.4 144.2
7.96 1071.3 14.4 144.2
8.06 1176.5 14.4 144.2
7.44 1309.3 14.4 144.2
Pamb
kPa
99.7
99.8
99.8
100.0
100.1
99.9
99.9
99.9
136
Table B.4
dn
z
o
o
μm mm mm
C
C kPa
69.3 10 1 water 25.22 24.12 261
69.3 10 1 water 25.07 24.15 261
69.3 10 1 water 24.80 24.12 262
69.3 10 1 water 25.14 23.96 261
Tw
C
27.23
30.43
35.36
40.73
o
qw
W/cm2
7.36
19.89
33.51
53.31
Vflow
ml/min
579.4
575.2
578.0
574.5
vjets
m/s
6.44
6.40
6.43
6.39
Pr
5.94
5.72
5.41
5.06
h
W/cm2 oC
3.67
3.71
3.17
3.42
Xair
Nu
Re
s/dn
z/dn
97.0%
97.0%
97.0%
97.0%
4.17
4.20
3.58
3.83
514.0
527.7
557.3
587.5
14.4
14.4
14.4
14.4
144.2
144.2
144.2
144.2
Pamb
kPa
99.7
99.4
99.6
99.6
Table B.5
z
Tw
qw
dn
o
o
μm mm mm
C
C kPa oC W/cm2
69.3 10 1 water 25.35 23.88 202 27.21 7.75
69.3 10 1 water 24.94 24.09 201 30.58 18.09
69.3 10 1 water 25.51 24.17 202 34.29 36.52
69.3 10 1 water 25.31 25.55 200 45.51 75.49
69.3 10 1 water 26.05 24.44 198 61.20 136.90
69.3 10 1 water 25.95 24.31 196 81.83 213.99
Vflow
ml/min
417.1
416.1
415.6
412.8
411.8
411.1
vjets
m/s
4.64
4.63
4.62
4.59
4.58
4.57
Pr
5.93
5.72
5.43
4.79
4.03
3.33
h
W/cm2 oC
4.17
3.21
4.16
3.74
3.90
3.83
Xair
Nu
Re
s/dn
z/dn
97.1%
97.0%
97.0%
96.8%
97.0%
97.1%
4.74
3.63
4.69
4.16
4.27
4.12
370.5
381.8
399.2
443.4
514.9
609.1
14.4
14.4
14.4
14.4
14.4
14.4
144.2
144.2
144.2
144.2
144.2
144.2
Xair
Nu
Re
s/dn
z/dn
97.0%
97.1%
97.0%
97.1%
1.91
2.58
2.69
2.67
223.5
235.1
250.2
294.7
14.4
14.4
14.4
14.4
144.2
144.2
144.2
144.2
Xair
Nu
Re
s/dn
z/dn
97.2%
97.2%
97.2%
97.2%
4.38
4.80
4.77
4.52
534.0
557.6
616.4
693.0
14.4
14.4
14.4
14.4
144.2
144.2
144.2
144.2
Pamb
kPa
99.7
99.6
99.8
100.6
99.9
100.0
Table B.6
137
z
dn
o
o
μm mm mm
C
C kPa
69.3 10 1 water 24.58 23.70 144
69.3 10 1 water 25.19 24.02 143
69.3 10 1 water 25.05 24.19 143
69.3 10 1 water 25.49 23.97 142
Tw
C
28.69
33.18
39.52
56.91
o
qw
W/cm2
6.89
18.25
34.70
76.34
Vflow
ml/min
249.7
248.5
248.0
246.1
vjets
m/s
2.78
2.76
2.76
2.74
Pr
5.88
5.53
5.14
4.24
h
W/cm2 oC
1.68
2.29
2.40
2.43
Pamb
kPa
99.2
99.7
99.8
99.9
Table B.7
z
dn
o
o
μm mm mm
C
C kPa
69.3 10 1 water 25.25 22.99 274
69.3 10 1 water 25.48 22.94 273
69.3 10 1 water 25.85 22.97 271
69.3 10 1 water 25.57 23.31 269
Tw
C
29.62
33.73
43.91
57.95
o
qw
W/cm2
16.87
35.14
77.23
133.04
Vflow
ml/min
586.1
584.2
579.9
573.0
vjets
m/s
6.52
6.50
6.45
6.37
Pr
5.77
5.47
4.85
4.19
h
W/cm2 oC
3.86
4.26
4.28
4.11
Pamb
kPa
99.6
99.5
99.8
99.8
Table B.8
z
Tw
qw
dn
o
o
μm mm mm
C
C kPa oC W/cm2
69.3 10 1 water 25.10 23.80 206 27.74 7.18
69.3 10 1 water 25.30 24.11 206 31.90 18.59
69.3 10 1 water 25.33 24.24 205 37.78 33.41
69.3 10 1 water 25.55 24.66 204 51.24 73.14
69.3 10 1 water 25.76 24.97 202 68.52 128.66
69.3 10 1 water 25.78 25.22 200 92.15 199.93
Vflow
ml/min
432.4
423.2
420.0
416.6
410.8
405.6
vjets
m/s
4.81
4.71
4.67
4.63
4.57
4.51
Pr
5.91
5.60
5.22
4.49
3.77
3.05
h
W/cm2 oC
2.72
2.82
2.68
2.85
3.01
3.01
Xair
Nu
Re
s/dn
z/dn
97.1%
97.0%
97.0%
97.0%
96.9%
96.9%
3.09
3.19
3.01
3.15
3.27
3.21
385.3
395.4
417.6
473.7
545.6
648.9
14.4
14.4
14.4
14.4
14.4
14.4
144.2
144.2
144.2
144.2
144.2
144.2
Xair
Nu
Re
s/dn
z/dn
96.9%
96.9%
96.9%
96.8%
96.8%
96.8%
96.8%
96.9%
3.00
2.93
2.96
2.92
2.99
3.06
3.24
3.31
378.1
384.7
391.9
399.9
408.9
461.5
533.9
626.1
14.4
14.4
14.4
14.4
14.4
14.4
14.4
14.4
144.2
144.2
144.2
144.2
144.2
144.2
144.2
144.2
Pamb
kPa
100.1
100.3
100.5
100.8
100.8
100.9
Table B.9
138
z
Tw
qw
Vflow
dn
o
o
o
2
μm mm mm
C
C kPa
C W/cm ml/min
69.3 10 1 water 25.30 24.66 188 25.96 1.75 431.8
69.3 10 1 water 25.36 24.80 189 27.08 4.44 433.6
69.3 10 1 water 25.42 24.98 190 28.55 8.15 434.4
69.3 10 1 water 25.33 25.10 190 30.54 13.41 434.1
69.3 10 1 water 25.41 25.64 191 32.39 18.46 434.8
69.3 10 1 water 25.51 25.78 191 44.46 52.07 433.4
69.3 10 1 water 25.71 25.88 190 60.40 102.68 431.3
69.3 10 1 water 25.88 25.55 189 80.46 167.66 427.4
vjets
m/s
4.80
4.82
4.83
4.83
4.84
4.82
4.80
4.75
Pr
6.03
5.94
5.83
5.69
5.56
4.83
4.08
3.37
h
W/cm2 oC
2.63
2.58
2.61
2.57
2.64
2.75
2.96
3.07
Pamb
kPa
100.0
100.1
100.3
100.4
100.6
100.9
101.0
100.9
Table B.10
z
Tw
qw
Vflow
vjets
dn
o
o
μm mm mm
C
76.4 10 2 water 18.81 22.12 127 21.36 1.75
97.4 2.79
76.4 10 2 water 18.69 22.16 127 28.48 6.48
97.4 2.79
76.4 10 2 water 18.69 22.21 127 38.00 13.70 97.4 2.79
76.4 10 2 water 18.71 22.23 126 50.61 24.26 95.7 2.74
76.4 10 2 water 18.73 22.38 126 61.92 38.69 97.4 2.79
76.4 10 2 water 18.72 22.64 126 79.30 56.68 94.0 2.69
76.4 10 2 water 18.79 23.09 126 97.28 79.12 95.7 2.74
Pr
6.98
6.35
5.64
4.87
4.31
3.64
3.10
h
W/cm2 oC
0.69
0.66
0.71
0.76
0.90
0.94
1.01
Xair
Nu
Re
s/dn
z/dn
97.4%
97.4%
97.4%
97.4%
97.3%
97.3%
97.2%
0.88
0.84
0.88
0.93
1.09
1.12
1.19
212.7
231.1
256.9
287.4
325.8
365.6
428.6
26.2
26.2
26.2
26.2
26.2
26.2
26.2
130.9
130.9
130.9
130.9
130.9
130.9
130.9
Xair
Nu
Re
s/dn
z/dn
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.11
139
dn
z
Tw
qw
Vflow
o
o
o
2
μm mm mm
C
C kPa
C W/cm ml/min
76.4 10 2 water 18.07 22.42 241 21.53 7.47 259.3
76.4 10 2 water 18.12 22.48 241 25.29 15.65 259.3
76.4 10 2 water 18.21 22.53 240 31.22 28.39 257.6
76.4 10 2 water 18.32 22.56 237 38.86 45.65 254.1
76.4 10 2 water 18.31 22.70 236 47.26 64.06 254.1
76.4 10 2 water 18.37 22.92 236 58.38 90.15 254.1
76.4 10 2 water 18.53 23.28 236 70.75 117.86 254.1
76.4 10 2 water 18.64 22.45 236 93.24 177.02 254.1
76.4 10 2 water 18.64 22.43 234 100.30 195.62 250.6
76.4 10 2 water 18.68 22.28 238 99.79 195.11 254.1
vjets
m/s
7.43
7.43
7.38
7.28
7.28
7.28
7.28
7.28
7.18
7.28
Pr
7.03
6.68
6.17
5.60
5.08
4.49
3.95
3.21
3.03
3.04
h
W/cm2 oC
2.16
2.18
2.18
2.22
2.21
2.25
2.26
2.37
2.40
2.41
97.3%
97.3%
97.3%
97.3%
97.3%
97.2%
97.2%
97.4%
97.4%
97.4%
2.75 562.2 26.2 130.9
2.77 588.6 26.2 130.9
2.74 626.9 26.2 130.9
2.77 673.6 26.2 130.9
2.73 735.1 26.2 130.9
2.75 819.6 26.2 130.9
2.72 917.6 26.2 130.9
2.80 1102.5 26.2 130.9
2.81 1146.1 26.2 130.9
2.83 1158.0 26.2 130.9
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.12
z
Tw
qw
Vflow
dn
o
o
μm mm mm
C
76.4 10 2 water 17.98 20.75 165 19.74 2.33 160.2
76.4 10 2 water 17.92 20.84 165 24.61 8.56 160.2
76.4 10 2 water 17.92 23.24 165 32.70 19.09 160.2
76.4 10 2 water 18.03 23.41 164 42.31 31.26 156.7
76.4 10 2 water 18.11 23.04 165 52.50 47.43 160.2
76.4 10 2 water 18.14 22.96 165 63.88 65.25 158.4
76.4 10 2 water 18.13 23.45 165 77.05 85.51 160.2
76.4 10 2 water 18.20 23.17 166 87.37 108.56 160.2
76.4 10 2 water 18.28 23.19 165 101.04 134.07 160.2
vjets
m/s
4.59
4.59
4.59
4.49
4.59
4.54
4.59
4.59
4.59
Pr
7.22
6.76
6.08
5.40
4.80
4.25
3.74
3.40
3.02
h
W/cm2 oC
1.33
1.28
1.29
1.29
1.38
1.43
1.45
1.57
1.62
140
Xair
Nu
Re
s/dn
z/dn
97.6%
97.6%
97.2%
97.2%
97.2%
97.2%
97.1%
97.1%
97.1%
1.69
1.63
1.62
1.60
1.69
1.73
1.74
1.86
1.90
339.3
359.7
395.0
429.5
487.1
536.4
608.2
661.7
734.4
26.2
26.2
26.2
26.2
26.2
26.2
26.2
26.2
26.2
130.9
130.9
130.9
130.9
130.9
130.9
130.9
130.9
130.9
Xair
Nu
Re
s/dn
z/dn
97.6%
97.6%
97.6%
97.2%
97.1%
97.0%
96.8%
96.9%
96.9%
96.7%
96.5%
3.59
3.58
3.61
3.70
3.76
3.85
3.96
4.06
4.09
4.18
4.22
901.1
945.7
1003.9
1088.2
1162.7
1264.3
1362.6
1467.0
1579.9
1705.5
1850.3
26.2
26.2
26.2
26.2
26.2
26.2
26.2
26.2
26.2
26.2
26.2
130.9
130.9
130.9
130.9
130.9
130.9
130.9
130.9
130.9
130.9
130.9
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.13
z
Tw
qw
Vflow
vjets
Pr
h
dn
o
o
o
2
μm mm mm
C
C kPa
C W/cm ml/min m/s
W/cm2 oC
76.4 10 2 water 18.41 20.82 405 21.82 9.63 412.4 11.81 6.97
2.82
76.4 10 2 water 18.43 20.68 405 25.84 20.95 412.4 11.81 6.60
2.83
76.4 10 2 water 18.49 20.69 405 30.96 35.79 412.4 11.81 6.17
2.87
76.4 10 2 water 18.64 23.31 406 38.11 57.82 412.4 11.81 5.63
2.97
76.4 10 2 water 18.73 23.93 403 44.74 78.99 410.7 11.77 5.20
3.04
76.4 10 2 water 18.94 24.64 403 52.49 105.38 412.4 11.82 4.76
3.14
76.4 10 2 water 19.02 25.53 405 60.30 134.37 412.4 11.82 4.37
3.26
76.4 10 2 water 19.20 24.96 406 68.34 165.44 412.4 11.82 4.02
3.37
76.4 10 2 water 19.29 25.00 405 76.93 197.29 412.4 11.81 3.70
3.42
76.4 10 2 water 19.53 26.36 406 86.14 234.40 412.4 11.82 3.39
3.52
76.4 10 2 water 19.63 27.10 405 97.29 278.84 410.7 11.76 3.08
3.59
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.14
z
Tw
qw
Vflow
dn
o
o
μm mm mm
C
76.4 10 2 water 20.12 23.20 228 27.41 14.76 247.5
76.4 10 2 water 20.24 23.68 228 34.06 28.18 247.5
76.4 10 2 water 20.29 21.75 226 41.90 44.57 247.1
76.4 10 2 water 20.27 21.15 225 52.19 67.91 247.1
76.4 10 2 water 20.30 21.06 226 62.96 93.04 247.1
76.4 10 2 water 20.36 21.10 226 73.11 117.25 247.1
76.4 10 2 water 20.40 21.32 224 87.24 150.89 245.4
vjets
m/s
7.09
7.09
7.08
7.08
7.08
7.08
7.03
Pr
6.32
5.81
5.28
4.70
4.20
3.80
3.33
h
W/cm2 oC
2.03
2.04
2.06
2.13
2.18
2.22
2.26
Xair
97.2%
97.1%
97.4%
97.5%
97.6%
97.6%
97.5%
Nu
Re
2.56 589.4
2.55 635.9
2.55 690.6
2.60 765.2
2.64 846.2
2.67 925.2
2.68 1030.5
s/dn
z/dn
26.2
26.2
26.2
26.2
26.2
26.2
26.2
130.9
130.9
130.9
130.9
130.9
130.9
130.9
s/dn
z/dn
26.2
26.2
26.2
26.2
26.2
26.2
130.9
130.9
130.9
130.9
130.9
130.9
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.15
141
dn
z
Tw
qw
o
o
o
μm mm mm
C
C kPa
C W/cm2
76.4 10 2 water 24.86 22.96 227 25.76 1.59
76.4 10 2 water 25.08 23.74 232 28.99 6.92
76.4 10 2 water 25.05 24.28 229 34.55 17.45
76.4 10 2 water 25.24 25.32 232 50.26 50.85
76.4 10 2 water 25.29 25.60 231 70.72 99.90
76.4 10 2 water 25.21 25.88 233 93.35 154.41
Vflow
ml/min
247.1
243.7
240.2
243.7
245.4
247.1
vjets
m/s
7.08
6.98
6.88
6.98
7.03
7.08
Pr
6.08
5.82
5.44
4.55
3.71
3.04
h
W/cm2 oC
1.75
1.77
1.84
2.03
2.20
2.27
Xair
97.2%
97.1%
97.0%
96.9%
96.8%
96.8%
Nu
Re
2.20 609.6
2.21 624.5
2.28 653.2
2.48 776.6
2.63 938.4
2.66 1127.0
Pamb
kPa
99.2
99.7
100.0
100.8
100.8
100.9
Table B.16
dn
μm
122.6
122.6
122.6
122.6
122.6
122.6
122.6
z
Tw
qw
Vflow
vjets
o
o
mm mm
C
10 3 water 18.99 21.31 144 22.83 1.56
45.9 1.06
10 3 water 19.20 21.34 143 33.02 6.40
45.2 1.05
10 3 water 19.21 21.30 144 32.98 6.42
45.9 1.06
10 3 water 19.30 21.41 143 46.81 14.53 45.9 1.06
10 3 water 19.34 21.53 142 64.20 25.88 45.2 1.05
10 3 water 19.37 21.90 141 86.79 42.51 45.4 1.05
10 3 water 19.39 22.54 140 94.57 48.70 45.2 1.05
Pr
6.82
5.96
5.96
5.05
4.19
3.38
3.16
h
W/cm2 oC
0.41
0.46
0.47
0.53
0.58
0.63
0.65
Xair
Nu
Re
s/dn
z/dn
97.5%
97.5%
97.5%
97.5%
97.5%
97.4%
97.4%
0.83
0.93
0.94
1.05
1.12
1.20
1.23
132.7
147.4
149.5
173.2
201.5
244.4
258.6
24.5
24.5
24.5
24.5
24.5
24.5
24.5
81.6
81.6
81.6
81.6
81.6
81.6
81.6
Xair
Nu
Re
s/dn
z/dn
97.6%
97.6%
97.6%
97.5%
97.5%
97.3%
97.3%
2.51
2.54
2.55
2.46
2.47
2.36
2.34
346.5
373.4
415.8
469.8
532.6
624.0
680.8
24.5
24.5
24.5
24.5
24.5
24.5
24.5
81.6
81.6
81.6
81.6
81.6
81.6
81.6
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.17
142
dn
μm
122.6
122.6
122.6
122.6
122.6
122.6
122.6
z
Tw
qw
Vflow
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min
10 3 water 18.71 20.56 354 23.99 6.51 118.7
10 3 water 18.66 20.77 352 31.14 15.70 117.8
10 3 water 18.61 20.91 354 40.29 27.72 118.7
10 3 water 18.64 21.22 356 52.78 42.65 118.2
10 3 water 18.68 21.89 356 67.46 62.08 116.9
10 3 water 18.73 23.07 353 86.16 83.53 117.1
10 3 water 18.78 22.84 354 96.65 96.27 117.8
vjets
m/s
2.75
2.73
2.75
2.74
2.71
2.71
2.73
Pr
6.74
6.14
5.49
4.76
4.08
3.42
3.12
h
W/cm2 oC
1.23
1.26
1.28
1.25
1.27
1.24
1.24
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.18
dn
μm
122.6
122.6
122.6
122.6
122.6
122.6
122.6
z
Tw
qw
Vflow
vjets
o
o
mm mm
C
10 3 water 19.00 21.15 185 21.40 1.82
76.1 1.76
10 3 water 19.04 20.98 184 28.32 6.96
76.1 1.76
10 3 water 19.09 20.88 184 39.52 15.96 76.1 1.76
10 3 water 19.17 21.23 183 56.49 30.98 75.3 1.74
10 3 water 19.27 21.56 182 73.51 47.32 75.3 1.74
10 3 water 19.28 21.65 182 93.02 67.76 75.4 1.75
10 3 water 19.33 23.19 180 99.71 73.03 74.5 1.72
Pr
6.95
6.34
5.51
4.54
3.82
3.20
3.03
h
W/cm2 oC
0.76
0.75
0.78
0.83
0.87
0.92
0.91
Xair
Nu
Re
s/dn
z/dn
97.5%
97.6%
97.6%
97.5%
97.5%
97.5%
97.3%
1.55
1.52
1.56
1.63
1.68
1.74
1.71
215.9
234.5
265.5
311.7
363.3
425.8
442.1
24.5
24.5
24.5
24.5
24.5
24.5
24.5
81.6
81.6
81.6
81.6
81.6
81.6
81.6
Xair
Nu
Re
s/dn
z/dn
3.30 588.2 24.5
3.36 636.1 24.5
3.34 700.0 24.5
3.39 774.5 24.5
3.45 862.9 24.5
3.52 941.7 24.5
3.57 1045.5 24.5
3.57 1109.6 24.5
81.6
81.6
81.6
81.6
81.6
81.6
81.6
81.6
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.19
143
dn
μm
122.6
122.6
122.6
122.6
122.6
122.6
122.6
122.6
z
Tw
qw
Vflow
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min
10 3 water 19.28 21.08 659 25.46 10.05 196.7
10 3 water 19.32 21.07 654 32.27 21.58 196.7
10 3 water 19.37 21.08 646 41.92 37.86 194.9
10 3 water 19.41 21.23 639 52.85 57.72 193.2
10 3 water 19.49 21.24 627 65.39 81.56 191.5
10 3 water 19.57 21.60 614 77.63 106.43 188.0
10 3 water 19.61 21.78 608 91.95 136.32 186.3
10 3 water 19.70 22.10 599 99.85 151.68 186.3
vjets
m/s
4.55
4.55
4.51
4.47
4.43
4.35
4.31
4.31
Pr
6.56
6.00
5.34
4.71
4.13
3.67
3.22
3.01
h
W/cm2 oC
1.63
1.67
1.68
1.73
1.78
1.83
1.88
1.89
97.5%
97.5%
97.5%
97.5%
97.5%
97.5%
97.5%
97.4%
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.20
dn
μm
122.6
122.6
122.6
122.6
122.6
z
Tw
o
o
mm mm
C
C kPa oC
10 3 water 25.03 23.53 443 29.82
10 3 water 25.09 24.31 442 36.07
10 3 water 25.33 25.39 439 44.52
10 3 water 25.48 29.37 431 64.33
10 3 water 25.43 35.84 419 91.87
qw
W/cm2
6.88
16.79
32.15
69.73
121.39
Vflow
ml/min
176.4
176.4
175.7
173.2
169.1
vjets
m/s
4.08
4.08
4.07
4.01
3.92
Pr
5.77
5.35
4.84
3.93
3.07
h
W/cm2 oC
1.43
1.53
1.68
1.79
1.83
Xair
Nu
Re
s/dn
z/dn
97.2%
97.0%
96.9%
96.2%
94.8%
2.88
3.04
3.30
3.47
3.45
591.3
632.5
688.1
815.2
991.3
24.5
24.5
24.5
24.5
24.5
81.6
81.6
81.6
81.6
81.6
Re
s/dn
z/dn
Pamb
kPa
101.0
101.4
102.2
104.5
108.8
Table B.21
144
dn
μm
122.6
122.6
122.6
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 3 water 24.35 23.58
10 3 water 24.66 24.77
10 3 water 24.65 25.82
Pjets
Tw
qw
Vflow
vjets
o
2
kPa
C W/cm ml/min m/s
190 36.81 6.70
74.5 1.72
188 51.61 17.81 72.9 1.69
189 84.34 48.54 72.9 1.69
Pr
h
Xair
Nu
2o
W/cm C
5.35
0.54
97.1% 1.07
4.52
0.66
96.9% 1.29
3.29
0.81
96.8% 1.54
Pamb
kPa
267.0 24.5 81.6 99.4
303.6 24.5 81.6 100.4
401.3 24.5 81.6 100.7
Table B.22
dn
μm
122.6
122.6
122.6
122.6
122.6
z
Tw
o
o
o
mm mm
C
C kPa
C
10 3 water 24.84 24.22 200 26.74
10 3 water 25.14 25.16 200 34.21
10 3 water 25.21 25.12 200 46.31
10 3 water 25.29 24.69 198 63.66
10 3 water 25.33 24.75 196 80.19
qw
Vflow
vjets
2
W/cm ml/min m/s
1.55
76.8 1.78
7.53
76.0 1.76
17.96 76.0 1.76
33.79 76.0 1.76
50.39 76.0 1.76
Pr
6.01
5.46
4.75
3.97
3.40
h
W/cm2 oC
0.81
0.83
0.85
0.88
0.92
Xair
Nu
Re
s/dn
z/dn
97.0%
96.9%
96.9%
97.0%
97.0%
1.64
1.66
1.68
1.70
1.75
248.5
267.5
302.6
355.2
407.4
24.5
24.5
24.5
24.5
24.5
81.6
81.6
81.6
81.6
81.6
Pamb
kPa
100.3
100.9
101.0
100.9
100.9
Table B.23
dn
μm
122.6
122.6
122.6
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 3 water 25.30 24.93
10 3 water 25.22 24.97
10 3 water 25.19 25.02
Pjets
Tw
qw
Vflow
vjets
kPa oC W/cm2 ml/min m/s
144 29.57 1.53
45.2 1.05
144 35.28 4.18
45.2 1.05
144 59.84 17.45 45.2 1.05
Pr
h
Xair
Nu
W/cm2 oC
5.76
0.36
96.9% 0.72
5.39
0.42
96.9% 0.83
4.12
0.50
96.9% 0.98
Re
s/dn
z/dn
Pamb
kPa
151.7 24.5 81.6 100.9
161.1 24.5 81.6 100.9
204.1 24.5 81.6 100.9
Table B.24
145
dn
μm
122.6
122.6
122.6
122.6
122.6
122.6
z
Tw
qw
o
o
o
mm mm
C
C kPa
C W/cm2
10 3 water 25.07 24.71 305 26.59 1.62
10 3 water 25.16 24.88 307 28.82 4.33
10 3 water 25.25 25.22 307 31.30 7.40
10 3 water 25.28 25.76 307 35.71 13.31
10 3 water 25.29 27.57 305 50.48 34.06
10 3 water 25.35 31.79 302 77.70 73.25
Vflow
ml/min
119.6
120.6
120.6
120.6
120.6
120.6
vjets
m/s
2.77
2.79
2.79
2.79
2.79
2.79
Pr
6.00
5.83
5.65
5.36
4.54
3.47
h
W/cm2 oC
1.06
1.18
1.22
1.28
1.35
1.40
Xair
Nu
Re
s/dn
z/dn
96.9%
96.9%
96.8%
96.7%
96.4%
95.6%
2.14
2.37
2.45
2.54
2.65
2.67
387.2
400.3
411.7
431.5
499.7
633.3
24.5
24.5
24.5
24.5
24.5
24.5
81.6
81.6
81.6
81.6
81.6
81.6
Pamb
kPa
100.1
100.3
100.5
100.9
102.1
104.6
Table B.25
dn
μm
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
z
Tw
qw
Vflow
vjets
o
o
mm mm
C
10 1 water 25.40 25.39 153 25.96 4.69 1511.8 5.74
10 1 water 25.43 25.42 153 26.52 8.02 1510.9 5.73
10 1 water 25.50 25.43 153 27.74 13.95 1511.7 5.74
10 1 water 25.45 24.44 153 28.82 19.15 1513.5 5.74
10 1 water 25.55 24.26 153 30.30 26.77 1513.2 5.74
10 1 water 25.63 24.19 153 32.06 35.76 1513.0 5.74
10 1 water 25.92 24.13 152 40.56 78.05 1508.6 5.72
10 1 water 26.37 24.38 152 53.74 135.04 1504.6 5.71
10 1 water 26.75 24.38 152 67.14 209.29 1499.0 5.69
Pr
6.02
5.98
5.88
5.81
5.70
5.57
5.03
4.34
3.78
h
W/cm2 oC
8.33
7.34
6.22
5.68
5.65
5.56
5.33
4.93
5.18
146
Xair
Nu
Re
s/dn
z/dn
96.8%
96.8%
96.8%
97.0%
97.0%
97.0%
97.1%
97.0%
97.1%
16.24
14.30
12.10
11.03
10.95
10.77
10.21
9.31
9.65
774.0
778.7
790.3
800.2
813.9
830.1
906.6
1030.6
1159.1
8.4
8.4
8.4
8.4
8.4
8.4
8.4
8.4
8.4
84.2
84.2
84.2
84.2
84.2
84.2
84.2
84.2
84.2
Xair
Nu
Re
s/dn
z/dn
9.78 760.9 8.4
8.57 764.6 8.4
8.58 774.4 8.4
8.80 785.4 8.4
9.06 796.2 8.4
9.28 827.4 8.4
9.27 906.5 8.4
9.14 1023.6 8.4
9.50 1171.3 8.4
84.2
84.2
84.2
84.2
84.2
84.2
84.2
84.2
84.2
Pamb
kPa
101.6
101.6
101.6
100.9
100.9
100.9
100.8
100.9
100.9
Table B.26
dn
μm
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
z
Tw
qw
Vflow
vjets
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min m/s
10 1 water 24.29 22.61 153 24.56 1.39 1528.9 5.80
10 1 water 24.37 22.90 154 25.22 3.71 1523.6 5.78
10 1 water 24.42 23.11 154 26.05 7.18 1527.9 5.80
10 1 water 24.47 23.29 154 27.17 12.18 1529.4 5.80
10 1 water 24.53 23.44 154 28.35 17.77 1529.3 5.80
10 1 water 24.64 23.66 155 31.76 34.09 1529.4 5.80
10 1 water 24.98 24.25 155 40.32 74.15 1526.7 5.79
10 1 water 25.47 24.52 155 52.58 130.96 1523.1 5.78
10 1 water 26.14 24.52 154 67.36 210.10 1519.8 5.77
Pr
6.22
6.16
6.09
6.00
5.91
5.66
5.09
4.43
3.80
h
W/cm2 oC
5.00
4.39
4.39
4.51
4.65
4.79
4.83
4.83
5.10
97.3%
97.2%
97.2%
97.2%
97.1%
97.1%
97.0%
97.0%
97.1%
Pamb
kPa
99.7
99.9
100.0
100.1
100.2
100.4
100.7
100.9
100.8
Table B.27
dn
μm
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
z
Tw
qw
Vflow
o
o
mm mm
C
10 2 water 17.80 20.61 111 29.80 13.87 184.5
10 2 water 17.85 20.37 112 37.77 22.38 184.5
10 2 water 17.86 20.30 111 44.95 34.55 184.5
10 2 water 18.02 20.30 111 56.96 52.32 184.5
10 2 water 18.01 20.67 111 67.09 67.73 184.5
10 2 water 18.05 20.87 111 79.13 86.29 184.5
10 2 water 18.12 20.79 112 86.70 104.33 184.5
10 2 water 18.16 20.87 111 92.89 118.21 184.5
10 2 water 18.20 21.35 111 96.93 123.81 181.0
10 2 water 18.24 21.29 111 104.83 136.32 181.0
vjets
m/s
2.38
2.38
2.38
2.38
2.38
2.38
2.38
2.38
2.33
2.33
Pr
6.32
5.71
5.24
4.58
4.12
3.67
3.42
3.24
3.13
2.93
h
W/cm2 oC
1.16
1.12
1.28
1.34
1.38
1.41
1.52
1.58
1.57
1.57
Nu
Re
s/dn
z/dn
97.6%
97.6%
97.7%
97.7%
97.6%
97.6%
97.6%
97.6%
97.5%
97.5%
2.17
2.09
2.35
2.45
2.49
2.52
2.69
2.79
2.76
2.75
295.0
322.6
348.1
392.6
430.9
478.0
508.4
533.7
540.0
572.2
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
Xair
Nu
Re
s/dn
z/dn
97.6%
97.6%
97.6%
97.6%
97.6%
97.6%
97.6%
97.6%
97.6%
97.6%
97.6%
5.34
5.30
5.33
5.24
5.43
5.58
5.62
5.72
5.68
5.78
5.76
757.6
793.8
835.0
885.3
941.6
1016.8
1102.7
1196.6
1302.3
1378.9
1475.7
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
147
Xair
Table B.28
dn
μm
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
z
Tw
qw
Vflow
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min
10 2 water 17.88 20.78 159 23.77 16.58 508.1
10 2 water 17.95 20.62 159 27.64 27.26 508.1
10 2 water 18.04 20.57 158 31.97 39.65 508.1
10 2 water 18.12 20.59 159 37.17 53.68 508.1
10 2 water 18.19 20.61 160 42.89 72.56 508.1
10 2 water 18.25 20.58 159 50.38 97.74 508.1
10 2 water 18.43 20.64 159 59.37 126.82 504.6
10 2 water 18.63 20.71 158 68.97 160.19 501.2
10 2 water 18.88 20.69 157 80.38 196.33 494.2
10 2 water 19.01 20.78 157 87.40 223.54 494.2
10 2 water 19.21 21.07 157 97.98 258.58 487.2
vjets
m/s
6.55
6.55
6.55
6.55
6.55
6.55
6.51
6.46
6.37
6.37
6.28
Pr
6.84
6.49
6.13
5.74
5.35
4.91
4.44
4.02
3.60
3.37
3.07
h
W/cm2 oC
2.82
2.81
2.85
2.82
2.94
3.04
3.10
3.18
3.19
3.27
3.28
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.29
dn
μm
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
z
Tw
qw
Vflow
o
o
mm mm
C
10 2 water 17.78 24.19 132 21.56 9.06 320.2
10 2 water 17.84 24.46 132 25.70 18.94 320.2
10 2 water 17.89 24.62 132 31.20 32.49 320.2
10 2 water 18.00 22.92 131 37.51 49.07 316.7
10 2 water 18.07 23.04 131 44.95 68.82 316.7
10 2 water 18.47 23.19 131 75.47 156.88 316.7
10 2 water 18.66 23.25 131 85.33 186.00 316.7
10 2 water 18.74 23.43 131 96.22 218.27 313.3
10 2 water 18.95 23.71 131 102.96 238.19 316.7
vjets
m/s
4.13
4.13
4.13
4.08
4.08
4.08
4.08
4.04
4.08
Pr
7.06
6.67
6.20
5.72
5.23
3.78
3.44
3.13
2.96
h
W/cm2 oC
2.40
2.41
2.44
2.52
2.56
2.75
2.79
2.82
2.84
148
Xair
Nu
Re
s/dn
z/dn
97.0%
97.0%
96.9%
97.2%
97.2%
97.2%
97.2%
97.2%
97.2%
4.56
4.55
4.58
4.68
4.72
4.92
4.94
4.95
4.95
464.3
488.3
520.8
553.2
598.9
798.6
867.1
933.2
992.9
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
Xair
Nu
Re
s/dn
z/dn
97.1%
97.1%
97.1%
97.0%
97.0%
97.0%
96.9%
96.9%
96.8%
96.8%
5.57
5.54
5.58
5.60
5.61
5.56
5.33
5.37
5.39
5.36
772.7
815.5
866.5
927.3
996.4
1091.1
1210.0
1310.3
1414.3
1517.5
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.30
dn
μm
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
z
Tw
qw
Vflow
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min
10 2 water 18.49 23.89 155 24.81 18.64 508.1
10 2 water 18.53 23.79 155 29.69 32.89 506.4
10 2 water 18.63 23.90 155 35.31 49.90 504.7
10 2 water 18.73 24.22 155 41.54 69.10 504.6
10 2 water 18.85 24.39 155 48.78 91.51 502.9
10 2 water 18.97 24.49 155 57.34 117.37 506.4
10 2 water 19.20 24.79 156 68.10 144.90 508.1
10 2 water 19.37 24.97 155 77.67 175.51 506.4
10 2 water 19.50 25.09 154 87.47 207.34 504.6
10 2 water 19.64 25.22 154 97.05 236.75 502.9
vjets
m/s
6.55
6.53
6.51
6.51
6.48
6.53
6.55
6.53
6.51
6.48
Pr
6.69
6.27
5.83
5.40
4.96
4.51
4.03
3.67
3.35
3.09
h
W/cm2 oC
2.95
2.95
2.99
3.03
3.06
3.06
2.96
3.01
3.05
3.06
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.31
dn
μm
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
z
Tw
qw
Vflow
o
o
mm mm
C
10 2 water 18.43 20.82 123 22.93 9.49 315.0
10 2 water 18.45 20.84 123 27.44 18.93 315.0
10 2 water 18.49 20.89 123 33.20 31.96 315.0
10 2 water 18.55 20.88 123 41.63 50.94 313.3
10 2 water 18.62 21.06 123 51.13 73.67 315.0
10 2 water 18.73 21.36 123 61.51 98.18 313.3
10 2 water 18.85 21.52 123 74.69 130.76 315.0
10 2 water 18.96 21.33 123 87.67 161.76 313.3
10 2 water 19.07 21.77 123 99.10 187.48 313.3
vjets
m/s
4.06
4.06
4.06
4.04
4.06
4.04
4.06
4.04
4.04
Pr
6.86
6.46
6.00
5.41
4.85
4.33
3.79
3.36
3.05
h
W/cm2 oC
2.11
2.10
2.17
2.21
2.27
2.29
2.34
2.35
2.34
149
Xair
Nu
Re
s/dn
z/dn
97.6%
97.6%
97.6%
97.6%
97.5%
97.5%
97.5%
97.5%
97.5%
4.00
3.96
4.06
4.08
4.15
4.16
4.19
4.16
4.10
468.0
493.8
527.6
575.1
637.3
700.2
791.6
875.6
955.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
Xair
Nu
Re
s/dn
z/dn
97.5%
97.4%
97.4%
97.4%
97.4%
97.3%
97.2%
97.2%
97.2%
97.1%
6.79
6.66
6.68
6.74
6.81
6.93
7.15
7.28
7.37
7.50
990.6
1031.5
1080.6
1141.7
1213.2
1299.5
1410.0
1513.6
1609.4
1724.4
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
87.8
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.32
dn
μm
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
113.9
z
Tw
qw
Vflow
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min
10 2 water 21.35 21.46 205 23.92 9.27 636.5
10 2 water 21.37 21.65 205 27.31 21.10 637.2
10 2 water 21.42 21.90 204 31.47 35.95 636.8
10 2 water 21.58 21.87 204 36.51 54.22 635.8
10 2 water 21.72 22.17 203 42.63 77.39 633.0
10 2 water 21.84 22.64 203 49.88 106.41 630.1
10 2 water 22.03 23.30 203 57.85 141.34 633.0
10 2 water 22.24 23.58 202 66.17 178.02 629.5
10 2 water 22.43 23.77 201 73.83 212.46 626.0
10 2 water 22.69 24.74 201 82.78 254.56 622.5
vjets
m/s
8.21
8.22
8.21
8.20
8.16
8.12
8.16
8.12
8.07
8.03
Pr
6.51
6.23
5.91
5.54
5.15
4.74
4.35
3.99
3.70
3.40
h
W/cm2 oC
3.60
3.55
3.58
3.63
3.70
3.79
3.95
4.05
4.13
4.24
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.33
dn
μm
113.9
113.9
113.9
113.9
113.9
z
Tw
o
o
mm mm
C
C kPa oC
10 2 water 20.52 18.28 443 23.96
10 2 water 20.87 18.46 441 32.15
10 2 water 21.18 18.94 436 39.72
10 2 water 21.71 19.75 432 51.67
10 2 water 22.11 20.77 429 60.97
qw
W/cm2
20.45
67.54
113.32
191.31
256.00
Vflow
ml/min
1120.0
1124.0
1111.9
1100.8
1099.7
vjets
m/s
14.44
14.49
14.34
14.19
14.18
Pr
6.58
5.90
5.36
4.66
4.21
h
W/cm2 oC
5.95
5.99
6.11
6.39
6.59
Xair
Nu
Re
s/dn
z/dn
97.8%
97.7%
97.7%
97.6%
97.5%
11.23
11.18
11.31
11.64
11.89
1727.0
1910.5
2056.5
2307.0
2522.3
17.6
17.6
17.6
17.6
17.6
87.8
87.8
87.8
87.8
87.8
Xair
Nu
Re
s/dn
z/dn
97.7%
97.7%
97.7%
97.6%
97.4%
97.2%
9.21
9.20
9.21
9.38
9.68
9.81
1380.1
1429.5
1540.9
1709.7
1946.6
2147.4
17.6
17.6
17.6
17.6
17.6
17.6
87.8
87.8
87.8
87.8
87.8
87.8
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
Table B.34
150
dn
μm
113.9
113.9
113.9
113.9
113.9
113.9
z
Tw
qw
o
o
mm mm
C
C kPa oC W/cm2
10 2 water 20.53 19.14 331 26.67 30.07
10 2 water 20.59 19.36 331 29.48 43.64
10 2 water 20.83 19.13 328 36.28 76.59
10 2 water 21.19 20.20 324 47.14 132.76
10 2 water 21.66 22.93 320 61.39 213.13
10 2 water 22.05 24.66 317 73.13 280.85
Vflow
ml/min
867.1
869.2
867.1
857.0
848.9
842.9
vjets
m/s
11.18
11.21
11.18
11.05
10.95
10.87
Pr
6.35
6.12
5.61
4.92
4.21
3.74
h
W/cm2 oC
4.90
4.91
4.96
5.12
5.36
5.50
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
Table B.35
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
Tw
qw
Vflow
vjets
o
o
mm mm
C
10 3 water 18.57 21.28 108 28.99 6.60
90.7 2.33
10 3 water 18.56 21.55 108 38.25 12.63 91.5 2.35
10 3 water 18.70 21.76 108 47.72 20.99 91.5 2.35
10 3 water 18.93 22.95 108 59.89 33.45 90.7 2.33
10 3 water 19.08 22.70 108 73.71 48.10 91.5 2.35
10 3 water 19.09 22.27 108 90.69 65.91 91.5 2.35
10 3 water 18.95 21.74 108 98.29 74.16 91.5 2.35
Pr
6.32
5.63
5.03
4.40
3.82
3.27
3.07
h
W/cm2 oC
0.63
0.64
0.72
0.82
0.88
0.92
0.93
Xair
Nu
Re
s/dn
z/dn
97.5%
97.5%
97.4%
97.2%
97.3%
97.3%
97.4%
1.21
1.22
1.36
1.51
1.61
1.66
1.67
295.3
330.3
365.0
407.6
465.6
534.2
565.0
25.8
25.8
25.8
25.8
25.8
25.8
25.8
86.0
86.0
86.0
86.0
86.0
86.0
86.0
Xair
Nu
Re
s/dn
z/dn
97.6%
97.6%
97.6%
97.6%
97.6%
97.6%
97.3%
97.0%
97.0%
97.2%
97.1%
4.92
4.80
4.76
4.83
4.92
5.08
5.25
5.41
5.50
5.53
5.57
1196.1
1259.7
1355.8
1473.5
1589.6
1742.2
1904.2
2079.0
2241.1
2392.7
2508.4
25.8
25.8
25.8
25.8
25.8
25.8
25.8
25.8
25.8
25.8
25.8
86.0
86.0
86.0
86.0
86.0
86.0
86.0
86.0
86.0
86.0
86.0
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.36
151
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
Tw
qw
Vflow
vjets
Pr
h
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min m/s
W/cm2 oC
10 3 water 18.08 20.64 244 21.34 8.27 404.4 10.40 7.05
2.54
10 3 water 18.12 20.63 244 25.61 18.62 404.4 10.40 6.65
2.49
10 3 water 18.16 20.58 243 32.09 34.68 403.7 10.38 6.11
2.49
10 3 water 18.54 20.84 244 38.90 51.90 405.5 10.43 5.59
2.55
10 3 water 18.69 20.83 242 46.87 73.82 402.0 10.34 5.08
2.62
10 3 water 18.91 20.95 242 56.01 101.29 402.0 10.34 4.58
2.73
10 3 water 19.18 23.13 243 64.91 130.27 403.7 10.38 4.16
2.85
10 3 water 19.44 24.88 244 74.76 163.95 403.7 10.38 3.77
2.96
10 3 water 19.66 24.27 243 84.25 196.22 402.0 10.34 3.45
3.04
10 3 water 19.67 23.39 242 93.36 226.94 399.9 10.28 3.18
3.08
10 3 water 19.82 23.72 243 98.86 246.08 402.0 10.34 3.03
3.11
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.37
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
Tw
qw
Vflow
o
o
mm mm
C
10 3 water 18.76 21.86 161 22.49 7.41 248.9
10 3 water 18.73 21.76 161 26.71 15.59 248.9
10 3 water 18.78 21.71 160 33.09 28.07 247.2
10 3 water 18.85 21.75 160 42.30 46.09 245.4
10 3 water 18.92 21.83 160 53.17 67.07 247.1
10 3 water 19.03 22.18 160 64.28 87.67 247.2
10 3 water 19.09 22.41 160 83.74 129.13 247.1
10 3 water 19.17 22.79 160 99.34 165.27 248.9
vjets
m/s
6.40
6.40
6.36
6.31
6.36
6.36
6.36
6.40
Pr
6.87
6.50
5.98
5.35
4.72
4.20
3.48
3.04
h
W/cm2 oC
1.99
1.96
1.96
1.97
1.96
1.94
2.00
2.06
Xair
Nu
Re
s/dn
z/dn
97.4%
97.4%
97.4%
97.4%
97.4%
97.4%
97.4%
97.3%
3.85
3.76
3.74
3.71
3.65
3.57
3.62
3.69
752.6
790.9
845.2
927.5
1042.4
1157.5
1366.0
1551.1
25.8
25.8
25.8
25.8
25.8
25.8
25.8
25.8
86.0
86.0
86.0
86.0
86.0
86.0
86.0
86.0
Xair
Nu
Re
s/dn
z/dn
97.3%
97.3%
97.3%
97.3%
97.3%
97.3%
97.1%
97.0%
2.72
2.70
2.74
2.72
2.76
2.82
2.89
2.88
464.8
494.0
535.5
594.1
678.3
768.4
863.8
912.8
25.8
25.8
25.8
25.8
25.8
25.8
25.8
25.8
86.0
86.0
86.0
86.0
86.0
86.0
86.0
86.0
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
152
Table B.38
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
Tw
qw
Vflow
o
o
mm mm
C
10 3 water 19.28 22.58 125 23.20 5.51 151.5
10 3 water 19.27 22.54 124 28.82 13.45 150.8
10 3 water 19.30 22.56 124 36.03 24.14 150.8
10 3 water 19.36 22.58 124 46.56 39.44 149.7
10 3 water 19.44 22.68 124 59.46 59.54 150.8
10 3 water 19.44 22.90 124 73.54 83.41 150.8
10 3 water 19.48 24.20 124 87.90 109.52 150.8
10 3 water 19.52 24.39 124 96.02 122.79 149.7
vjets
m/s
3.90
3.88
3.88
3.85
3.88
3.88
3.88
3.85
Pr
6.76
6.28
5.73
5.06
4.39
3.81
3.34
3.12
h
W/cm2 oC
1.41
1.41
1.44
1.45
1.49
1.54
1.60
1.61
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.39
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
Tw
qw
Vflow
vjets
o
o
mm mm
C
10 3 water 19.64 21.09 108 27.90 5.11
91.0 2.34
10 3 water 19.58 21.14 108 36.85 11.86 90.8 2.34
10 3 water 19.57 21.11 108 47.70 21.02 91.5 2.35
10 3 water 19.59 21.16 108 59.39 32.20 91.5 2.35
10 3 water 19.59 21.26 108 73.57 46.45 91.5 2.35
10 3 water 19.67 23.23 108 89.11 62.11 91.5 2.35
10 3 water 19.71 21.52 108 98.15 71.49 91.5 2.35
Pr
6.32
5.66
4.98
4.39
3.81
3.30
3.06
h
W/cm2 oC
0.62
0.69
0.75
0.81
0.86
0.89
0.91
Xair
Nu
Re
s/dn
z/dn
97.5%
97.5%
97.5%
97.5%
97.5%
97.3%
97.5%
1.19
1.30
1.40
1.50
1.57
1.61
1.63
296.3
326.5
368.1
411.9
467.0
530.0
567.5
25.8
25.8
25.8
25.8
25.8
25.8
25.8
86.0
86.0
86.0
86.0
86.0
86.0
86.0
Xair
Nu
Re
s/dn
z/dn
97.3%
97.3%
97.3%
97.3%
97.3%
97.4%
97.4%
97.4%
11.53
10.09
10.26
10.26
10.45
10.69
11.04
11.10
662.0
671.0
678.4
692.1
701.6
777.6
884.7
1015.7
5.5
5.5
5.5
5.5
5.5
5.5
5.5
5.5
54.9
54.9
54.9
54.9
54.9
54.9
54.9
54.9
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.40
153
dn
μm
182.1
182.1
182.1
182.1
182.1
182.1
182.1
182.1
z
Tw
qw
Vflow
vjets
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min m/s
10 1 water 25.37 22.79 114 25.82 1.71 1987.4 3.20
10 1 water 25.38 22.67 115 26.63 4.20 1996.3 3.22
10 1 water 25.40 22.49 115 27.59 7.52 1996.5 3.22
10 1 water 25.45 22.55 115 29.35 13.41 1996.6 3.22
10 1 water 25.48 22.42 114 30.73 18.43 1993.2 3.21
10 1 water 25.76 22.27 114 40.27 52.74 1994.2 3.22
10 1 water 26.11 22.12 115 53.47 104.22 1991.2 3.21
10 1 water 26.55 21.91 115 69.06 165.25 1986.1 3.20
Pr
6.04
5.97
5.90
5.77
5.67
5.05
4.36
3.72
h
W/cm2 oC
3.85
3.38
3.44
3.44
3.52
3.63
3.81
3.89
Pamb
kPa
100.9
100.9
100.9
101.0
100.9
100.9
100.9
100.9
Table B.41
dn
μm
182.1
182.1
182.1
182.1
182.1
182.1
182.1
z
Tw
qw
Vflow
o
o
mm mm
C
10 1 water 25.39 22.38 110 26.09 1.92 1500.0
10 1 water 25.40 22.47 109 27.19 4.53 1499.0
10 1 water 25.41 22.46 109 28.50 7.66 1498.7
10 1 water 25.43 22.49 109 30.74 13.10 1500.8
10 1 water 25.48 22.45 109 33.08 18.74 1498.0
10 1 water 25.70 22.37 109 46.59 52.49 1493.2
10 1 water 25.98 22.32 110 64.68 102.07 1490.9
vjets
m/s
2.42
2.42
2.42
2.42
2.42
2.41
2.40
Pr
6.01
5.93
5.83
5.67
5.51
4.71
3.90
h
W/cm2 oC
2.72
2.53
2.48
2.47
2.47
2.51
2.64
Xair
Nu
Re
s/dn
z/dn
97.3%
97.3%
97.3%
97.3%
97.3%
97.4%
97.4%
8.15
7.56
7.38
7.33
7.32
7.34
7.56
501.3
507.2
514.4
528.0
540.7
619.3
731.1
5.5
5.5
5.5
5.5
5.5
5.5
5.5
54.9
54.9
54.9
54.9
54.9
54.9
54.9
Xair
Nu
Re
s/dn
z/dn
97.4%
97.4%
97.3%
97.3%
97.3%
97.3%
97.3%
97.2%
5.28
5.64
4.73
4.50
4.55
4.62
4.82
4.74
364.8
385.9
429.6
483.5
535.4
597.7
664.8
733.7
11.2
11.2
11.2
11.2
11.2
11.2
11.2
11.2
56.0
56.0
56.0
56.0
56.0
56.0
56.0
56.0
Pamb
kPa
100.9
100.9
100.9
101.0
100.9
100.9
100.9
Table B.42
154
dn
μm
178.5
178.5
178.5
178.5
178.5
178.5
178.5
178.5
z
Tw
qw
Vflow
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min
10 2 water 17.72 21.98 106 22.95 9.28 388.1
10 2 water 17.77 21.97 106 27.63 18.81 388.1
10 2 water 17.82 22.28 106 37.51 31.91 386.3
10 2 water 17.86 22.31 106 48.79 48.29 386.3
10 2 water 17.93 22.47 106 59.71 66.82 384.6
10 2 water 18.10 22.44 105 71.81 88.23 384.6
10 2 water 18.22 22.68 105 84.48 114.94 384.6
10 2 water 18.18 23.28 105 97.89 137.39 382.9
vjets
m/s
2.04
2.04
2.03
2.03
2.02
2.02
2.02
2.01
Pr
6.93
6.50
5.73
5.02
4.45
3.93
3.48
3.10
h
W/cm2 oC
1.78
1.91
1.62
1.56
1.60
1.64
1.73
1.72
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.43
dn
μm
178.5
178.5
178.5
178.5
178.5
178.5
178.5
178.5
178.5
z
Tw
qw
Vflow
o
o
mm mm
C
10 2 water 17.82 21.96 111 21.40 7.56 478.6
10 2 water 17.88 22.00 111 26.76 18.75 476.8
10 2 water 17.94 21.85 111 33.12 31.38 475.1
10 2 water 17.97 21.73 111 41.64 50.21 476.8
10 2 water 18.01 21.69 111 51.23 72.47 476.8
10 2 water 18.23 22.47 111 64.68 101.41 476.8
10 2 water 18.46 24.32 111 75.87 128.89 476.8
10 2 water 18.53 21.77 111 88.75 158.26 475.1
10 2 water 18.59 21.72 111 95.62 174.44 473.3
vjets
m/s
2.51
2.50
2.49
2.50
2.50
2.50
2.50
2.49
2.48
Pr
7.07
6.57
6.04
5.44
4.87
4.21
3.77
3.34
3.15
h
W/cm2 oC
2.11
2.11
2.07
2.12
2.18
2.18
2.25
2.25
2.26
155
Xair
Nu
Re
s/dn
z/dn
97.4%
97.4%
97.4%
97.4%
97.4%
97.3%
97.0%
97.4%
97.4%
6.29
6.24
6.06
6.16
6.26
6.18
6.29
6.24
6.24
442.0
470.0
504.0
555.1
612.3
696.6
769.5
851.5
894.5
11.2
11.2
11.2
11.2
11.2
11.2
11.2
11.2
11.2
56.0
56.0
56.0
56.0
56.0
56.0
56.0
56.0
56.0
Xair
Nu
Re
s/dn
z/dn
11.2
11.2
11.2
11.2
11.2
11.2
11.2
11.2
11.2
56.0
56.0
56.0
56.0
56.0
56.0
56.0
56.0
56.0
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.44
dn
μm
178.5
178.5
178.5
178.5
178.5
178.5
178.5
178.5
178.5
z
Tw
qw
Vflow
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min
10 2 water 40.24 21.90 111 40.82 1.11 476.4
10 2 water 40.36 22.07 111 43.73 6.64 476.4
10 2 water 40.25 21.84 111 48.26 15.85 476.4
10 2 water 40.26 21.94 111 54.02 27.97 476.4
10 2 water 40.35 22.02 111 61.28 43.43 476.4
10 2 water 40.58 21.91 111 68.96 59.84 476.4
10 2 water 40.23 22.65 111 77.19 80.57 476.3
10 2 water 40.55 22.20 110 86.21 101.27 476.4
10 2 water 40.43 22.04 110 96.47 126.71 474.6
vjets
m/s
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.49
Pr
4.29
4.16
3.98
3.77
3.52
3.28
3.07
2.84
2.63
h
W/cm2 oC
1.93
1.97
1.98
2.03
2.08
2.11
2.18
2.22
2.26
97.4%
97.4%
97.4%
97.4%
97.4%
97.4%
97.4%
97.4%
97.4%
5.47 684.4
5.56 703.4
5.57 731.4
5.69 768.4
5.77 816.4
5.83 868.9
5.99 921.9
6.05 986.0
6.13 1052.7
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.45
dn
μm
178.5
178.5
178.5
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 2 water 25.36 23.92
10 2 water 25.58 24.56
10 2 water 25.68 24.66
Pjets
Tw
qw
Vflow
kPa oC W/cm2 ml/min
108 35.07 18.42 476.8
108 52.14 52.92 475.7
108 75.12 103.87 474.1
vjets
m/s
2.50
2.50
2.49
Pr
h
Xair
Nu
W/cm2 oC
5.39
1.90
97.1% 5.50
4.45
1.99
97.0% 5.67
3.55
2.10
97.0% 5.85
Re
s/dn
z/dn
Pamb
kPa
559.9 11.2 56.0 100.0
662.6 11.2 56.0 100.5
807.0 11.2 56.0 100.6
Table B.46
156
dn
μm
178.5
178.5
178.5
178.5
178.5
178.5
z
Tw
qw
o
o
o
mm mm
C
C kPa
C W/cm2
10 2 water 25.42 23.40 189 26.80 8.18
10 2 water 25.62 23.89 190 29.14 17.64
10 2 water 25.91 24.19 191 32.17 36.07
10 2 water 26.13 25.07 192 40.22 75.54
10 2 water 26.60 25.04 192 50.91 136.34
10 2 water 27.00 25.22 191 63.03 208.58
Vflow
ml/min
1738.1
1748.3
1754.3
1756.6
1753.6
1748.2
vjets
m/s
9.12
9.17
9.21
9.22
9.20
9.17
Pr
5.96
5.77
5.54
5.03
4.46
3.92
h
W/cm2 oC
5.93
5.01
5.76
5.36
5.61
5.79
Xair
Nu
Re
s/dn
z/dn
97.1%
97.1%
97.0%
96.9%
96.9%
96.9%
17.37
14.62
16.76
15.44
15.96
16.27
1868.2
1932.1
2009.4
2191.8
2437.9
2719.7
11.2
11.2
11.2
11.2
11.2
11.2
56.0
56.0
56.0
56.0
56.0
56.0
Xair
Nu
Re
s/dn
z/dn
96.9%
96.9%
96.8%
96.8%
96.9%
96.8%
18.27
16.99
16.73
16.44
16.48
16.85
1901.4
1941.6
2007.5
2173.0
2409.3
2706.0
11.2
11.2
11.2
11.2
11.2
11.2
56.0
56.0
56.0
56.0
56.0
56.0
Pamb
kPa
99.4
100.0
100.2
100.6
100.9
100.9
Table B.47
dn
μm
178.5
178.5
178.5
178.5
178.5
178.5
z
Tw
qw
o
o
o
mm mm
C
C kPa
C W/cm2
10 2 water 25.60 24.83 193 26.87 7.94
10 2 water 25.68 25.01 193 28.87 18.52
10 2 water 25.83 25.22 193 31.82 34.44
10 2 water 26.17 25.33 193 39.26 74.64
10 2 water 26.60 25.48 193 49.63 133.19
10 2 water 27.15 25.78 192 62.23 210.15
Vflow
ml/min
1764.4
1760.8
1760.8
1757.9
1753.8
1749.1
vjets
m/s
9.26
9.24
9.24
9.22
9.20
9.18
Pr
5.94
5.79
5.57
5.09
4.52
3.95
h
W/cm2 oC
6.24
5.82
5.75
5.70
5.78
5.99
Pamb
kPa
100.5
100.6
100.7
100.9
100.9
100.9
Table B.48
dn
μm
178.5
178.5
178.5
178.5
178.5
178.5
z
Tw
qw
o
o
mm mm
C
C kPa oC W/cm2
10 2 water 25.52 25.51 108 26.19 1.95
10 2 water 25.49 25.54 108 28.49 7.79
10 2 water 25.44 25.48 107 32.93 18.80
10 2 water 25.50 25.42 107 45.68 52.02
10 2 water 25.61 25.52 108 47.05 52.85
10 2 water 25.70 25.32 106 67.49 103.73
Vflow
ml/min
468.3
467.1
466.0
464.7
463.6
461.3
vjets
m/s
2.46
2.45
2.45
2.44
2.43
2.42
Pr
6.00
5.83
5.53
4.77
4.69
3.81
h
W/cm2 oC
2.91
2.60
2.51
2.58
2.46
2.48
Xair
Nu
Re
s/dn
z/dn
96.8%
96.8%
96.8%
96.8%
96.8%
96.9%
8.53
7.60
7.30
7.38
7.05
6.96
500.4
511.8
535.4
608.3
615.6
737.3
11.2
11.2
11.2
11.2
11.2
11.2
56.0
56.0
56.0
56.0
56.0
56.0
Xair
Nu
Re
s/dn
z/dn
96.9%
96.9%
96.9%
96.9%
96.8%
96.8%
96.9%
97.0%
5.96
6.23
6.76
6.93
6.85
6.98
6.74
6.88
498.7
510.9
520.2
534.0
549.1
633.3
768.0
923.4
11.2
11.2
11.2
11.2
11.2
11.2
11.2
11.2
56.0
56.0
56.0
56.0
56.0
56.0
56.0
56.0
Pamb
kPa
100.8
100.9
100.9
100.9
100.9
100.9
Table B.49
157
dn
μm
178.5
178.5
178.5
178.5
178.5
178.5
178.5
178.5
z
Tw
qw
Vflow
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min
10 2 water 25.31 24.62 108 26.00 1.39 468.8
10 2 water 25.35 24.80 108 27.49 4.55 472.2
10 2 water 25.39 24.93 108 28.69 7.63 474.2
10 2 water 25.41 25.05 108 30.99 13.28 474.6
10 2 water 25.43 25.20 109 33.47 18.96 475.3
10 2 water 25.53 25.52 108 47.68 54.11 474.4
10 2 water 25.75 25.54 108 68.99 104.05 474.3
10 2 water 25.97 25.23 109 92.58 166.98 473.1
vjets
m/s
2.46
2.48
2.49
2.49
2.49
2.49
2.49
2.48
Pr
6.03
5.91
5.82
5.66
5.49
4.67
3.75
3.04
h
W/cm2 oC
2.03
2.13
2.31
2.38
2.36
2.44
2.41
2.51
Pamb
kPa
100.0
100.2
100.3
100.4
100.5
100.8
101.0
100.9
Table B.50
dn
μm
178.5
178.5
178.5
178.5
178.5
178.5
178.5
z
Tw
qw
Vflow
o
o
mm mm
C
10 2 water 25.31 24.77 104 26.24 1.30 388.8
10 2 water 25.34 24.83 105 28.38 4.24 390.2
10 2 water 25.34 25.00 104 30.67 7.44 390.7
10 2 water 25.40 25.20 104 34.29 12.57 390.9
10 2 water 25.46 26.04 105 47.50 33.85 390.6
10 2 water 25.60 25.66 105 71.58 73.88 388.8
10 2 water 25.72 25.60 104 96.32 127.82 387.4
vjets
m/s
2.04
2.05
2.05
2.05
2.05
2.04
2.03
Pr
6.01
5.85
5.69
5.44
4.68
3.67
2.95
h
W/cm2 oC
1.40
1.40
1.40
1.41
1.54
1.61
1.81
Xair
Nu
Re
s/dn
z/dn
96.9%
96.9%
96.9%
96.8%
96.7%
96.8%
96.8%
4.11
4.09
4.07
4.11
4.39
4.49
4.96
414.7
426.3
437.7
455.4
520.1
642.6
775.4
11.2
11.2
11.2
11.2
11.2
11.2
11.2
56.0
56.0
56.0
56.0
56.0
56.0
56.0
Xair
Nu
Re
s/dn
z/dn
96.8%
96.8%
96.8%
96.8%
96.7%
96.8%
96.8%
12.25
10.84
10.47
10.26
10.33
10.50
10.14
859.1
870.0
884.7
899.6
992.8
1124.4
1318.8
11.2
11.2
11.2
11.2
11.2
11.2
11.2
56.0
56.0
56.0
56.0
56.0
56.0
56.0
Pamb
kPa
100.1
100.2
100.3
100.4
100.8
100.9
100.8
Table B.51
158
dn
μm
178.5
178.5
178.5
178.5
178.5
178.5
178.5
z
Tw
qw
Vflow
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min
10 2 water 25.40 25.49 123 26.47 4.46 802.5
10 2 water 25.45 25.41 122 27.61 8.00 802.1
10 2 water 25.51 25.37 122 29.28 13.52 800.2
10 2 water 25.51 25.34 122 30.90 18.98 799.6
10 2 water 25.74 25.73 122 40.71 53.68 794.9
10 2 water 26.04 25.81 123 54.35 104.73 787.4
10 2 water 26.48 25.58 122 73.41 170.76 780.5
vjets
m/s
4.21
4.21
4.20
4.20
4.17
4.13
4.10
Pr
5.98
5.90
5.77
5.66
5.03
4.32
3.57
h
W/cm2 oC
4.18
3.71
3.59
3.52
3.59
3.70
3.64
Pamb
kPa
100.5
100.4
100.4
100.5
100.8
100.9
100.9
Table B.52
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
Tw
qw
Vflow
o
o
mm mm
C
10 3 water 19.33 21.21 107 22.59 5.55 226.3
10 3 water 19.35 21.17 107 26.92 12.57 226.3
10 3 water 19.40 21.04 106 33.07 23.11 226.3
10 3 water 19.45 21.17 106 41.01 37.01 226.3
10 3 water 19.50 21.26 106 49.35 53.26 226.3
10 3 water 19.57 23.73 106 62.07 77.94 226.3
10 3 water 19.79 24.97 106 74.37 103.76 226.3
10 3 water 19.83 25.56 106 88.73 131.11 226.3
10 3 water 19.94 22.83 106 97.27 150.53 226.3
vjets
m/s
2.61
2.61
2.61
2.61
2.61
2.61
2.61
2.61
2.61
Pr
6.81
6.43
5.94
5.39
4.89
4.27
3.77
3.31
3.07
h
W/cm2 oC
1.70
1.66
1.69
1.72
1.78
1.83
1.90
1.90
1.95
159
Xair
Nu
Re
s/dn
z/dn
97.5%
97.5%
97.5%
97.5%
97.5%
97.2%
96.8%
96.7%
97.3%
4.92
4.76
4.82
4.84
4.98
5.06
5.18
5.12
5.20
462.3
486.6
522.0
568.9
619.7
699.6
780.7
876.8
936.1
17.3
17.3
17.3
17.3
17.3
17.3
17.3
17.3
17.3
57.6
57.6
57.6
57.6
57.6
57.6
57.6
57.6
57.6
Xair
Nu
Re
s/dn
z/dn
97.4%
97.4%
97.4%
97.4%
97.4%
97.4%
97.4%
97.4%
97.5%
97.5%
8.65
8.39
8.33
8.47
8.56
8.74
8.85
8.78
8.74
8.70
1211.3
1259.7
1332.4
1411.6
1529.3
1655.0
1813.0
2017.3
2216.4
2361.8
17.3
17.3
17.3
17.3
17.3
17.3
17.3
17.3
17.3
17.3
57.6
57.6
57.6
57.6
57.6
57.6
57.6
57.6
57.6
57.6
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.53
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
Tw
qw
Vflow
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min
10 3 water 19.43 22.20 145 24.17 14.23 581.2
10 3 water 19.48 22.16 145 27.86 24.52 578.5
10 3 water 19.54 22.04 145 32.63 38.31 579.4
10 3 water 19.61 22.01 145 38.21 55.70 577.3
10 3 water 19.78 21.82 145 45.99 80.08 575.9
10 3 water 19.92 21.71 144 53.78 106.48 576.5
10 3 water 20.12 21.69 145 63.34 138.99 576.8
10 3 water 20.50 21.72 144 75.84 178.76 574.2
10 3 water 20.76 21.73 144 88.27 219.27 569.8
10 3 water 21.02 21.69 144 97.12 247.76 567.1
vjets
m/s
6.71
6.68
6.69
6.67
6.65
6.66
6.66
6.63
6.58
6.55
Pr
6.66
6.34
5.96
5.56
5.07
4.64
4.19
3.69
3.29
3.05
h
W/cm2 oC
3.00
2.93
2.93
3.00
3.06
3.14
3.22
3.23
3.25
3.26
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.54
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
s
Fluid
Tjets
o
Tamb Pjets
o
Tw
o
qw
Vflow
2
mm mm
C
C kPa
C
W/cm ml/min
10 3 water 19.92 20.72 119 26.23 13.88 358.5
10 3 water 19.99 20.86 119 31.64 25.76 356.8
10 3 water 20.06 20.90 119 38.34 41.09 355.0
10 3 water 20.13 20.95 119 47.17 62.74 356.8
10 3 water 20.22 21.15 119 56.56 86.44 355.0
10 3 water 20.42 21.53 119 67.00 113.31 355.0
10 3 water 20.55 21.64 119 79.02 143.89 356.8
10 3 water 20.67 21.88 119 92.98 176.77 355.0
10 3 water 20.78 21.72 118 98.89 192.48 354.3
vjets
m/s
4.14
4.12
4.10
4.12
4.10
4.10
4.12
4.10
4.09
Pr
h
Xair
Nu
Re
s/dn
z/dn
Pamb
2o
6.44
6.00
5.52
4.98
4.49
4.03
3.59
3.17
3.01
W/cm C
kPa
2.20
97.6% 6.31 769.9 17.3 57.6 100.0
2.21
97.6% 6.31 815.5 17.3 57.6 100.0
2.25
97.6% 6.35 873.4 17.3 57.6 100.0
2.32
97.6% 6.49 962.1 17.3 57.6 100.0
2.38
97.5% 6.59 1049.4 17.3 57.6 100.0
2.43
97.5% 6.67 1155.8 17.3 57.6 100.0
2.46
97.5% 6.67 1287.2 17.3 57.6 100.0
2.44
97.5% 6.55 1430.2 17.3 57.6 100.0
2.46
97.5% 6.57 1492.4 17.3 57.6 100.0
160
Table B.55
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
Tw
qw
Vflow
o
o
mm mm
C
10 3 water 21.31 22.01 275 25.51 21.63 1093.7
10 3 water 21.41 22.29 275 27.89 33.45 1093.7
10 3 water 21.78 23.46 274 38.18 87.37 1091.6
10 3 water 22.09 24.35 273 46.27 133.66 1086.6
10 3 water 22.46 24.78 272 55.15 188.10 1085.6
10 3 water 22.77 23.26 270 63.61 242.14 1078.5
10 3 water 23.10 23.25 268 73.88 310.21 1079.5
vjets
m/s
12.63
12.63
12.61
12.55
12.54
12.46
12.47
Pr
6.38
6.18
5.42
4.92
4.45
4.07
3.67
h
W/cm2 oC
5.16
5.16
5.33
5.53
5.75
5.93
6.11
Xair
Nu
Re
s/dn
z/dn
97.5%
97.4%
97.3%
97.2%
97.1%
97.2%
97.2%
14.80
14.75
15.03
15.45
15.92
16.27
16.60
2366.9
2435.0
2730.5
2961.4
3233.7
3479.0
3812.7
17.3
17.3
17.3
17.3
17.3
17.3
17.3
57.6
57.6
57.6
57.6
57.6
57.6
57.6
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Table B.56
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
Tw
qw
Vflow
o
o
mm mm
C
10 3 water 21.08 22.79 212 24.76 15.50 842.9
10 3 water 21.18 23.13 212 27.28 25.65 844.9
10 3 water 21.32 23.40 211 30.98 40.78 844.9
10 3 water 21.59 23.94 211 39.18 76.01 844.9
10 3 water 21.87 24.50 210 48.87 121.38 837.8
10 3 water 22.24 25.02 209 60.07 176.66 834.8
10 3 water 22.48 24.97 206 71.02 233.85 829.7
10 3 water 22.87 26.21 203 83.85 303.11 820.6
vjets
m/s
9.74
9.76
9.76
9.76
9.68
9.64
9.58
9.48
Pr
6.47
6.25
5.95
5.37
4.79
4.24
3.80
3.36
h
W/cm2 oC
4.22
4.20
4.22
4.32
4.50
4.67
4.82
4.97
Xair
Nu
Re
s/dn
z/dn
97.4%
97.4%
97.3%
97.3%
97.2%
97.1%
97.1%
97.0%
12.12
12.03
12.02
12.18
12.54
12.86
13.13
13.39
1803.6
1863.2
1945.5
2131.3
2337.4
2596.4
2846.5
3134.6
17.3
17.3
17.3
17.3
17.3
17.3
17.3
17.3
57.6
57.6
57.6
57.6
57.6
57.6
57.6
57.6
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
3.54
3.52
3.73
4.07
72.4
76.4
90.5
112.4
14.4
14.4
14.4
14.4
144.2
144.2
144.2
144.2
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
6.09
5.89
6.07
6.63
157.8
178.0
203.9
245.3
14.4
14.4
14.4
14.4
144.2
144.2
144.2
144.2
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
161
Table B.57
z
dn
o
o
μm mm mm
C
C kPa
69.3 10 1 FC40 22.71 22.92 178
69.3 10 1 FC40 22.67 22.88 181
69.3 10 1 FC40 22.86 23.25 184
69.3 10 1 FC40 23.37 23.87 183
Tw
qw
C W/cm2
26.26 1.18
29.95 2.41
43.21 7.09
62.49 14.69
o
Vflow
ml/min
165.7
166.7
167.4
166.8
vjets
m/s
1.84
1.85
1.86
1.86
Pr
52.59
50.29
43.02
34.96
h
W/cm2 oC
0.33
0.33
0.35
0.38
Pamb
kPa
100.0
100.0
100.0
100.0
Table B.58
z
dn
o
o
μm mm mm
C
C kPa
69.3 10 1 FC40 22.83 22.88 303
69.3 10 1 FC40 23.29 23.38 295
69.3 10 1 FC40 23.70 23.54 294
69.3 10 1 FC40 24.35 23.79 299
Tw
qw
C W/cm2
28.44 3.21
37.44 7.81
50.05 14.87
65.64 25.23
o
Vflow
ml/min
350.4
351.0
345.3
348.6
vjets
m/s
3.90
3.90
3.84
3.88
Pr
51.12
45.70
39.58
33.57
h
W/cm2 oC
0.57
0.55
0.56
0.61
Pamb
kPa
100.0
100.0
100.0
100.0
Table B.59
z
Tw
qw
dn
o
o
μm mm mm
C
C kPa oC W/cm2
69.3 10 1 FC40 23.05 22.51 551 23.61 0.40
69.3 10 1 FC40 23.11 22.57 581 25.07 1.38
69.3 10 1 FC40 23.60 22.52 597 35.67 8.73
69.3 10 1 FC40 24.04 22.57 605 44.45 15.60
69.3 10 1 FC40 24.79 22.41 607 56.92 26.15
Vflow
ml/min
536.4
535.2
534.6
532.0
518.9
vjets
m/s
5.97
5.95
5.95
5.92
5.77
Pr
54.13
53.10
46.48
41.89
36.44
h
W/cm2 oC
0.71
0.71
0.72
0.76
0.81
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
99.6%
7.51
7.50
7.72
8.20
8.79
227.4
231.5
266.2
295.8
334.6
14.4
14.4
14.4
14.4
14.4
144.2
144.2
144.2
144.2
144.2
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
99.7%
1.43
1.34
1.38
1.42
1.61
68.4
73.0
75.7
81.4
103.7
26.2
26.2
26.2
26.2
26.2
130.9
130.9
130.9
130.9
130.9
Re
s/dn
z/dn
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
Table B.60
162
dn
z
Tw
qw
Vflow
vjets
Pr
h
o
o
o
2
μm mm mm
C
C kPa
C W/cm ml/min m/s
W/cm2 oC
76.4 10 2 FC40 22.82 24.03 137 25.90 0.38
55.4 1.59 52.75
0.12
76.4 10 2 FC40 23.10 24.05 137 32.15 1.04
54.3 1.55 48.72
0.11
76.4 10 2 FC40 23.09 23.91 138 31.93 1.04
56.5 1.62 48.86
0.12
76.4 10 2 FC40 23.20 23.87 138 39.31 1.94
55.4 1.59 44.78
0.12
76.4 10 2 FC40 22.43 21.13 139 61.51 5.27
55.4 1.59 35.63
0.13
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
Table B.61
z
s Fluid Tjets Tamb
dn
o
o
μm mm mm
C
C
76.4 10 2 FC40 22.02 21.14
76.4 10 2 FC40 22.12 21.18
76.4 10 2 FC40 22.25 21.22
Pjets
Tw
qw
kPa oC W/cm2
203 28.39 1.08
205 34.18 2.07
201 52.95 5.98
Vflow
ml/min
109.2
109.2
107.1
vjets
Pr
h
Xair
Nu
m/s
W/cm2 oC
3.13 51.66
0.17
99.7% 1.98
3.13 48.12
0.17
99.7% 2.01
3.07 38.98
0.19
99.7% 2.31
Pamb
kPa
138.0 26.2 130.9 100.0
148.8 26.2 130.9 100.0
182.5 26.2 130.9 100.0
Table B.62
z
dn
o
o
μm mm mm
C
C kPa
76.4 10 2 FC40 22.54 21.65 305
76.4 10 2 FC40 22.87 22.00 306
76.4 10 2 FC40 22.97 22.02 305
76.4 10 2 FC40 23.20 22.31 305
Tw
qw
C W/cm2
26.86 1.03
33.34 2.51
47.93 6.72
69.13 14.15
o
Vflow
ml/min
163.2
163.2
163.2
163.1
vjets
m/s
4.67
4.67
4.67
4.67
Pr
52.30
48.18
40.81
32.82
h
W/cm2 oC
0.24
0.24
0.27
0.31
Xair
Nu
Re
s/dn
z/dn
99.7%
99.6%
99.6%
99.6%
2.78
2.81
3.18
3.69
203.5
222.0
264.7
333.7
26.2
26.2
26.2
26.2
130.9
130.9
130.9
130.9
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
99.6%
3.63
3.38
3.40
3.86
4.32
338.1
352.7
382.0
458.4
531.5
26.2
26.2
26.2
26.2
26.2
130.9
130.9
130.9
130.9
130.9
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.7%
1.49
1.51
1.49
1.55
43.3
44.1
48.5
55.1
24.5
24.5
24.5
24.5
81.6
81.6
81.6
81.6
Pamb
kPa
100.0
100.0
100.0
100.0
Table B.63
163
z
Tw
qw
dn
o
o
μm mm mm
C
C kPa oC W/cm2
76.4 10 2 FC40 23.33 22.77 681 24.61 0.40
76.4 10 2 FC40 23.37 22.85 697 28.25 1.41
76.4 10 2 FC40 23.51 22.97 726 34.17 3.08
76.4 10 2 FC40 23.76 23.28 736 49.43 8.37
76.4 10 2 FC40 23.88 24.38 727 64.07 14.55
Vflow
ml/min
276.4
274.8
275.7
275.3
271.9
vjets
m/s
7.92
7.87
7.90
7.89
7.79
Pr
53.27
50.90
47.34
39.82
34.25
h
W/cm2 oC
0.31
0.29
0.29
0.33
0.36
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
Table B.64
dn
μm
122.6
122.6
122.6
122.6
z
o
o
mm mm
C
C kPa
10 3 FC40 22.54 22.49 174
10 3 FC40 22.45 22.28 176
10 3 FC40 22.44 22.19 177
10 3 FC40 22.17 21.64 173
Tw
qw
Vflow
vjets
Pr
h
2
C W/cm ml/min m/s
W/cm2 oC
24.41 0.15
27.7 0.64 53.93
0.08
25.91 0.28
27.7 0.64 52.99
0.08
30.47 0.64
28.7 0.66 50.11
0.08
41.00 1.54
28.7 0.66 44.45
0.08
o
Pamb
kPa
100.0
100.0
100.0
100.0
Table B.65
dn
μm
122.6
122.6
122.6
122.6
122.6
z
Tw
qw
o
o
mm mm
C
C kPa oC W/cm2
10 3 FC40 23.64 23.78 785 25.65 0.25
10 3 FC40 23.87 23.64 783 27.52 0.45
10 3 FC40 23.54 22.31 790 29.55 0.91
10 3 FC40 23.29 22.01 794 35.48 1.85
10 3 FC40 24.11 24.55 760 57.95 5.62
Vflow
ml/min
131.6
130.6
130.6
129.6
125.6
vjets
m/s
3.05
3.02
3.02
3.00
2.91
Pr
52.38
51.04
50.00
46.74
36.31
h
W/cm2 oC
0.13
0.12
0.15
0.15
0.17
Xair
Nu
Re
s/dn
z/dn
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
99.6%
99.6%
99.6%
99.6%
99.6%
2.36
2.34
2.85
2.87
3.17
212.6
216.8
221.6
236.1
299.2
24.5
24.5
24.5
24.5
24.5
81.6
81.6
81.6
81.6
81.6
Re
s/dn
z/dn
90.8
93.7
101.5
8.4
8.4
8.4
Pamb
kPa
84.2 100.0
84.2 100.0
84.2 100.0
Table B.66
164
dn
μm
118.7
118.7
118.7
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 1 FC40 23.46 21.38
10 1 FC40 23.60 21.32
10 1 FC40 24.30 24.38
Pjets
Tw
qw
o
kPa
C W/cm2
112 26.17 0.90
113 28.73 1.61
114 34.53 3.13
Vflow
ml/min
352.6
351.4
350.9
vjets
Pr
h
Xair
Nu
2o
m/s
W/cm C
1.34 52.16
0.33
99.6% 6.02
1.33 50.47
0.31
99.6% 5.71
1.33 46.72
0.31
99.6% 5.59
Table B.67
dn
μm
118.7
118.7
118.7
118.7
118.7
118.7
z
Tw
qw
o
o
o
mm mm
C
C kPa
C W/cm2
10 1 FC40 24.77 23.36 218 25.99 0.71
10 1 FC40 24.77 23.39 218 26.85 1.53
10 1 FC40 24.83 23.34 218 28.87 2.87
10 1 FC40 24.94 23.31 219 31.57 4.72
10 1 FC40 25.05 23.34 220 34.17 6.57
10 1 FC40 25.41 23.47 220 45.45 15.22
Vflow
ml/min
1109.2
1109.3
1106.1
1109.1
1104.8
1102.3
vjets
m/s
4.21
4.21
4.20
4.21
4.19
4.18
Pr
51.44
50.90
49.63
48.01
46.51
40.82
h
W/cm2 oC
0.59
0.74
0.71
0.71
0.72
0.76
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
99.6%
99.6%
10.67
13.44
12.95
12.99
13.16
13.97
289.9
293.1
300.2
311.8
321.2
367.9
8.4
8.4
8.4
8.4
8.4
8.4
84.2
84.2
84.2
84.2
84.2
84.2
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
Table B.68
dn
μm
113.9
113.9
113.9
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 2 FC40 22.14 20.91
10 2 FC40 22.28 21.15
10 2 FC40 22.62 22.15
Pjets
Tw
qw
Vflow
vjets
Pr
h
Xair
Nu
W/cm2 oC
110 28.47 1.09 100.9 1.30 51.53
0.17
99.7% 3.01
110 34.86 2.11 100.3 1.29 47.64
0.17
99.6% 2.94
109 55.09 5.76
98.4 1.27 37.97
0.18
99.6% 3.14
Re
s/dn
z/dn
Pamb
kPa
85.8 17.6 87.8 100.0
92.6 17.6 87.8 100.0
115.6 17.6 87.8 100.0
Re
s/dn
z/dn
Table B.69
165
dn
μm
113.9
113.9
113.9
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 2 FC40 23.10 23.48
10 2 FC40 23.19 23.50
10 2 FC40 23.46 23.56
Pjets
Tw
qw
o
kPa
C W/cm2
142 28.05 1.55
142 32.29 2.69
141 48.26 7.47
Vflow
ml/min
222.2
221.6
219.2
vjets
Pr
h
Xair
Nu
2o
m/s
W/cm C
2.87 51.19
0.31
99.6% 5.47
2.86 48.59
0.30
99.6% 5.17
2.83 40.45
0.30
99.6% 5.32
Pamb
kPa
190.2 17.6 87.8 100.0
200.4 17.6 87.8 100.0
240.8 17.6 87.8 100.0
Table B.70
dn
μm
113.9
113.9
113.9
113.9
113.9
z
Tw
qw
o
o
o
mm mm
C
C kPa
C W/cm2
10 2 FC40 23.33 23.78 181 27.18 1.56
10 2 FC40 23.33 23.65 178 27.15 1.58
10 2 FC40 23.45 23.56 178 33.22 3.68
10 2 FC40 23.73 23.94 177 45.59 8.46
10 2 FC40 24.30 23.23 184 59.43 15.26
Vflow
ml/min
342.8
336.7
335.4
333.1
334.6
vjets
m/s
4.42
4.34
4.32
4.29
4.31
Pr
51.60
51.61
47.91
41.51
35.71
h
W/cm2 oC
0.41
0.41
0.38
0.39
0.43
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
99.6%
7.07
7.21
6.58
6.82
7.71
291.0
285.7
307.9
355.9
419.7
17.6
17.6
17.6
17.6
17.6
87.8
87.8
87.8
87.8
87.8
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
Table B.71
dn
μm
113.9
113.9
113.9
113.9
113.9
z
Tw
qw
o
o
mm mm
C
C kPa oC W/cm2
10 2 FC40 23.32 22.71 310 25.20 1.05
10 2 FC40 23.32 22.81 307 25.11 1.02
10 2 FC40 23.47 22.63 315 28.93 3.06
10 2 FC40 23.75 22.65 315 36.70 7.47
10 2 FC40 24.22 22.87 313 48.75 15.07
Vflow
ml/min
575.1
572.0
572.9
571.5
573.0
vjets
m/s
7.42
7.38
7.39
7.37
7.39
Pr
52.88
52.94
50.42
45.85
39.91
h
W/cm2 oC
0.56
0.57
0.56
0.58
0.61
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
99.6%
9.78
9.92
9.78
10.12
10.84
475.7
472.6
498.3
549.7
638.5
17.6
17.6
17.6
17.6
17.6
87.8
87.8
87.8
87.8
87.8
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
11.11
11.33
12.10
12.86
621.3
643.1
712.2
816.1
17.6
17.6
17.6
17.6
87.8
87.8
87.8
87.8
Xair
Nu
Re
s/dn
z/dn
99.8%
99.8%
99.8%
99.8%
99.8%
3.71
3.72
3.86
4.64
5.40
284.0
299.8
326.7
408.1
505.6
25.8
25.8
25.8
25.8
25.8
86.0
86.0
86.0
86.0
86.0
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
Table B.72
166
dn
μm
113.9
113.9
113.9
113.9
z
o
o
mm mm
C
C kPa
10 2 FC40 23.58 22.43 446
10 2 FC40 23.69 22.51 449
10 2 FC40 23.98 22.72 448
10 2 FC40 24.42 23.12 447
Tw
qw
C W/cm2
26.05 1.57
28.95 3.41
37.11 9.06
48.46 17.52
o
Vflow
ml/min
740.3
737.1
734.7
733.1
vjets
m/s
9.55
9.50
9.47
9.45
Pr
52.16
50.27
45.51
39.95
h
W/cm2 oC
0.64
0.65
0.69
0.73
Pamb
kPa
100.0
100.0
100.0
100.0
Table B.73
dn
μm
116.3
116.3
116.3
116.3
116.3
z
Tw
qw
o
o
o
mm mm
C
C kPa
C W/cm2
10 3 FC40 8.03 20.57 320 12.09 0.86
10 3 FC40 7.94 20.57 321 15.64 1.63
10 3 FC40 7.98 20.20 321 21.22 2.90
10 3 FC40 8.33 20.79 316 37.15 7.52
10 3 FC40 8.70 21.05 310 54.86 13.88
Vflow
ml/min
254.3
254.1
254.1
252.1
248.5
vjets
m/s
6.54
6.53
6.53
6.48
6.39
Pr
78.24
74.25
68.40
54.94
44.25
h
W/cm2 oC
0.21
0.21
0.22
0.26
0.30
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
Table B.74
dn
μm
116.3
116.3
116.3
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 3 FC40 23.91 23.62
10 3 FC40 23.91 23.67
10 3 FC40 24.08 23.92
Pjets
Tw
qw
kPa oC W/cm2
177 30.30 1.31
177 35.50 2.39
175 52.96 6.45
Vflow
ml/min
152.0
150.9
149.6
vjets
Pr
h
Xair
Nu
m/s
W/cm2 oC
3.91 49.33
0.21
99.6% 3.67
3.88 46.40
0.21
99.6% 3.69
3.85 38.23
0.22
99.6% 4.03
Re
s/dn
z/dn
Pamb
kPa
275.7 25.8 86.0 100.0
292.1 25.8 86.0 100.0
355.5 25.8 86.0 100.0
Re
s/dn
z/dn
Table B.75
167
dn
μm
116.3
116.3
116.3
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 3 FC40 23.98 23.73
10 3 FC40 24.08 23.84
10 3 FC40 24.29 24.03
Pjets
Tw
qw
o
kPa
C W/cm2
274 28.84 1.40
272 35.02 3.23
269 47.25 7.35
Vflow
ml/min
267.1
265.9
263.5
vjets
Pr
h
Xair
Nu
2o
m/s
W/cm C
6.87 50.16
0.29
99.6% 5.16
6.84 46.57
0.30
99.6% 5.29
6.78 40.52
0.32
99.6% 5.77
Pamb
kPa
476.0 25.8 86.0 100.0
512.6 25.8 86.0 100.0
588.6 25.8 86.0 100.0
Table B.76
dn
μm
182.1
182.1
182.1
182.1
182.1
z
Tw
qw
Vflow
vjets
Pr
h
o
o
mm mm
C
W/cm2 oC
10 1 FC40 24.71 22.01 168 26.04 0.82 1547.4 2.49 51.44
0.62
10 1 FC40 24.69 22.15 168 27.79 1.93 1547.4 2.49 50.37
0.62
10 1 FC40 24.75 22.25 168 30.65 3.65 1547.4 2.49 48.64
0.62
10 1 FC40 24.89 22.36 166 36.99 7.49 1534.7 2.47 45.10
0.62
10 1 FC40 25.25 22.60 166 48.66 15.06 1536.4 2.48 39.51
0.64
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
99.6%
17.25
17.40
17.32
17.36
18.18
263.5
269.5
279.6
300.4
346.1
5.5
5.5
5.5
5.5
5.5
54.9
54.9
54.9
54.9
54.9
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
Table B.77
dn
μm
182.1
182.1
182.1
182.1
z
o
o
mm mm
C
C kPa
10 1 FC40 23.96 22.28 104
10 1 FC40 24.00 22.22 104
10 1 FC40 24.29 22.35 104
10 1 FC40 24.73 22.61 104
Tw
qw
C W/cm2
27.20 1.01
30.55 2.04
43.64 6.10
60.92 11.88
o
Vflow
ml/min
524.0
524.9
525.7
527.2
vjets
m/s
0.84
0.85
0.85
0.85
Pr
51.19
49.13
42.15
35.03
h
W/cm2 oC
0.31
0.31
0.32
0.33
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
8.64
8.71
8.88
9.33
89.7
93.9
110.6
135.0
5.5
5.5
5.5
5.5
54.9
54.9
54.9
54.9
Pamb
kPa
100.0
100.0
100.0
100.0
Table B.78
168
dn
μm
182.1
182.1
182.1
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 1 FC40 25.59 23.91
10 1 FC40 25.65 24.07
10 1 FC40 25.70 24.16
Pjets
Tw
qw
Vflow
vjets
Pr
h
Xair
Nu
Re
s/dn z/dn Pamb
o
2
2o
kPa
C W/cm ml/min m/s
W/cm C
kPa
160 26.91 0.82 1559.9 2.51 50.36
0.63
99.6% 17.53 271.7 5.5 54.9 100.0
168 28.04 1.45 1559.8 2.51 49.64
0.61
99.6% 16.99 275.9 5.5 54.9 100.0
168 29.64 2.41 1559.8 2.51 48.68
0.61
99.6% 17.10 281.6 5.5 54.9 100.0
Table B.79
dn
μm
182.1
182.1
182.1
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 1 FC40 25.09 24.92
10 1 FC40 25.19 25.22
10 1 FC40 25.52 25.56
Pjets
Tw
qw
kPa oC W/cm2
172 29.85 3.03
172 33.28 5.08
170 42.12 10.46
Vflow
ml/min
1582.1
1581.9
1581.7
vjets
Pr
h
Xair
Nu
Re
s/dn z/dn Pamb
m/s
W/cm2 oC
kPa
2.55 48.90
0.64
99.6% 17.81 284.3 5.5 54.9 100.0
2.55 46.91
0.63
99.6% 17.60 297.0 5.5 54.9 100.0
2.55 42.28
0.63
99.6% 17.74 331.5 5.5 54.9 100.0
Table B.80
dn
μm
178.5
178.5
178.5
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 2 FC40 22.52 20.93
10 2 FC40 23.03 23.62
10 2 FC40 23.23 22.70
Pjets
Tw
qw
kPa oC W/cm2
100 28.39 1.09
100 35.97 2.37
100 56.76 6.56
Vflow
ml/min
161.4
161.0
159.7
vjets
Pr
h
Xair
Nu
m/s
W/cm2 oC
0.85 51.35
0.19
99.6% 5.08
0.84 46.62
0.18
99.6% 5.04
0.84 37.09
0.20
99.6% 5.43
Re
s/dn
z/dn
Pamb
kPa
87.8 11.2 56.0 100.0
97.0 11.2 56.0 100.0
122.8 11.2 56.0 100.0
Table B.81
169
dn
μm
178.5
178.5
178.5
178.5
z
o
o
mm mm
C
C kPa
10 2 FC40 22.97 22.04 114
10 2 FC40 23.16 22.28 114
10 2 FC40 23.28 22.29 113
10 2 FC40 23.76 21.88 113
Tw
qw
C W/cm2
27.22 1.36
30.89 2.40
45.31 7.04
63.84 13.77
o
Vflow
ml/min
339.0
337.8
336.5
333.9
vjets
m/s
1.78
1.77
1.77
1.75
Pr
51.80
49.43
41.85
34.36
h
W/cm2 oC
0.32
0.31
0.32
0.34
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
8.75
8.52
8.82
9.58
182.8
191.5
227.5
278.4
11.2
11.2
11.2
11.2
56.0
56.0
56.0
56.0
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
11.51
11.20
11.47
12.44
277.1
293.9
336.8
391.0
11.2
11.2
11.2
11.2
56.0
56.0
56.0
56.0
Pamb
kPa
100.0
100.0
100.0
100.0
Table B.82
dn
μm
178.5
178.5
178.5
178.5
z
o
o
mm mm
C
C kPa
10 2 FC40 23.06 21.57 130
10 2 FC40 23.25 21.99 129
10 2 FC40 23.62 22.54 129
10 2 FC40 24.01 22.78 129
Tw
qw
C W/cm2
26.55 1.47
31.13 3.22
42.07 7.67
55.02 13.89
o
Vflow
ml/min
517.7
516.4
515.5
514.0
vjets
m/s
2.72
2.71
2.71
2.70
Pr
52.17
49.23
43.21
37.45
h
W/cm2 oC
0.42
0.41
0.42
0.45
Pamb
kPa
100.0
100.0
100.0
100.0
Table B.83
dn
μm
178.5
178.5
178.5
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 2 FC40 23.69 23.53
10 2 FC40 23.91 23.67
10 2 FC40 24.33 23.47
Pjets
Tw
qw
kPa oC W/cm2
171 29.88 3.63
171 38.29 8.68
170 49.24 15.76
Vflow
ml/min
869.9
865.4
862.9
vjets
Pr
h
Xair
Nu
Re
m/s
W/cm2 oC
4.56 49.72
0.59
99.6% 16.08 489.9
4.54 44.94
0.60
99.6% 16.61 542.4
4.53 39.66
0.63
99.6% 17.51 617.6
s/dn
z/dn
Pamb
kPa
11.2 56.0 100.0
11.2 56.0 100.0
11.2 56.0 100.0
Table B.84
170
dn
μm
178.5
178.5
178.5
178.5
z
o
o
mm mm
C
C kPa
10 2 FC40 8.13 21.34 110
10 2 FC40 7.98 21.12 110
10 2 FC40 8.28 21.57 110
10 2 FC40 8.49 21.70 110
Tw
qw
C W/cm2
18.35 2.23
24.70 3.63
35.52 6.21
56.42 11.89
o
Vflow
ml/min
277.8
277.8
276.8
275.4
vjets
m/s
1.46
1.46
1.45
1.45
Pr
71.14
65.13
56.13
43.58
h
W/cm2 oC
0.22
0.22
0.23
0.25
Xair
Nu
Re
s/dn
z/dn
99.8%
99.8%
99.8%
99.8%
5.90
5.89
6.21
6.84
107.3
117.7
137.2
178.3
11.2
11.2
11.2
11.2
56.0
56.0
56.0
56.0
Pamb
kPa
100.0
100.0
100.0
100.0
Table B.85
dn
μm
178.5
178.5
178.5
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 2 FC40 6.73 21.81
10 2 FC40 7.23 22.35
10 2 FC40 8.82 22.54
Pjets
Tw
qw
kPa oC W/cm2
141 12.57 2.18
140 18.37 4.13
139 30.90 8.60
Vflow
ml/min
558.7
558.1
555.4
vjets
Pr
h
Xair
Nu
Re
s/dn z/dn Pamb
m/s
W/cm2 oC
kPa
2.93 79.24
0.37
99.8% 10.06 192.8 11.2 56.0 100.0
2.93 72.07
0.37
99.8% 9.99 212.7 11.2 56.0 100.0
2.91 59.20
0.39
99.8% 10.58 260.2 11.2 56.0 100.0
Table B.86
dn
μm
173.6
173.6
173.6
173.6
173.6
z
Tw
qw
o
o
mm mm
C
C kPa oC W/cm2
10 3 FC40 7.98 21.84 156 11.49 1.08
10 3 FC40 7.72 21.40 157 13.21 1.63
10 3 FC40 7.74 22.31 157 17.77 2.92
10 3 FC40 8.17 21.89 156 32.37 7.66
10 3 FC40 8.46 21.95 155 49.27 14.46
Vflow
ml/min
386.2
386.9
387.3
385.6
384.2
vjets
m/s
4.46
4.47
4.47
4.45
4.44
Pr
79.04
77.29
72.16
58.57
47.32
h
W/cm2 oC
0.31
0.30
0.29
0.32
0.35
Xair
Nu
Re
s/dn
z/dn
99.8%
99.8%
99.8%
99.8%
99.8%
8.05
7.79
7.64
8.37
9.46
286.1
293.4
315.6
391.2
488.2
17.3
17.3
17.3
17.3
17.3
57.6
57.6
57.6
57.6
57.6
Re
s/dn
z/dn
s/dn
z/dn
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
Table B.87
171
dn
μm
173.6
173.6
173.6
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 3 FC40 23.11 21.45
10 3 FC40 23.16 21.59
10 3 FC40 23.97 23.87
Pjets
Tw
qw
kPa oC W/cm2
122 27.06 1.07
122 30.68 1.96
121 46.74 6.36
Vflow
ml/min
235.7
235.5
233.9
vjets
Pr
h
Xair
Nu
m/s
W/cm2 oC
2.72 51.81
0.27
99.6% 7.19
2.72 49.56
0.26
99.6% 6.96
2.70 40.89
0.28
99.6% 7.51
Pamb
kPa
272.0 17.3 57.6 100.0
284.9 17.3 57.6 100.0
346.9 17.3 57.6 100.0
Table B.88
dn
μm
173.6
173.6
173.6
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 3 FC40 23.96 23.63
10 3 FC40 24.01 23.67
10 3 FC40 24.30 23.82
Pjets
Tw
qw
o
kPa
C W/cm2
158 27.13 1.31
157 30.76 2.64
157 41.54 6.93
Vflow
ml/min
412.0
407.9
411.6
vjets
Pr
h
Xair
Nu
Re
2o
m/s
W/cm C
4.76 51.23
0.41
99.6% 10.99 481.3
4.71 49.01
0.39
99.6% 10.45 499.3
4.75 43.14
0.40
99.6% 10.78 576.7
Pamb
kPa
17.3 57.6 100.0
17.3 57.6 100.0
17.3 57.6 100.0
Table B.89
z
s Fluid Tjets Tamb
dn
o
o
μm mm mm
C
C
173.6 10 3 FC40 24.17 23.54
173.6 10 3 FC40 24.51 23.69
Pjets
Tw
qw
Vflow
vjets
Pr
h
Xair
Nu
Re
s/dn z/dn Pamb
W/cm2 oC
kPa
231 28.97 2.60 665.8 7.69 49.97
0.54
99.6% 14.44 798.4 17.3 57.6 100.0
230 38.67 7.91 665.3 7.69 44.44
0.56
99.6% 14.96 903.3 17.3 57.6 100.0
Table B.90
172
dn
μm
173.6
173.6
173.6
z
s Fluid Tjets Tamb
o
o
mm mm
C
C
10 3 FC40 23.69 23.67
10 3 FC40 23.74 23.77
10 3 FC40 23.77 23.88
Pjets
Tw
qw
Vflow
vjets
Pr
h
Xair
Nu
W/cm2 oC
97 26.43 0.35
81.1 0.94 51.84
0.13
99.6% 3.40
100 33.09 1.01
81.1 0.94 47.82
0.11
99.6% 2.88
100 44.52 2.17
82.2 0.95 41.98
0.10
99.6% 2.81
Re
s/dn
z/dn
Pamb
kPa
93.6 17.3 57.6 100.0
101.9 17.3 57.6 100.0
118.6 17.3 57.6 100.0
Table B.91
dn
μm
173.6
173.6
173.6
173.6
173.6
z
Tw
qw
o
o
o
mm mm
C
C kPa
C W/cm2
10 3 FC40 6.54 21.59 250 9.20
1.10
10 3 FC40 6.51 21.59 251 10.73 1.69
10 3 FC40 6.65 21.34 251 14.40 3.15
10 3 FC40 6.87 21.19 248 24.77 7.40
10 3 FC40 7.63 21.29 245 39.86 15.24
Vflow
ml/min
648.0
648.9
648.2
645.4
644.4
vjets
m/s
7.48
7.50
7.49
7.45
7.44
Pr
83.78
81.83
77.15
66.08
53.57
h
W/cm2 oC
0.41
0.40
0.41
0.41
0.47
Xair
Nu
Re
s/dn
z/dn
99.8%
99.8%
99.8%
99.8%
99.8%
10.77
10.48
10.63
10.89
12.56
451.6
463.5
492.4
576.7
718.1
17.3
17.3
17.3
17.3
17.3
57.6
57.6
57.6
57.6
57.6
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
Table B.92
dn
μm
250.0
250.0
250.0
250.0
250.0
250.0
z
Tw
qw
o
o
mm mm
C
C kPa oC W/cm2
10 1 FC40 23.41 21.56 99 25.07 0.27
10 1 FC40 23.67 21.81 99 26.88 0.64
10 1 FC40 24.29 24.26 100 30.60 1.40
10 1 FC40 22.61 24.53 100 30.10 1.59
10 1 FC40 22.72 24.41 100 35.33 2.78
10 1 FC40 22.87 24.34 100 47.12 5.29
Vflow
ml/min
965.5
964.2
961.8
963.6
961.4
955.1
vjets
m/s
0.83
0.82
0.82
0.82
0.82
0.82
Pr
52.91
51.57
48.94
50.23
47.14
41.21
h
W/cm2 oC
0.16
0.20
0.22
0.21
0.22
0.22
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
99.6%
99.6%
6.22
7.62
8.50
8.17
8.48
8.45
116.3
119.3
125.8
122.6
130.8
149.8
4.0
4.0
4.0
4.0
4.0
4.0
40.0
40.0
40.0
40.0
40.0
40.0
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
99.6%
15.25
14.82
14.75
14.80
15.46
218.6
226.3
234.0
242.3
269.1
4.0
4.0
4.0
4.0
4.0
40.0
40.0
40.0
40.0
40.0
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
100.0
173
Table B.93
dn
μm
250.0
250.0
250.0
250.0
250.0
z
Tw
qw
Vflow
vjets
Pr
h
o
o
o
2
mm mm
C
C kPa
C W/cm ml/min m/s
W/cm2 oC
10 1 FC40 22.57 22.06 115 23.73 0.46 1868.4 1.60 54.37
0.40
10 1 FC40 22.69 22.21 116 25.78 1.20 1879.6 1.61 52.92
0.39
10 1 FC40 22.72 22.30 116 27.88 1.99 1889.8 1.62 51.54
0.39
10 1 FC40 22.78 22.40 115 30.85 3.11 1882.5 1.61 49.67
0.39
10 1 FC40 22.95 22.28 115 39.07 6.46 1884.4 1.61 45.03
0.40
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
Table B.94
dn
μm
250.0
250.0
250.0
250.0
250.0
z
Tw
qw
Vflow
vjets
Pr
h
o
o
mm mm
C
W/cm2 oC
10 1 FC40 22.84 22.06 124 23.17 0.11 2287.6 1.96 54.58
0.34
10 1 FC40 22.97 22.18 124 24.67 0.70 2308.0 1.97 53.46
0.41
10 1 FC40 23.13 22.41 125 27.75 1.97 2328.5 1.99 51.36
0.43
10 1 FC40 23.19 22.36 125 30.39 3.15 2318.1 1.98 49.71
0.44
10 1 FC40 23.54 24.64 124 35.86 5.64 2307.7 1.97 46.40
0.46
Xair
Nu
Re
s/dn
z/dn
99.6%
99.6%
99.6%
99.6%
99.6%
12.88
15.68
16.31
16.78
17.61
266.6
274.9
289.3
298.2
319.3
4.0
4.0
4.0
4.0
4.0
40.0
40.0
40.0
40.0
40.0
Xair
Nu
Re
99.6%
99.6%
99.6%
99.6%
99.6%
6.2
6.4
6.4
6.5
7.0
265.3
275.5
289.6
299.1
351.8
Xair
Nu
Re
99.6%
99.6%
99.6%
99.6%
99.6%
10.6
9.7
9.7
9.8
10.2
467.4
476.3
485.6
516.9
544.8
Pamb
kPa
100.0
100.0
100.0
100.0
100.0
Table B.95
174
dn
z
Tw
qw
o
o
o
μm
mm mm
C
C
kPa
C W/cm2
173.56 5
3 FC40 23.50 21.51 119.1 24.27 0.18
173.56 5
3 FC40 23.68 21.53 119.0 26.65 0.72
173.56 5
3 FC40 23.73 21.59 119.0 30.86 1.71
173.56 5
3 FC40 23.75 21.61 119.0 33.41 2.36
173.56 5
3 FC40 23.95 21.91 118.7 46.93 6.01
Vflow
ml/min
237.2
238.2
237.1
237.1
236.7
vjets
m/s
2.74
2.75
2.74
2.74
2.73
Pr
53.38
51.71
49.10
47.63
40.82
h
W/cm2 oC
0.23
0.24
0.24
0.24
0.26
s/dn z/dn
17.3
17.3
17.3
17.3
17.3
28.8
28.8
28.8
28.8
28.8
Pamb
kPa
99.97
99.97
99.97
99.97
99.97
Table B.96
dn
z
Tw
qw
o
o
o
μm
mm mm
C
C
kPa
C W/cm2
173.56 5
3 FC40 24.05 21.54 158.1 24.68 0.25
173.56 5
3 FC40 24.05 21.60 158.1 25.93 0.69
173.56 5
3 FC40 24.07 21.62 158.1 27.60 1.29
173.56 5
3 FC40 24.76 24.36 157.8 31.75 2.58
173.56 5
3 FC40 25.06 24.59 158.1 35.55 4.00
Vflow
ml/min
412.7
413.7
412.6
413.1
414.0
vjets
m/s
4.77
4.78
4.77
4.77
4.78
Pr
52.75
51.94
50.87
48.00
45.76
h
W/cm2 oC
0.40
0.36
0.36
0.37
0.38
s/dn z/dn
17.3
17.3
17.3
17.3
17.3
28.8
28.8
28.8
28.8
28.8
Pamb
kPa
99.97
99.97
99.97
99.97
99.97
Table B.97
dn
μm
173.56
173.56
173.56
173.56
173.56
z
Tw
qw
o
o
o
mm mm
C
C
kPa
C W/cm2
2.1 3 FC40 23.66 21.51 120.2 24.23 0.16
2.1 3 FC40 23.65 21.45 120.3 25.98 0.60
2.1 3 FC40 23.65 21.41 120.3 28.24 1.16
2.1 3 FC40 23.66 21.44 120.3 31.49 1.98
2.1 3 FC40 23.81 21.60 119.9 46.35 6.03
Vflow
ml/min
242.4
242.4
242.4
242.3
241.1
vjets
m/s
2.80
2.80
2.80
2.80
2.78
Pr
53.30
52.16
50.73
48.78
41.13
h
W/cm2 oC
0.29
0.26
0.25
0.25
0.27
Xair
Nu
Re
99.6%
99.6%
99.6%
99.6%
99.6%
7.8
6.8
6.7
6.7
7.2
271.5
277.8
286.0
298.1
355.2
Xair
Nu
Re
99.6%
99.6%
99.6%
99.6%
99.6%
99.6%
10.3
9.2
9.3
9.3
9.4
10.0
463.2
471.7
483.8
493.6
507.5
577.1
s/dn z/dn
17.3
17.3
17.3
17.3
17.3
12.1
12.1
12.1
12.1
12.1
Pamb
kPa
99.97
99.97
99.97
99.97
99.97
Table B.98
175
dn
μm
173.56
173.56
173.56
173.56
173.56
173.56
z
Tw
qw
o
o
o
mm mm
C
C
kPa
C W/cm2
2.1 3 FC40 23.98 21.45 158.4 24.61 0.24
2.1 3 FC40 24.02 21.49 158.2 25.98 0.68
2.1 3 FC40 24.07 21.53 158.2 27.70 1.27
2.1 3 FC40 24.11 21.49 158.2 29.44 1.86
2.1 3 FC40 24.16 21.60 158.1 31.59 2.61
2.1 3 FC40 24.52 21.77 157.5 42.75 6.79
Vflow
ml/min
409.7
409.6
410.6
409.5
409.4
405.0
vjets
m/s
4.73
4.73
4.74
4.73
4.73
4.68
Pr
52.84
51.92
50.81
49.73
48.44
42.46
h
W/cm2 oC
0.39
0.35
0.35
0.35
0.35
0.37
s/dn z/dn
17.3
17.3
17.3
17.3
17.3
17.3
12.1
12.1
12.1
12.1
12.1
12.1
Pamb
kPa
99.97
99.97
99.97
99.97
99.97
99.97
Table B.99
z
Tw
qw
dn
o
o
o
μm
mm mm
C
C
kPa
C W/cm2
173.56 4
3 FC40 24.11 23.93 119.6 25.17 0.23
173.56 4
3 FC40 24.24 24.08 119.4 27.49 0.70
173.56 4
3 FC40 24.24 23.45 119.5 29.61 1.33
173.56 4
3 FC40 24.33 23.65 119.2 32.16 1.83
173.56 4
3 FC40 24.65 23.89 118.8 52.37 6.95
Vflow
ml/min
241.0
239.9
240.0
239.9
238.4
vjets
m/s
2.78
2.77
2.77
2.77
2.75
Pr
52.38
50.84
49.55
48.01
38.24
h
W/cm2 oC
0.22
0.21
0.25
0.23
0.25
176
Xair
Nu
Re
99.6%
99.6%
99.6%
99.6%
99.6%
5.9
5.7
6.6
6.2
6.8
275.0
282.6
290.3
300.1
379.7
Xair
Nu
Re
99.6%
99.6%
99.6%
99.6%
14.4
11.0
10.5
10.8
463.8
481.3
499.3
576.7
s/dn z/dn
17.3
17.3
17.3
17.3
17.3
23.0
23.0
23.0
23.0
23.0
Pamb
kPa
99.97
99.97
99.97
99.97
99.97
Table B.100
dn
μm
173.56
173.56
173.56
173.56
z
o
o
mm mm
C
C
kPa
10 3 FC40 23.90 23.73 158.4
10 3 FC40 23.96 23.63 158.4
10 3 FC40 24.01 23.67 157.3
10 3 FC40 24.30 23.82 156.9
Tw
qw
C W/cm2
24.71 0.44
27.13 1.31
30.76 2.64
41.54 6.93
o
Vflow
ml/min
410.0
412.0
407.9
411.6
vjets
m/s
4.74
4.76
4.71
4.75
Pr
52.82
51.23
49.01
43.14
h
W/cm2 oC
0.54
0.41
0.39
0.40
s/dn z/dn
17.3
17.3
17.3
17.3
57.6
57.6
57.6
57.6
Pamb
kPa
99.97
99.97
99.97
99.97
Table B.101 Calibration data (T1-T4 are the thermocouples in the copper block, 1 being the closest to the free surface and 4 the
farthest away).
Tref
o
C
0
19.5
99.65
T1
o
C
-0.01
19.55
100.09
T2
o
C
-0.10
19.44
99.76
T3
o
C
-0.09
19.42
99.76
T4
o
C
-0.12
19.42
99.78
Tjets
o
C
-0.18
19.35
99.70
Tbox
o
C
-0.10
19.38
99.57
Tflowmeter
o
C
-0.08
19.43
100.00
Pbox
Pa
Pjets
Pa
99944
100231
A
AP
PP
PE
EN
ND
DIIX
XC
C
In this section all the data regarding the closed system tests described in Chapter 4
are listed.
177
C.1 Closed system - variable air content data
Table C.1
178
dn
μm
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
z
s
Tjets Tboxavg Pjets Tw
qw
o
o
mm mm oC
C
kPa
C W/cm2
10
1 100.7 100.5 106.2 104.5 10.9
10
1 100.7 100.6 106.4 105.7 15.2
10
1 100.8 100.6 107.0 107.3 21.8
10
1 100.8 100.5 106.9 109.1 29.5
10
1 100.7 100.6 107.2 110.7 36.3
10
1 100.8 100.6 107.2 112.7 46.6
10
1 100.7 100.6 107.4 113.4 49.4
10
1 100.8 100.5 107.1 114.4 55.3
10
1 100.8 100.6 107.2 116.3 66.2
10
1 100.8 100.5 107.3 120.1 90.6
10
1 100.9 100.5 107.0 123.2 118.1
Vflow
ml/min
520.3
519.0
518.5
518.2
517.6
517.7
517.6
517.6
517.9
516.5
516.9
vjets
m/s
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
Pr
1.71
1.70
1.68
1.67
1.65
1.64
1.63
1.62
1.61
1.58
1.55
h
W/cm2 oC
2.93
3.06
3.37
3.55
3.63
3.93
3.91
4.06
4.28
4.70
5.30
Xair
-2.5%
-2.4%
-2.4%
-2.4%
-2.4%
-2.4%
-2.5%
-2.2%
-2.5%
-2.3%
-2.3%
PsatA TsatA
103.3
103.4
103.5
103.2
103.5
103.4
103.6
103.1
103.4
103.3
103.2
99.8
99.9
99.9
99.9
99.9
99.9
99.9
99.9
99.9
99.9
99.9
Nu
Re
5.13
5.35
5.89
6.20
6.33
6.86
6.83
7.09
7.46
8.18
9.22
816.1
819.0
824.7
831.1
835.9
844.1
846.4
850.8
858.7
870.7
884.4
s/dn Pamb
kPa
8.4 100.7
8.4 100.9
8.4 101.1
8.4 100.8
8.4 101.0
8.4 101.0
8.4 101.0
8.4 100.9
8.4 101.0
8.4 100.9
8.4 100.9
Table C.2
dn
μm
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
z
s
Tjets Tboxavg
o
mm mm oC
C
10
1 96.7 96.8
10
1 96.8 96.8
10
1 96.9 96.7
10
1 97.0 96.7
10
1 97.0 96.7
10
1 96.9 96.6
10
1 96.9 96.7
10
1 97.0 96.7
10
1 96.9 96.7
10
1 96.8 96.8
Pjets
kPa
107.9
107.4
107.8
107.7
108.0
107.8
107.7
107.6
107.7
108.1
Tw
qw
o
C W/cm2
101.9 11.2
103.2 15.3
105.1 21.8
107.2 29.5
108.9 35.9
110.8 45.2
112.5 56.3
113.9 66.4
117.9 94.2
121.7 121.5
Vflow
ml/min
515.8
516.5
516.7
516.8
516.4
516.3
516.1
515.7
515.5
513.8
vjets
m/s
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
1.9
Pr
1.77
1.76
1.74
1.72
1.70
1.69
1.67
1.66
1.62
1.59
h
W/cm2 oC
2.17
2.37
2.65
2.90
3.01
3.23
3.61
3.94
4.50
4.88
Xair
10.8%
10.8%
11.0%
11.0%
11.0%
11.1%
11.1%
11.0%
10.9%
10.8%
PsatA TsatA
Nu
90.2 100.0 3.80
90.1 99.9 4.16
89.9 99.9 4.65
89.8 99.9 5.08
89.8 99.9 5.27
89.7 99.9 5.65
89.8 99.9 6.31
89.9 99.9 6.89
90.0 99.9 7.86
90.3 100.0 8.50
Re
783.2
789.8
798.0
806.8
812.5
819.4
825.7
831.0
845.8
857.5
s/dn Pamb
kPa
8.4 101.1
8.4 101.1
8.4 101.0
8.4 101.0
8.4 101.0
8.4 100.9
8.4 101.0
8.4 100.9
8.4 101.1
8.4 101.2
179
Table C.3
dn
μm
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
z
s
Tjets Tboxavg
o
mm mm oC
C
10
1 91.3 92.3
10
1 91.0 92.2
10
1 91.0 91.0
10
1 91.2 90.1
10
1 91.3 90.9
10
1 91.1 90.7
10
1 91.4 90.6
10
1 91.0 90.5
10
1 91.1 90.6
Pjets
kPa
113.9
114.0
114.4
112.9
114.8
114.8
115.2
115.1
115.4
Tw
qw
o
C W/cm2
94.9 11.6
96.1 16.1
98.2 23.1
100.5 31.0
102.2 37.9
104.0 47.5
106.2 57.6
108.3 69.0
116.6 121.7
Vflow
ml/min
516.7
516.3
516.4
515.2
513.9
513.6
513.4
512.3
511.7
vjets
m/s
2.0
2.0
2.0
2.0
2.0
1.9
1.9
1.9
1.9
Pr
1.90
1.89
1.87
1.84
1.82
1.80
1.78
1.76
1.69
h
W/cm2 oC
3.22
3.17
3.19
3.36
3.47
3.68
3.91
4.00
4.77
Xair
24.4%
24.6%
28.2%
29.0%
28.3%
28.7%
29.1%
29.4%
29.1%
PsatA TsatA
Nu
76.4 99.9 5.68
76.1 99.9 5.57
72.7 100.0 5.60
70.5 99.4 5.90
72.5 99.9 6.09
72.0 99.9 6.46
71.7 99.9 6.86
71.3 99.9 7.00
71.8 100.0 8.35
Re
736.9
739.5
748.0
755.8
761.0
766.9
775.9
780.7
812.2
s/dn Pamb
kPa
8.4 101.0
8.4 101.0
8.4 101.2
8.4 99.3
8.4 101.1
8.4 101.0
8.4 101.0
8.4 101.0
8.4 101.2
Table C.4
dn
μm
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
z
s
Tjets Tboxavg
o
mm mm oC
C
10
1 81.9 81.6
10
1 82.0 81.5
10
1 82.0 81.4
10
1 82.0 81.5
10
1 82.1 81.4
10
1 82.3 81.4
10
1 82.5 81.5
10
1 82.3 81.4
Pjets
kPa
109.1
109.3
109.4
109.6
110.1
109.9
110.1
110.1
Tw
qw
o
C W/cm2
86.7 11.8
88.9 17.1
91.4 23.7
94.4 31.7
100.3 48.1
105.8 69.5
111.3 92.7
117.0 118.9
Vflow
ml/min
520.2
520.4
519.7
520.1
518.9
518.7
518.0
517.0
vjets
m/s
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
Pr
2.11
2.08
2.05
2.01
1.94
1.88
1.82
1.76
h
W/cm2 oC
2.48
2.48
2.51
2.56
2.64
2.97
3.22
3.43
Xair
PsatA TsatA
Nu
Re
50.1%
50.3%
50.5%
50.3%
50.5%
50.4%
50.2%
50.4%
50.4 99.9
50.2 99.9
50.0 99.9
50.2 99.9
50.1 99.9
50.2 99.9
50.4 99.9
50.2 100.0
4.39
4.39
4.45
4.53
4.65
5.22
5.66
6.00
674.0
683.3
692.1
703.9
725.2
747.2
768.1
788.0
Xair
PsatA TsatA
Nu
Re
4.60
4.51
4.48
4.52
4.55
4.65
4.74
5.23
507.6
515.2
521.0
530.9
541.0
564.8
595.5
651.0
s/dn Pamb
kPa
8.4 101.1
8.4 101.1
8.4 101.0
8.4 101.1
8.4 101.1
8.4 101.1
8.4 101.1
8.4 101.2
180
Table C.5
dn
μm
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
z
s
Tjets Tboxavg
o
mm mm oC
C
10
1 61.7 60.7
10
1 61.8 60.8
10
1 61.8 60.9
10
1 61.7 60.5
10
1 61.9 60.1
10
1 62.1 59.8
10
1 62.7 59.9
10
1 62.8 59.7
Pjets
kPa
112.1
112.1
111.8
111.8
112.3
112.3
112.0
112.3
Tw
qw
o
C W/cm2
64.7
7.5
66.9 12.7
68.8 17.4
71.8 25.4
74.6 32.0
81.2 49.5
89.5 71.0
104.7 123.4
Vflow
ml/min
511.0
510.4
509.9
509.3
508.5
507.6
506.5
505.3
vjets
m/s
1.9
1.9
1.9
1.9
1.9
1.9
1.9
1.9
Pr
2.85
2.80
2.76
2.70
2.64
2.51
2.36
2.13
h
W/cm2 oC
2.53
2.49
2.48
2.50
2.52
2.59
2.65
2.95
79.7%
79.6%
79.5%
79.9%
80.2%
80.5%
80.5%
80.6%
20.5
20.7
20.7
20.4
20.0
19.8
19.8
19.6
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
s/dn Pamb
kPa
8.4 101.2
8.4 101.2
8.4 101.2
8.4 101.3
8.4 101.2
8.4 101.2
8.4 101.3
8.4 101.4
Table C.6
181
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
s
qw
o
o
mm mm oC
C
kPa
C W/cm2
10
3 99.1 100.3 164.9 104.1 13.7
10
3 99.1 100.4 165.1 105.1 18.7
10
3 99.1 100.3 164.9 106.0 23.0
10
3 99.1 100.3 164.9 107.4 29.7
10
3 99.2 100.4 165.0 109.2 37.9
10
3 99.3 100.4 164.9 112.7 55.6
10
3 98.9 100.4 165.3 116.3 76.7
10
3 98.8 100.4 165.4 119.2 101.0
10
3 98.8 100.4 165.5 122.5 129.2
Vflow
ml/min
233.1
233.3
233.1
233.1
233.4
233.3
233.4
232.9
232.8
vjets
m/s
6.0
6.0
6.0
6.0
6.0
6.0
6.0
6.0
6.0
Pr
1.73
1.72
1.71
1.70
1.68
1.65
1.62
1.60
1.57
h
W/cm2 oC
2.74
3.08
3.31
3.57
3.80
4.14
4.41
4.94
5.44
Xair
-2.5%
-2.5%
-2.5%
-2.5%
-2.5%
-2.5%
-2.4%
-2.4%
-2.4%
PsatA TsatA
102.6
102.6
102.6
102.5
102.6
102.7
102.6
102.6
102.6
99.7
99.7
99.7
99.6
99.7
99.7
99.7
99.7
99.7
Nu
Re
4.70
5.28
5.67
6.12
6.50
7.08
7.55
8.45
9.30
2403.8
2419.0
2427.0
2444.1
2468.8
2510.3
2547.5
2574.5
2611.9
Nu
Re
4.56
4.81
5.40
6.40
7.38
8.26
8.89
2381.6
2402.1
2438.3
2478.4
2519.3
2562.4
2596.3
s/dn Pamb
kPa
25.8 100.1
25.8 100.1
25.8 100.1
25.8 100.0
25.8 100.1
25.8 100.2
25.8 100.1
25.8 100.2
25.8 100.2
Table C.7
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 96.8 96.9
10
3 96.8 96.9
10
3 96.6 96.9
10
3 96.7 96.8
10
3 96.9 96.8
10
3 97.0 96.9
10
3 96.8 96.9
Pjets
kPa
144.3
144.2
144.1
144.2
143.8
144.4
144.4
Tw
qw
o
C W/cm2
103.3 17.1
104.9 22.5
108.3 36.9
111.4 55.0
115.0 78.0
118.4 103.1
122.0 130.9
Vflow
ml/min
234.4
234.6
234.5
234.7
234.4
234.5
233.9
vjets
m/s
6.0
6.0
6.0
6.0
6.0
6.0
6.0
Pr
1.76
1.74
1.71
1.68
1.65
1.62
1.59
h
W/cm2 oC
2.65
2.80
3.15
3.73
4.31
4.83
5.20
Xair
9.6%
9.6%
9.5%
9.5%
9.5%
9.3%
9.4%
PsatA TsatA
90.5
90.5
90.5
90.3
90.4
90.6
90.7
99.7
99.6
99.6
99.6
99.6
99.6
99.7
s/dn Pamb
kPa
25.8 100.1
25.8 100.0
25.8 100.0
25.8 99.8
25.8 99.9
25.8 99.9
25.8 100.1
Table C.8
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 93.4 93.7
10
3 93.3 93.6
10
3 93.4 93.5
10
3 93.5 93.6
10
3 93.7 93.6
10
3 93.7 93.7
10
3 93.7 93.8
Pjets
kPa
153.0
153.2
152.9
152.7
152.9
153.2
153.5
Tw
qw
o
C W/cm2
101.7 18.8
102.9 23.0
107.3 37.2
111.1 54.8
114.4 77.5
117.4 102.0
120.9 130.1
Vflow
ml/min
230.8
231.2
231.3
232.0
231.9
232.2
232.0
vjets
m/s
5.9
5.9
5.9
6.0
6.0
6.0
6.0
Pr
1.80
1.79
1.75
1.71
1.68
1.66
1.63
h
W/cm2 oC
2.26
2.41
2.68
3.12
3.74
4.29
4.78
Xair
19.5%
19.7%
19.8%
19.5%
19.4%
19.2%
19.0%
PsatA TsatA
80.6
80.2
80.0
80.2
80.4
80.7
80.9
99.6
99.6
99.6
99.5
99.5
99.6
99.6
Nu
Re
3.88
4.14
4.60
5.34
6.41
7.34
8.18
2288.8
2304.9
2356.5
2410.1
2448.6
2486.7
2525.2
Nu
Re
3.91
3.90
3.94
4.04
4.33
4.65
5.39
6.11
2017.3
2038.8
2067.1
2147.6
2201.7
2280.1
2318.5
2363.5
s/dn Pamb
kPa
25.8 100.1
25.8 99.9
25.8 99.7
25.8 99.6
25.8 99.7
25.8 99.8
25.8 99.9
Table C.9
182
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 82.9 83.0
10
3 82.9 83.1
10
3 83.0 83.0
10
3 83.4 82.6
10
3 83.1 82.4
10
3 83.1 82.5
10
3 83.1 82.8
10
3 82.7 82.8
Pjets
kPa
160.6
161.0
160.6
160.6
160.3
160.8
161.1
160.7
Tw
qw
o
C W/cm2
88.7 12.9
90.9 18.1
93.0 22.7
99.7 38.2
105.0 54.9
111.8 77.5
115.5 101.6
119.2 129.9
Vflow
ml/min
230.5
230.1
230.5
230.6
230.2
230.3
229.8
230.6
vjets
m/s
5.9
5.9
5.9
5.9
5.9
5.9
5.9
5.9
Pr
2.07
2.04
2.02
1.93
1.88
1.81
1.77
1.74
h
W/cm2 oC
2.26
2.25
2.27
2.34
2.51
2.70
3.14
3.56
Xair
46.5%
46.4%
46.6%
47.5%
47.9%
47.6%
47.2%
47.0%
PsatA TsatA
53.5
53.7
53.4
52.5
52.1
52.4
52.9
53.0
99.6
99.7
99.7
99.6
99.6
99.6
99.7
99.7
s/dn Pamb
kPa
25.8 99.9
25.8 100.2
25.8 100.1
25.8 99.9
25.8 99.9
25.8 100.0
25.8 100.1
25.8 100.1
Table C.10
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 20.3 21.7
10
3 20.3 21.4
10
3 20.3 21.1
10
3 20.3 21.0
10
3 20.3 21.0
10
3 20.4 20.9
10
3 20.4 21.0
10
3 20.4 22.8
Pjets
kPa
174.9
174.5
174.0
173.5
173.2
172.6
173.7
175.1
Tw
qw
o
C W/cm2
25.2
8.8
28.5 14.2
31.5 19.4
40.8 35.6
50.9 54.1
62.2 78.0
74.0 104.8
100.3 169.7
Vflow
ml/min
229.1
228.5
227.7
226.6
225.7
224.6
226.2
227.0
vjets
m/s
5.9
5.9
5.9
5.8
5.8
5.8
5.8
5.8
Pr
6.50
6.22
5.99
5.35
4.77
4.23
3.76
2.99
h
W/cm2 oC
1.79
1.72
1.73
1.74
1.77
1.86
1.95
2.13
Xair
97.4%
97.5%
97.5%
97.5%
97.5%
97.5%
97.5%
97.3%
PsatA TsatA
2.6
2.5
2.5
2.5
2.5
2.5
2.5
2.8
99.8
99.8
99.8
99.8
99.8
99.8
99.8
100.1
Nu
Re
3.45 728.3
3.30 754.9
3.31 777.8
3.28 856.4
3.31 944.1
3.43 1045.2
3.57 1166.2
3.80 1437.3
s/dn Pamb
kPa
25.8 100.4
25.8 100.4
25.8 100.4
25.8 100.4
25.8 100.5
25.8 100.4
25.8 100.5
25.8 101.5
183
Table C.11
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
s
qw
o
o
mm mm oC
C
kPa
C W/cm2
10
3 100.7 100.8 216.9 103.6 9.7
10
3 100.7 100.7 216.8 104.5 14.6
10
3 100.8 100.7 217.0 105.5 19.8
10
3 100.8 100.7 216.9 108.2 34.4
10
3 100.8 100.7 216.8 111.4 51.7
10
3 100.8 100.7 217.2 115.1 73.3
10
3 100.9 100.7 217.9 121.9 131.0
Vflow
ml/min
230.2
230.0
230.6
230.5
230.3
230.3
230.5
vjets
m/s
5.9
5.9
5.9
5.9
5.9
5.9
5.9
Pr
1.72
1.71
1.70
1.67
1.65
1.62
1.56
h
W/cm2 oC
3.42
3.90
4.24
4.62
4.86
5.14
6.24
Xair
-2.8%
-2.8%
-2.7%
-2.6%
-2.6%
-2.5%
-2.4%
PsatA TsatA
104.1
104.0
103.9
103.8
103.8
103.8
103.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Nu
Re
5.86
6.69
7.27
7.92
8.31
8.78
10.65
2387.5
2395.8
2415.4
2444.4
2479.3
2521.4
2603.6
s/dn Pamb
kPa
25.8 101.2
25.8 101.2
25.8 101.2
25.8 101.2
25.8 101.2
25.8 101.3
25.8 101.4
Table C.12
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
z
s
qw
o
o
mm mm oC
C
kPa
C W/cm2
10
3 100.2 100.7 152.7 104.0 12.0
10
3 100.1 100.6 152.8 104.9 16.4
10
3 100.1 100.6 152.7 107.7 31.0
10
3 100.2 100.6 153.2 110.9 48.9
10
3 100.2 100.6 152.9 118.3 97.2
10
3 100.2 100.6 153.2 121.9 126.3
Vflow
ml/min
227.9
227.4
227.1
227.5
227.1
227.1
vjets
m/s
5.9
5.8
5.8
5.8
5.8
5.8
Pr
1.72
1.71
1.68
1.66
1.59
1.57
h
W/cm2 oC
3.11
3.45
4.12
4.55
5.35
5.84
Xair
-2.5%
-2.2%
-2.2%
-2.3%
-2.2%
-2.2%
PsatA TsatA
103.7
103.4
103.4
103.5
103.6
103.7
100.0
100.0
100.0
100.0
100.0
100.0
Nu
Re
5.34
5.92
7.06
7.80
9.15
9.97
2362.3
2366.7
2395.6
2435.7
2517.2
2558.1
Nu
Re
7.41
7.79
8.91
9.61
10.30
10.85
11.34
11.64
12.43
12.80
13.42
3704.3
3696.4
3718.6
3728.8
3729.5
3740.3
3762.7
3775.3
3824.0
3873.0
3930.2
s/dn Pamb
kPa
25.8 101.2
25.8 101.2
25.8 101.2
25.8 101.2
25.8 101.4
25.8 101.4
Table C.13
184
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
s
qw
o
o
o
mm mm
C
C
kPa
C W/cm2
10
3 100.6 100.5 201.0 103.2 11.0
10
3 100.5 100.5 201.5 103.8 15.0
10
3 100.4 100.5 203.4 104.6 21.9
10
3 100.3 100.5 204.0 105.6 29.4
10
3 100.3 100.4 204.0 106.4 37.0
10
3 100.1 100.4 204.2 107.4 45.9
10
3 100.1 100.4 204.4 108.9 58.2
10
3 100.1 100.4 204.8 109.9 66.1
10
3 100.3 100.4 204.9 112.9 92.1
10
3 100.2 100.4 205.3 116.1 118.8
10
3 100.2 100.5 205.6 119.6 152.0
Vflow
ml/min
358.1
356.5
357.3
356.7
355.6
355.1
354.7
354.3
353.6
353.0
352.7
vjets
m/s
9.2
9.2
9.2
9.2
9.1
9.1
9.1
9.1
9.1
9.1
9.1
Pr
1.72
1.72
1.71
1.70
1.69
1.69
1.67
1.67
1.64
1.61
1.59
h
W/cm2 oC
4.32
4.54
5.19
5.61
6.01
6.33
6.62
6.80
7.27
7.48
7.86
Xair
-2.1%
-2.0%
-2.2%
-2.1%
-2.0%
-2.0%
-2.0%
-2.0%
-2.1%
-2.0%
-2.0%
PsatA TsatA
103.2
103.3
103.1
103.2
102.9
102.8
102.7
102.7
102.8
102.8
103.0
100.0
100.0
99.9
99.9
99.9
99.8
99.8
99.8
99.8
99.9
99.9
s/dn Pamb
kPa
25.8 101.2
25.8 101.3
25.8 100.9
25.8 101.1
25.8 100.9
25.8 100.7
25.8 100.7
25.8 100.7
25.8 100.8
25.8 100.9
25.8 101.0
Table C.14
185
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 97.6 96.9
10
3 97.3 96.9
10
3 96.8 96.9
10
3 97.3 96.9
10
3 97.5 96.8
10
3 97.3 96.9
10
3 97.2 96.9
10
3 97.2 96.9
10
3 97.1 96.9
10
3 97.1 97.0
10
3 97.2 97.0
Pjets
kPa
206.3
206.7
196.7
197.1
198.4
198.5
198.8
198.9
199.7
200.3
201.0
Tw
qw
o
C W/cm2
100.3 11.1
101.3 15.8
102.6 22.4
104.0 29.6
105.2 36.9
106.4 45.7
107.9 58.5
109.0 67.0
111.5 91.0
114.0 118.4
117.2 151.4
Vflow
ml/min
351.9
351.5
351.6
349.9
351.1
350.1
349.2
348.1
347.4
347.4
346.3
vjets
m/s
9.1
9.0
9.0
9.0
9.0
9.0
9.0
9.0
8.9
8.9
8.9
Pr
1.78
1.77
1.76
1.74
1.73
1.72
1.71
1.70
1.68
1.66
1.63
h
W/cm2 oC
4.03
3.89
3.88
4.43
4.85
5.06
5.45
5.67
6.32
6.97
7.57
Xair
9.9%
9.9%
9.9%
9.8%
9.9%
9.9%
9.8%
9.7%
9.8%
9.6%
9.7%
PsatA TsatA
90.6
90.5
90.6
90.7
90.4
90.5
90.5
90.6
90.6
90.8
90.9
99.8
99.8
99.8
99.8
99.7
99.7
99.7
99.7
99.8
99.8
99.8
Nu
Re
6.92
6.68
6.67
7.60
8.31
8.68
9.34
9.71
10.82
11.93
12.95
3537.9
3545.5
3560.8
3575.7
3613.8
3620.5
3635.3
3641.9
3678.4
3721.3
3765.6
Nu
Re
6.40
6.36
6.35
6.45
6.74
7.01
7.87
8.65
9.83
10.86
3382.3
3397.2
3422.8
3452.9
3477.7
3493.6
3558.7
3592.6
3635.8
3681.5
s/dn Pamb
kPa
25.8 100.5
25.8 100.5
25.8 100.5
25.8 100.6
25.8 100.3
25.8 100.3
25.8 100.4
25.8 100.3
25.8 100.5
25.8 100.5
25.8 100.6
Table C.15
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 92.8 92.3
10
3 92.8 93.3
10
3 92.8 93.0
10
3 92.9 92.5
10
3 93.0 92.2
10
3 92.8 92.3
10
3 93.1 92.2
10
3 92.6 92.4
10
3 92.6 92.4
10
3 92.6 92.5
Pjets
kPa
200.5
200.7
200.0
200.6
200.7
200.4
200.8
201.0
201.3
201.8
Tw
qw
o
C W/cm2
95.9 11.3
97.1 16.0
98.9 22.6
101.0 30.3
102.5 37.3
104.1 45.8
107.8 67.5
110.8 91.5
113.5 120.2
116.4 151.0
Vflow
ml/min
352.4
351.8
351.3
350.5
349.9
349.2
348.8
347.9
347.5
347.0
vjets
m/s
9.1
9.0
9.0
9.0
9.0
9.0
9.0
8.9
8.9
8.9
Pr
1.87
1.86
1.84
1.82
1.80
1.79
1.75
1.72
1.70
1.67
h
W/cm2 oC
3.71
3.69
3.69
3.75
3.92
4.08
4.58
5.04
5.74
6.34
Xair
23.9%
21.2%
21.6%
23.4%
24.2%
23.9%
24.2%
23.8%
23.9%
23.5%
PsatA TsatA
76.6
79.3
78.5
77.0
76.2
76.4
76.2
76.6
76.7
77.1
99.8
99.8
99.7
99.8
99.8
99.7
99.8
99.8
99.9
99.9
s/dn Pamb
kPa
25.8 100.6
25.8 100.6
25.8 100.2
25.8 100.5
25.8 100.5
25.8 100.4
25.8 100.5
25.8 100.6
25.8 100.8
25.8 100.9
Table C.16
186
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 81.7 82.0
10
3 81.7 82.0
10
3 81.8 81.6
10
3 81.9 81.6
10
3 82.3 81.6
10
3 81.7 81.6
10
3 81.8 81.6
10
3 81.9 81.6
10
3 82.2 81.7
10
3 81.8 81.8
10
3 82.2 82.1
Pjets
kPa
202.6
202.6
202.5
205.8
204.6
204.5
204.6
204.5
204.2
204.0
204.4
Tw
qw
o
C W/cm2
85.4 11.9
86.7 16.3
89.3 24.4
91.1 31.2
93.8 39.0
95.9 48.7
99.0 58.8
101.7 70.3
106.4 94.0
110.9 120.5
114.6 154.2
Vflow
ml/min
350.4
349.8
347.2
353.0
352.3
352.2
352.0
351.2
351.3
350.0
350.0
vjets
m/s
9.0
9.0
8.9
9.1
9.1
9.1
9.1
9.0
9.0
9.0
9.0
Pr
2.13
2.12
2.08
2.06
2.02
2.00
1.96
1.93
1.87
1.83
1.79
h
W/cm2 oC
3.22
3.22
3.27
3.39
3.40
3.42
3.43
3.56
3.89
4.14
4.76
Xair
49.2%
49.1%
49.8%
49.8%
49.9%
49.9%
50.0%
49.9%
49.7%
49.5%
49.0%
PsatA TsatA
51.3
51.4
50.6
50.5
50.5
50.4
50.4
50.4
50.7
50.9
51.5
99.9
99.9
99.9
99.8
99.8
99.8
99.8
99.8
99.8
99.9
99.9
Nu
Re
5.59
5.59
5.67
5.87
5.88
5.92
5.92
6.15
6.70
7.12
8.17
2989.0
3006.6
3030.8
3112.9
3161.3
3186.6
3240.7
3281.1
3368.9
3429.2
3498.2
Nu
Re
5.39
5.35
5.42
5.45
5.48
5.33
5.36
5.45
5.58
5.92
2432.3
2463.2
2498.5
2544.9
2598.9
2557.5
2600.4
2716.1
2857.6
3017.0
s/dn Pamb
kPa
25.8 101.0
25.8 100.9
25.8 100.8
25.8 100.7
25.8 100.7
25.8 100.7
25.8 100.8
25.8 100.7
25.8 100.8
25.8 100.8
25.8 101.0
Table C.17
dn
μm
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
116.3
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 65.9 65.4
10
3 66.1 64.9
10
3 66.5 64.8
10
3 67.0 64.7
10
3 67.5 64.7
10
3 65.2 64.9
10
3 65.1 64.9
10
3 65.6 65.0
10
3 66.5 64.9
10
3 67.9 64.8
Pjets
kPa
211.6
211.1
210.7
210.2
209.9
210.2
209.9
209.3
208.7
208.4
Tw
qw
o
C W/cm2
68.0
6.6
70.0 11.8
71.9 16.4
74.5 23.2
77.4 31.0
77.9 38.3
80.8 47.9
87.8 69.2
95.8 94.0
103.7 122.0
Vflow
ml/min
350.2
349.5
349.2
348.7
348.3
346.5
346.1
345.1
344.3
344.6
vjets
m/s
9.0
9.0
9.0
9.0
9.0
8.9
8.9
8.9
8.9
8.9
Pr
2.69
2.64
2.60
2.54
2.48
2.51
2.46
2.34
2.20
2.07
h
W/cm2 oC
3.04
3.02
3.07
3.09
3.11
3.03
3.05
3.12
3.20
3.41
Xair
74.9%
75.3%
75.5%
75.6%
75.5%
75.3%
75.3%
75.2%
75.4%
75.4%
PsatA TsatA
25.4
24.9
24.8
24.7
24.7
24.9
24.9
25.0
24.9
24.8
99.9
99.9
99.9
99.9
99.9
99.9
99.9
99.9
99.9
99.9
s/dn Pamb
kPa
25.8 101.1
25.8 100.9
25.8 101.0
25.8 101.0
25.8 100.9
25.8 101.0
25.8 100.9
25.8 101.0
25.8 101.0
25.8 100.9
Table C.18
dn
μm
116.3
116.3
116.3
z
s
qw
o
o
mm mm oC
C
kPa
C W/cm2
10
3 17.9 17.7 226.8 20.9
7.5
10
3 18.0 17.6 226.2 22.9 12.4
10
3 18.0 17.6 225.7 24.9 17.1
Vflow
ml/min
354.0
353.1
352.8
vjets Pr
h
Xair PsatA
m/s
W/cm2 oC
9.1 7.10
2.52
97.9% 2.0
9.1 6.91
2.49
98.0% 2.0
9.1 6.72
2.46
98.0% 2.0
TsatA
Nu
Re
s/dn Pamb
kPa
99.3 4.90 1039.9 25.8 98.7
99.3 4.81 1063.1 25.8 98.7
99.3 4.76 1088.0 25.8 98.7
PsatA TsatA
Nu
Re
10.35
9.57
9.16
9.90
10.65
11.28
12.33
13.01
13.34
14.34
15.18
16.40
17.37
2717.7
2731.6
2729.7
2773.1
2793.9
2813.7
2833.2
2848.1
2865.6
2883.9
2899.3
2920.7
2931.8
Table C.19
187
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
s
qw
o
o
o
mm mm
C
C
kPa
C W/cm2
10
3 99.8 99.7 109.7 103.7 15.7
10
3 100.1 100.5 113.4 106.3 23.0
10
3 99.0 100.1 112.2 107.7 31.3
10
3 99.8 100.8 115.0 110.1 39.8
10
3 99.9 100.4 114.8 111.7 49.2
10
3 99.9 100.4 114.6 113.4 59.8
10
3 99.9 100.6 114.8 115.0 72.8
10
3 99.8 100.9 114.8 116.7 86.4
10
3 99.6 100.7 114.6 118.5 98.8
10
3 99.5 100.7 114.8 120.1 116.0
10
3 99.7 100.6 114.8 121.2 128.0
10
3 99.8 100.6 115.1 122.9 148.7
10
3 99.9 100.3 115.1 124.0 164.4
Vflow
ml/min
392.5
389.0
388.3
388.4
388.2
387.9
387.8
387.0
386.5
386.3
386.2
385.9
385.5
vjets
m/s
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
Pr
1.72
1.70
1.69
1.67
1.65
1.64
1.62
1.61
1.60
1.59
1.58
1.56
1.55
h
W/cm2 oC
4.04
3.74
3.58
3.87
4.17
4.42
4.83
5.10
5.23
5.63
5.96
6.44
6.82
Xair
-5.9%
-4.9%
-4.3%
-3.8%
-2.9%
-3.0%
-3.5%
-4.5%
-3.7%
-3.8%
-3.4%
-3.0%
-2.2%
100.2
103.3
101.6
104.1
102.9
103.0
103.6
104.6
103.9
104.0
103.6
103.4
102.6
98.1
99.2
98.9
99.7
99.6
99.6
99.6
99.7
99.7
99.7
99.7
99.7
99.7
s/dn Pamb
kPa
17.3 94.6
17.3 98.4
17.3 97.4
17.3 100.3
17.3 100.0
17.3 100.0
17.3 100.0
17.3 100.1
17.3 100.1
17.3 100.2
17.3 100.2
17.3 100.3
17.3 100.4
Table C.20
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
s
qw
o
o
mm mm oC
C
kPa
C W/cm2
10
3 99.8 101.1 103.2 105.1 15.0
10
3 99.6 100.9 103.2 106.7 19.7
10
3 99.6 100.6 103.1 108.6 26.3
10
3 99.8 100.1 103.0 110.8 34.3
10
3 99.5 99.9 103.1 112.6 42.6
10
3 99.1 99.9 103.0 114.0 51.3
10
3 99.1 99.9 103.0 117.0 73.4
10
3 99.3 99.9 102.9 119.4 99.2
10
3 99.2 100.0 103.0 121.6 131.9
10
3 99.2 99.9 102.7 101.1 5.4
Vflow
ml/min
230.9
231.8
231.8
230.5
232.5
235.9
230.5
229.1
229.8
228.8
vjets
m/s
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.6
2.7
2.6
Pr
1.71
1.70
1.68
1.66
1.65
1.64
1.61
1.59
1.58
1.75
h
W/cm2 oC
2.82
2.80
2.92
3.13
3.25
3.44
4.11
4.94
5.89
2.82
Xair
-5.3%
-4.7%
-3.4%
-1.7%
-1.0%
-0.9%
-0.8%
-0.9%
-0.9%
-0.7%
PsatA TsatA
105.3
104.8
103.4
101.8
101.1
100.9
101.0
101.0
101.2
100.8
99.6
99.6
99.6
99.6
99.6
99.6
99.7
99.7
99.7
99.7
Re
7.22
7.16
7.46
8.00
8.30
8.78
10.48
12.58
15.00
7.22
1609.2
1626.9
1642.0
1650.7
1676.0
1709.4
1693.0
1702.8
1724.3
1560.1
Nu
Re
4.80
5.19
5.32
5.37
6.27
7.60
9.21
11.25
1537.6
1556.8
1576.6
1600.0
1638.6
1667.6
1689.7
1707.3
s/dn Pamb
kPa
17.3 100.0
17.3 100.0
17.3 100.0
17.3 100.0
17.3 100.0
17.3 100.0
17.3 100.2
17.3 100.2
17.3 100.3
17.3 100.1
188
Nu
Table C.21
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 92.4 92.5
10
3 92.7 92.6
10
3 92.5 92.6
10
3 92.0 92.5
10
3 92.2 92.6
10
3 92.5 92.7
10
3 92.6 92.9
10
3 92.8 93.1
Pjets
kPa
103.1
103.2
103.1
103.2
103.3
103.3
103.4
103.1
Tw
qw
o
C W/cm2
101.6 17.1
103.5 21.8
106.0 28.2
109.3 36.3
114.1 53.6
117.5 74.6
120.2 99.3
122.3 130.1
Vflow
ml/min
232.7
233.1
233.3
233.5
233.5
233.5
233.5
233.6
vjets
m/s
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
Pr
1.81
1.79
1.77
1.74
1.70
1.67
1.64
1.62
h
W/cm2 oC
1.87
2.02
2.08
2.10
2.45
2.98
3.61
4.41
Xair
22.9%
22.7%
22.6%
22.9%
22.7%
22.5%
22.1%
21.5%
PsatA TsatA
77.2
77.3
77.4
77.1
77.3
77.6
78.1
78.7
99.6
99.6
99.6
99.6
99.6
99.7
99.7
99.7
s/dn Pamb
kPa
17.3 100.0
17.3 100.0
17.3 100.0
17.3 100.0
17.3 100.0
17.3 100.1
17.3 100.2
17.3 100.2
Table C.22
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 66.1 65.0
10
3 65.4 65.3
10
3 65.6 65.2
10
3 65.7 65.1
10
3 65.6 64.8
10
3 65.7 64.7
10
3 66.1 64.7
10
3 66.3 64.9
10
3 66.5 64.0
Pjets
kPa
103.1
103.2
103.3
103.2
103.4
103.4
103.6
103.7
103.5
Tw
qw
o
C W/cm2
71.3
9.6
72.7 13.2
76.0 18.3
78.6 22.7
86.9 37.8
97.0 56.5
106.1 75.9
115.7 100.7
120.4 128.4
Vflow
ml/min
228.8
228.7
228.9
228.6
228.4
227.9
227.6
227.6
227.4
vjets
m/s
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
Pr
2.62
2.61
2.54
2.49
2.35
2.20
2.07
1.95
1.89
h
W/cm2 oC
1.86
1.79
1.76
1.77
1.77
1.81
1.90
2.04
2.38
Xair
PsatA TsatA
75.1%
74.8%
74.8%
75.0%
75.3%
75.5%
75.4%
75.2%
76.2%
25.0
25.3
25.2
25.1
24.8
24.6
24.7
24.9
23.9
99.7
99.7
99.7
99.7
99.7
99.7
99.7
99.8
99.8
189
Nu
Re
4.90
4.73
4.64
4.64
4.63
4.70
4.91
5.26
6.13
1090.1
1094.7
1120.5
1139.3
1198.0
1270.2
1339.5
1412.8
1449.0
s/dn Pamb
kPa
17.3 100.3
17.3 100.3
17.3 100.3
17.3 100.3
17.3 100.3
17.3 100.4
17.3 100.4
17.3 100.5
17.3 100.6
Nu
Re
Table C.23
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
s
Tjets
o
mm mm
C
10
3
99.2
10
3
99.3
10
3
99.3
10
3
99.2
10
3
99.4
10
3
98.9
10
3
98.7
10
3
99.0
10
3
99.2
10
3
99.2
Tboxavg
o
C
100.3
100.2
100.2
100.2
100.2
100.2
100.2
100.3
100.3
100.3
Pjets
kPa
102.9
102.6
102.7
102.7
102.5
102.6
102.6
102.7
102.9
102.6
Tw
o
qw
Vflow
2
C W/cm
104.6 11.5
106.2 16.2
107.6 20.3
109.8 26.2
111.7 33.5
113.6 40.9
115.5 50.8
118.8 71.4
121.3 95.7
123.7 127.4
vjets
Pr
h
Xair
PsatA
TsatA
s/dn
Pamb
17.3
17.3
17.3
17.3
17.3
17.3
17.3
17.3
17.3
17.3
kPa
100.2
100.2
100.2
100.2
100.1
100.1
100.1
100.2
100.2
100.3
2o
ml/min m/s
W/cm C
232.8 2.7 1.72
2.11
-2.1% 102.3 99.7 5.41 1614.4
232.9 2.7 1.70
2.33
-2.0% 102.2 99.7 5.95 1628.2
232.6 2.7 1.69
2.43
-2.0% 102.2 99.7 6.21 1637.4
231.8 2.7 1.67
2.48
-2.0% 102.1 99.7 6.34 1646.9
230.9 2.7 1.66
2.71
-2.0% 102.2 99.7 6.93 1657.8
232.2 2.7 1.64
2.79
-2.0% 102.1 99.7 7.12 1677.7
232.6 2.7 1.63
3.02
-2.1% 102.2 99.7 7.70 1694.2
232.4 2.7 1.60
3.60
-2.1% 102.3 99.7 9.19 1720.5
231.7 2.7 1.58
4.32
-2.1% 102.3 99.7 11.01 1736.3
230.9 2.7 1.56
5.19
-2.1% 102.3 99.7 13.23 1748.8
Table C.24
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
s
qw
o
o
mm mm oC
C
kPa
C W/cm2
10
3 99.5 100.4 104.5 104.3 10.1
10
3 99.5 100.4 104.7 105.8 15.0
10
3 99.6 100.4 104.7 107.3 19.9
10
3 99.6 100.4 105.1 109.4 26.7
10
3 99.6 100.3 105.2 111.7 34.6
10
3 99.6 100.4 105.3 115.0 50.6
10
3 99.6 100.4 105.6 118.8 72.3
10
3 99.7 100.4 106.2 123.7 129.0
Vflow
ml/min
233.2
233.7
233.2
232.9
232.6
232.1
231.6
230.9
vjets
m/s
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
Pr
1.72
1.71
1.69
1.67
1.65
1.63
1.60
1.56
h
W/cm2 oC
2.09
2.39
2.56
2.73
2.88
3.28
3.77
5.39
Xair
-2.4%
-2.4%
-2.4%
-2.4%
-2.3%
-2.3%
-2.4%
-2.4%
PsatA TsatA
102.8
102.7
102.6
102.6
102.6
102.6
102.7
102.8
99.7
99.7
99.7
99.7
99.7
99.7
99.7
99.7
Nu
Re
5.35
6.12
6.55
6.98
7.35
8.37
9.61
13.73
1617.1
1632.2
1641.1
1655.8
1671.3
1693.6
1719.6
1752.5
Nu
Re
7.50
8.13
8.56
9.08
9.54
10.03
11.00
12.18
14.29
2498.5
2508.4
2520.7
2534.8
2556.6
2584.0
2632.2
2679.1
2713.0
s/dn Pamb
kPa
17.3 100.3
17.3 100.2
17.3 100.2
17.3 100.2
17.3 100.2
17.3 100.3
17.3 100.3
17.3 100.4
190
Table C.25
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
s
qw
o
o
mm mm oC
C
kPa
C W/cm2
10
3 99.7 100.3 114.2 103.7 11.6
10
3 99.6 100.3 114.1 104.6 16.0
10
3 99.5 100.3 114.2 105.7 21.0
10
3 99.5 100.3 114.6 107.2 27.4
10
3 99.4 100.3 114.6 108.9 35.4
10
3 99.0 100.3 114.7 112.4 52.5
10
3 99.1 100.3 114.5 116.4 74.3
10
3 99.3 100.3 114.6 120.0 99.0
10
3 99.6 100.3 114.5 122.7 129.6
Vflow
ml/min
361.0
361.1
361.1
360.6
360.9
359.5
359.3
359.5
359.2
vjets
m/s
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.1
Pr
1.72
1.72
1.71
1.69
1.68
1.65
1.62
1.59
1.57
h
W/cm2 oC
2.93
3.18
3.35
3.55
3.73
3.93
4.31
4.78
5.61
Xair
-2.0%
-2.1%
-2.0%
-2.1%
-2.1%
-2.1%
-2.1%
-2.1%
-2.1%
PsatA TsatA
102.4
102.3
102.3
102.3
102.4
102.4
102.4
102.4
102.4
99.7
99.7
99.7
99.7
99.7
99.7
99.7
99.7
99.7
s/dn Pamb
kPa
17.3 100.3
17.3 100.3
17.3 100.3
17.3 100.3
17.3 100.3
17.3 100.3
17.3 100.3
17.3 100.3
17.3 100.3
Table C.26
191
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 92.0 92.2
10
3 92.0 92.0
10
3 92.2 92.0
10
3 92.4 92.0
10
3 92.6 92.1
10
3 92.5 92.0
10
3 92.5 92.0
10
3 92.5 91.9
10
3 92.2 92.1
10
3 92.2 92.2
10
3 92.3 92.4
Pjets
kPa
110.9
111.0
111.2
111.1
111.1
111.3
110.9
110.6
111.1
110.9
111.0
Tw
qw
o
C W/cm2
95.6 11.2
96.5 13.4
98.0 16.9
99.9 21.8
101.8 27.7
103.4 33.1
106.0 41.1
110.7 58.1
115.6 80.3
118.8 104.0
122.1 135.4
Vflow
ml/min
360.6
361.0
361.2
361.2
361.1
361.4
361.2
361.3
361.4
361.3
360.5
vjets
m/s
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
Pr
1.88
1.87
1.85
1.83
1.81
1.80
1.77
1.73
1.68
1.66
1.63
h
W/cm2 oC
3.04
2.96
2.92
2.90
3.01
3.03
3.05
3.20
3.43
3.90
4.54
Xair
23.2%
23.9%
23.9%
23.8%
23.8%
24.0%
24.0%
23.9%
23.6%
23.2%
23.1%
PsatA TsatA
76.3
75.7
75.7
75.6
75.9
75.5
75.5
75.4
75.8
76.3
76.6
99.4
99.5
99.5
99.4
99.5
99.4
99.4
99.4
99.4
99.5
99.5
Nu
Re
7.83
7.62
7.51
7.44
7.71
7.78
7.81
8.19
8.77
9.97
11.59
2306.0
2319.5
2341.0
2366.2
2390.2
2411.0
2440.1
2498.5
2554.2
2592.1
2627.5
Nu
Re
8.56
8.43
8.12
7.63
7.46
7.72
7.88
8.19
8.93
10.08
11.22
2320.8
2339.0
2357.3
2379.0
2385.2
2407.7
2433.3
2494.0
2549.3
2602.2
2631.5
s/dn Pamb
kPa
17.3 99.3
17.3 99.4
17.3 99.5
17.3 99.2
17.3 99.5
17.3 99.3
17.3 99.3
17.3 99.1
17.3 99.2
17.3 99.4
17.3 99.6
Table C.27
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 92.3 91.5
10
3 92.6 91.5
10
3 92.7 91.4
10
3 92.5 91.4
10
3 92.3 91.4
10
3 92.3 91.4
10
3 92.4 91.9
10
3 92.4 91.8
10
3 92.5 92.0
10
3 92.7 92.0
10
3 92.3 92.4
Pjets
kPa
109.3
109.6
109.3
109.4
109.1
109.1
109.0
108.9
109.0
109.5
109.8
Tw
qw
o
C W/cm2
95.4 10.3
96.5 13.0
97.8 16.1
99.6 21.1
101.2 25.8
103.1 32.4
105.5 40.4
110.3 57.3
114.9 78.2
119.2 104.5
122.4 132.3
Vflow
ml/min
362.6
363.0
363.3
363.5
361.8
361.9
361.3
361.6
361.3
361.2
360.5
vjets
m/s
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
Pr
1.88
1.87
1.85
1.83
1.82
1.80
1.78
1.73
1.69
1.65
1.63
h
W/cm2 oC
3.33
3.28
3.16
2.97
2.91
3.01
3.08
3.20
3.49
3.95
4.40
Xair
25.3%
25.2%
25.3%
25.3%
25.3%
25.1%
23.6%
23.7%
23.4%
23.5%
22.4%
PsatA TsatA
74.2
74.3
73.8
73.9
73.8
73.9
75.3
75.1
75.5
75.6
76.8
99.5
99.4
99.3
99.3
99.3
99.3
99.2
99.2
99.2
99.3
99.3
s/dn Pamb
kPa
17.3 99.4
17.3 99.3
17.3 98.8
17.3 98.9
17.3 98.8
17.3 98.7
17.3 98.5
17.3 98.4
17.3 98.5
17.3 98.8
17.3 99.0
Table C.28
192
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 81.8 80.5
10
3 82.0 82.0
10
3 82.0 81.9
10
3 82.2 82.5
10
3 81.9 81.9
10
3 82.0 81.9
10
3 81.8 80.6
10
3 81.6 81.0
10
3 81.4 80.9
10
3 81.6 81.0
10
3 81.8 81.1
Pjets
kPa
109.9
109.9
110.0
109.9
110.3
110.3
110.4
110.4
110.6
110.6
110.7
Tw
qw
o
C W/cm2
85.3 10.6
86.6 13.5
88.0 16.9
90.1 21.7
92.0 26.9
94.8 33.6
97.9 42.1
103.1 58.4
109.2 78.3
116.0 102.5
120.5 129.5
Vflow
ml/min
359.2
359.3
359.7
359.9
360.2
359.8
359.8
359.7
359.2
359.2
358.7
vjets
m/s
4.1
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.1
4.1
4.1
Pr
2.13
2.11
2.09
2.06
2.04
2.01
1.97
1.91
1.85
1.78
1.73
h
W/cm2 oC
3.02
2.90
2.81
2.74
2.67
2.64
2.62
2.72
2.82
2.98
3.34
Xair
51.1%
48.1%
48.4%
47.1%
48.4%
48.4%
51.1%
50.4%
50.5%
50.5%
50.3%
PsatA TsatA
48.3
51.3
51.1
52.3
51.1
51.2
48.5
49.3
49.2
49.3
49.5
99.3
99.3
99.3
99.3
99.4
99.4
99.4
99.4
99.4
99.5
99.5
Nu
Re
7.84
7.51
7.28
7.09
6.90
6.82
6.75
7.01
7.25
7.63
8.56
2054.3
2072.7
2090.4
2118.5
2140.8
2172.2
2205.7
2264.8
2333.2
2416.9
2468.7
Nu
Re
8.19
7.81
8.04
8.49
8.81
8.79
9.00
9.40
10.27
11.12
12.55
2393.7
2396.4
2422.9
2445.2
2459.4
2477.5
2501.2
2548.5
2603.6
2648.6
2677.7
s/dn Pamb
kPa
17.3 98.8
17.3 98.8
17.3 99.0
17.3 99.0
17.3 99.1
17.3 99.2
17.3 99.1
17.3 99.3
17.3 99.3
17.3 99.5
17.3 99.6
Table C.29
dn
μm
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
173.6
z
s
Tjets Tboxavg
o
mm mm oC
C
10
3 96.2 96.5
10
3 96.0 96.2
10
3 96.3 95.9
10
3 96.5 96.0
10
3 96.5 95.9
10
3 96.4 95.9
10
3 96.5 95.8
10
3 96.5 95.9
10
3 96.5 96.0
10
3 96.6 96.1
10
3 96.4 96.0
Pjets
kPa
109.3
109.2
109.4
109.7
109.3
109.2
108.9
109.1
109.4
109.5
109.5
Tw
qw
o
C W/cm2
99.4 10.2
100.1 12.7
101.3 15.5
102.5 20.0
103.8 25.2
105.6 31.7
107.7 39.5
111.9 56.5
116.3 79.5
120.2 103.0
123.0 130.9
Vflow
ml/min
359.5
358.9
360.2
361.0
360.6
360.4
360.1
359.6
359.8
359.5
359.1
vjets
m/s
4.2
4.1
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.1
Pr
1.80
1.79
1.78
1.77
1.75
1.74
1.72
1.68
1.64
1.61
1.59
h
W/cm2 oC
3.19
3.05
3.14
3.31
3.44
3.43
3.52
3.68
4.02
4.36
4.92
Xair
10.3%
11.2%
12.0%
12.0%
12.1%
12.0%
12.0%
11.7%
11.9%
11.3%
11.7%
PsatA TsatA
89.2
88.3
87.5
87.5
87.2
87.4
87.1
87.5
87.6
88.1
87.8
99.5
99.5
99.5
99.5
99.4
99.4
99.4
99.4
99.5
99.4
99.5
s/dn Pamb
kPa
17.3 99.4
17.3 99.5
17.3 99.5
17.3 99.4
17.3 99.2
17.3 99.3
17.3 99.0
17.3 99.1
17.3 99.4
17.3 99.3
17.3 99.4
C.2 Closed system - high heat flux data
Table C.30
dn
193
μm
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
z
s
Tjets Tboxavg
o
Pjets
o
Tw
o
mm mm C
C
kPa
C
10 1 16.0 20.0 172.2 36.9
10 1 16.1 20.0 173.1 44.2
10 1 16.6 19.9 173.6 57.3
10 1 16.9 19.8 173.6 67.4
10 1 16.7 20.2 175.1 78.9
10 1 18.1 22.7 174.7 89.5
10 1 17.7 24.2 175.3 98.8
10 1 17.2 24.4 176.2 107.1
qw
Vflow
2
W/cm
133.5
192.0
299.7
385.8
486.4
564.5
654.7
721.2
ml/min
1760.3
1764.0
1764.1
1762.7
1765.9
1755.2
1764.2
1771.9
vjets
m/s
6.68
6.69
6.69
6.69
6.70
6.66
6.69
6.72
Pr
h
Xair
Psat
2o
5.90
5.40
4.63
4.16
3.72
3.33
3.09
2.90
Tsat
Nu
Re
s/dn Pamb
o
W/cm C
kPa
C
6.38
97.7% 2.34 99.6 12.43 917.4 8.4
6.82
97.7% 2.33 99.6 13.16 994.5 8.4
7.36
97.7% 2.32 99.7 13.98 1139.8 8.4
7.64
97.7% 2.31 99.9 14.37 1253.3 8.4
7.82
97.7% 2.37 100.0 14.55 1386.0 8.4
7.91
97.3% 2.75 100.3 14.56 1517.4 8.4
8.07
97.1% 3.02 100.5 14.76 1630.3 8.4
8.02
97.1% 3.05 100.6 14.59 1733.2 8.4
kPa
99.8
99.9
100.3
100.8
101.3
102.5
103.3
103.6
Table C.31
dn
μm
118.7
118.7
118.7
118.7
z
s
Tjets Tboxavg
o
o
Pjets
Tw
o
mm mm C
C
kPa
C
10 1 16.0 20.4 111.6 66.8
10 1 15.9 20.2 111.6 85.6
10 1 16.0 20.6 111.8 101.2
10 1 16.1 23.8 113.4 122.7
qw
Vflow
2
W/cm
131.1
194.8
258.0
350.0
ml/min
611.6
609.1
608.2
604.7
vjets
m/s
2.32
2.31
2.31
2.29
Pr
h
Xair
2o
4.22
3.52
3.07
2.59
Psat
Tsat
Nu
Re
s/dn Pamb
o
W/cm C
kPa
C
2.58
97.6% 2.39 99.8 4.86
2.79
97.6% 2.37 99.8 5.17
3.03
97.6% 2.43 100.0 5.53
3.28
97.1% 2.95 100.4 5.91
429.2
501.8
565.2
653.2
8.4
8.4
8.4
8.4
kPa
100.4
100.6
101.2
102.6
Table C.32
dn
μm
118.7
118.7
118.7
118.7
118.7
118.7
118.7
z
s
Tjets Tboxavg
o
Pjets
o
Tw
o
mm mm C
C
kPa
C
10 1 16.0 18.6 128.3 45.1
10 1 15.8 18.5 129.1 58.6
10 1 16.1 18.8 128.8 71.1
10 1 16.6 21.3 129.6 89.9
10 1 16.6 23.1 130.4 104.4
10 1 17.0 26.4 131.4 117.0
10 1 16.2 29.3 133.0 130.5
qw
Vflow
2
W/cm
146.2
216.4
281.0
370.3
448.0
511.9
614.3
ml/min
1035.7
1030.1
1022.7
1015.2
1016.8
1013.8
1016.2
vjets
m/s
3.93
3.91
3.88
3.85
3.86
3.85
3.86
Pr
h
Xair
Psat
2o
5.35
4.61
4.04
3.37
2.98
2.69
2.45
Tsat
Nu
Re
s/dn Pamb
o
W/cm C
kPa
C
5.01
97.8% 2.15 99.4 9.66 588.8 8.4
5.06
97.9% 2.13 99.6 9.61 668.9 8.4
5.11
97.8% 2.17 99.7 9.57 746.6 8.4
5.05
97.5% 2.53 100.1 9.32 869.5 8.4
5.10
97.2% 2.82 100.3 9.30 971.8 8.4
5.12
96.7% 3.44 100.6 9.24 1060.9 8.4
5.37
96.1% 4.09 100.9 9.63 1154.9 8.4
kPa
99.4
99.8
100.3
101.7
102.4
103.4
104.8
194
Table C.33
dn
μm
118.7
118.7
118.7
118.7
118.7
118.7
z
s
Tjets Tboxavg
o
o
Pjets
Tw
o
qw
Vflow
2
mm mm C
C
kPa
C W/cm ml/min
10 1 16.3 18.6 172.1 36.4 125.5 1753.4
10 1 17.3 19.9 171.6 65.1 350.1 1739.9
10 1 18.9 27.1 172.3 86.9 549.5 1724.0
10 1 17.9 33.6 175.9 102.8 714.3 1742.3
10 1 17.8 39.0 178.4 119.7 839.4 1745.0
10 1 19.7 38.5 177.0 114.4 791.9 1724.3
vjets
m/s
6.65
6.60
6.54
6.61
6.62
6.54
Pr
h
Xair
2o
5.92
4.23
3.39
2.98
2.62
2.69
Psat
Tsat
o
Nu
Re
s/dn Pamb
W/cm C
kPa
C
6.25
97.9% 2.14 99.8 12.17 911.1 8.4
7.32
97.7% 2.32 100.2 13.79 1217.5 8.4
8.07
96.6% 3.58 101.0 14.89 1469.1 8.4
8.41
95.1% 5.20 101.4 15.34 1661.4 8.4
8.24
93.6% 6.98 102.1 14.85 1869.5 8.4
8.37
93.8% 6.81 102.1 15.11 1804.9 8.4
kPa
100.6
102.0
104.9
106.7
109.0
109.2
Table C.34
dn
μm
118.7
118.7
118.7
118.7
z
s
Tjets Tboxavg
o
Pjets
o
Tw
o
mm mm C
C
kPa
C
10 1 16.3 19.0 174.5 45.6
10 1 16.7 18.9 174.3 65.8
10 1 17.1 21.1 173.8 82.8
10 1 19.1 36.4 176.6 108.7
qw
Vflow
2
W/cm
200.4
374.6
535.5
748.7
ml/min
1779.7
1772.6
1758.8
1732.2
vjets
m/s
6.75
6.73
6.67
6.57
Pr
h
Xair
Psat
2o
5.30
4.23
3.57
2.82
Tsat
Nu
Re
s/dn Pamb
o
W/cm C
kPa
C
6.84
97.8% 2.19 99.8 13.18
7.62
97.8% 2.19 100.0 14.36
8.15
97.6% 2.51 100.3 15.10
8.35
94.4% 6.08 101.8 15.15
1020.7
1240.3
1430.2
1737.6
8.4
8.4
8.4
8.4
kPa
100.8
101.2
102.4
108.0
Table C.35
dn
195
μm
118.7
118.7
118.7
118.7
118.7
118.7
118.7
118.7
z
s
Tjets Tboxavg
Pjets
Tw
qw
Vflow
vjets
Pr
h
o
o
mm mm oC
C
kPa
C W/cm2 ml/min m/s
W/cm2 oC
10 1 16.6 22.0 128.3 38.2 110.0 1027.7 3.90 5.77
5.10
10 1 16.9 22.0 127.7 71.9 297.3 1012.8 3.84 3.97
5.40
10 1 17.0 23.3 128.5 89.3 392.4 1006.9 3.82 3.37
5.43
10 1 17.8 25.7 128.5 105.7 456.9 1007.6 3.82 2.92
5.20
10 1 17.6 28.9 130.6 121.5 538.5 1006.6 3.82 2.59
5.18
10 1 17.4 31.2 131.8 132.8 608.1 1006.2 3.82 2.39
5.27
10 1 17.7 36.3 133.7 139.1 703.9 1010.3 3.83 2.28
5.80
10 1 17.0 41.1 135.2 144.1 765.1 1000.3 3.80 2.22
6.02
Xair
Psat
97.3%
97.4%
97.2%
96.8%
96.1%
95.6%
94.3%
92.8%
kPa
2.65
2.65
2.85
3.30
3.99
4.54
6.03
7.81
Tsat
Nu
Re
s/dn Pamb
o
C
99.6
99.6
99.8
100.1
100.4
100.8
101.3
101.9
9.90
10.12
10.01
9.45
9.33
9.42
10.34
10.71
546.2
749.9
861.6
980.2
1090.1
1169.3
1221.5
1241.3
8.4
8.4
8.4
8.4
8.4
8.4
8.4
8.4
kPa
99.9
99.9
100.6
101.7
102.8
104.2
106.2
108.3
Table C.36
dn
196
μm
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
z
s
Tjets Tboxavg
o
mm mm C
10
3 20.8
10
3 20.8
10
3 20.6
10
3 20.2
10
3 20.5
10
3 20.5
10
3 20.1
10
3 20.6
10
3 20.5
10
3 20.6
10
3 20.1
10
3 20.4
10
3 20.2
10
3 20.4
10
3 20.2
10
3 20.7
10
3 20.0
10
3 20.5
10
3 20.0
o
C
36.4
36.7
36.2
35.6
36.7
37.1
35.3
37.1
37.1
36.9
36.6
36.5
35.8
36.1
36.9
37.5
37.1
38.0
36.9
Pjets
kPa
125.3
124.5
125.6
124.3
125.1
125.4
124.5
125.0
125.1
124.9
123.1
124.2
123.5
124.2
124.2
124.5
124.1
123.9
123.5
Tw
o
C
24.7
46.6
49.6
62.6
79.5
88.4
98.3
108.7
116.9
127.1
131.2
132.3
137.0
137.8
139.7
141.3
142.6
141.7
192.1
qw
Vflow
2
vjets
Pr
h
Xair
2o
Psat
Tsat
Nu
Re
s/dn Pamb
o
W/cm ml/min m/s
W/cm C
kPa
C
0.2
213.6 1.07 6.50
0.04
94.9% 6.08 104.5 0.17 300.3
10.8 214.2 1.08 4.97
0.42
94.8% 6.18 104.7 1.78 381.8
15.6 214.1 1.08 4.82
0.54
95.0% 6.01 104.8 2.27 391.9
22.7 213.7 1.07 4.22
0.53
95.1% 5.82 104.7 2.23 440.8
32.9 214.6 1.08 3.57
0.56
94.8% 6.18 104.8 2.29 512.9
41.0 214.1 1.08 3.30
0.60
94.7% 6.32 104.8 2.46 549.2
54.0 214.5 1.08 3.04
0.69
95.2% 5.71 104.7 2.79 590.9
63.2 215.3 1.08 2.79
0.72
94.7% 6.30 104.8 2.88 640.8
72.7 215.4 1.08 2.62
0.75
94.7% 6.31 104.6 3.02 677.3
85.4 214.9 1.08 2.43
0.80
94.8% 6.25 104.8 3.19 722.0
95.4 215.5 1.08 2.37
0.86
94.8% 6.15 104.6 3.40 740.2
110.6 216.9 1.09 2.35
0.99
94.9% 6.10 104.8 3.91 752.0
165.9 217.9 1.10 2.28
1.42
95.1% 5.87 104.8 5.61 776.4
169.1 218.4 1.10 2.26
1.44
95.0% 5.99 104.8 5.68 782.6
195.6 218.3 1.10 2.24
1.64
94.8% 6.22 104.8 6.45 790.3
223.5 219.1 1.10 2.20
1.85
94.6% 6.43 104.8 7.30 803.1
253.5 219.1 1.10 2.20
2.07
94.7% 6.31 104.8 8.15 805.4
267.6 219.2 1.10 2.20
2.21
94.5% 6.62 104.8 8.70 804.1
163.8 219.2 1.10 1.65
0.95
94.8% 6.24 104.6 3.68 1043.2
11.4
11.4
11.4
11.4
11.4
11.4
11.4
11.4
11.4
11.4
11.4
11.4
11.4
11.4
11.4
11.4
11.4
11.4
11.4
kPa
118.9
119.8
119.9
119.5
119.8
119.8
119.8
119.9
119.2
119.9
119.3
119.8
119.9
119.8
119.8
120.0
119.9
120.1
119.2
Table C.37
dn
197
μm
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
z
s
Tjets Tboxavg
o
mm mm C
10
3 20.0
10
3 20.3
10
3 20.3
10
3 20.5
10
3 20.6
10
3 20.7
10
3 20.2
10
3 20.7
10
3 20.7
10
3 20.3
10
3 20.7
10
3 20.7
10
3 20.6
10
3 20.4
10
3 20.8
10
3 20.6
10
3 20.4
10
3 20.3
10
3 20.7
o
C
35.9
36.0
35.4
35.9
37.2
36.8
35.4
37.4
36.9
36.7
36.0
37.3
36.6
37.2
36.4
36.7
36.2
36.5
36.7
Pjets
kPa
135.4
134.9
134.3
134.9
135.4
135.6
133.9
135.3
135.6
135.3
134.2
134.5
134.4
135.0
135.0
134.6
135.0
134.7
134.0
Tw
o
C
24.1
31.8
34.6
40.8
48.0
53.3
60.1
67.5
74.4
80.8
86.8
91.9
101.8
119.0
140.6
143.9
145.3
144.6
146.6
qw
Vflow
2
vjets
Pr
h
Xair
2o
Psat
Tsat
o
Nu
Re
s/dn Pamb
W/cm ml/min m/s
W/cm C
kPa
C
kPa
0.3
343.2 1.73 6.62
0.08
95.1% 5.90 104.6 0.33 474.8 11.4 119.3
10.9 343.3 1.73 5.97
0.94
95.0% 5.94 104.5 4.06 520.5 11.4 118.9
15.2 343.7 1.73 5.76
1.06
95.2% 5.74 104.4 4.57 537.7 11.4 118.5
24.7 343.1 1.73 5.34
1.22
95.0% 5.92 104.5 5.22 574.2 11.4 118.9
35.0 342.6 1.72 4.91
1.28
94.7% 6.33 104.8 5.41 617.5 11.4 119.8
45.8 343.6 1.73 4.63
1.41
94.8% 6.20 104.7 5.91 652.9 11.4 119.7
57.2 342.7 1.72 4.33
1.44
95.2% 5.76 104.7 6.00 690.6 11.4 119.6
69.8 343.3 1.73 4.00
1.49
94.6% 6.42 104.8 6.18 742.4 11.4 119.8
82.3 341.0 1.72 3.74
1.53
94.8% 6.23 104.7 6.33 782.4 11.4 119.7
94.7 343.1 1.73 3.54
1.57
94.8% 6.19 104.8 6.42 827.2 11.4 119.9
105.8 342.8 1.72 3.34
1.60
95.0% 5.95 104.4 6.52 869.7 11.4 118.4
114.8 343.3 1.73 3.19
1.61
94.7% 6.37 104.8 6.55 905.7 11.4 119.9
132.3 343.8 1.73 2.95
1.63
94.9% 6.14 104.7 6.58 974.1 11.4 119.5
169.7 343.3 1.73 2.58
1.72
94.7% 6.35 104.8 6.86 1093.5 11.4 119.9
226.0 342.4 1.72 2.21
1.89
94.9% 6.06 104.7 7.43 1249.9 11.4 119.7
280.1 342.1 1.72 2.17
2.27
94.9% 6.16 104.7 8.93 1272.1 11.4 119.7
329.4 342.8 1.72 2.15
2.64
95.0% 5.99 104.8 10.37 1282.9 11.4 119.8
385.2 348.0 1.75 2.16
3.10
94.9% 6.11 104.8 12.20 1297.0 11.4 120.0
403.4 346.2 1.74 2.13
3.20
94.9% 6.17 104.8 12.60 1307.4 11.4 119.9
Table C.38
dn
198
μm
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
z
s
Tjets Tboxavg
o
mm mm C
10
3 20.5
10
3 20.4
10
3 20.7
10
3 20.8
10
3 20.6
10
3 20.4
10
3 20.4
10
3 20.9
10
3 20.5
10
3 20.6
10
3 20.9
10
3 20.8
10
3 20.8
10
3 20.6
10
3 21.2
10
3 20.7
10
3 21.0
10
3 21.2
10
3 20.9
10
3 21.5
10
3 21.4
o
C
35.7
35.3
35.4
35.9
36.7
36.3
35.8
36.9
36.4
36.7
36.0
36.2
37.4
36.1
36.8
37.1
37.3
36.7
35.8
37.1
36.5
Pjets
kPa
161.4
162.1
161.6
161.4
162.0
161.6
161.5
162.4
162.4
163.1
162.6
161.3
162.3
161.6
162.1
162.8
162.3
162.0
162.1
163.1
161.7
Tw
o
C
30.3
32.4
36.9
41.8
46.7
52.1
57.3
62.9
67.7
73.0
76.7
79.7
99.3
108.5
119.3
137.7
146.2
147.0
149.0
148.9
148.0
qw
Vflow
2
vjets
Pr
h
Xair
2o
Psat
Tsat
o
Nu
Re
s/dn Pamb
W/cm ml/min m/s
W/cm C
kPa
C
kPa
13.4 559.5 2.81 6.06
1.37
95.1% 5.85 104.5 5.94 836.3 11.4 118.9
17.9 560.4 2.82 5.92
1.49
95.2% 5.72 104.6 6.42 856.1 11.4 119.0
27.4 561.3 2.82 5.57
1.70
95.2% 5.74 104.5 7.28 904.0 11.4 118.9
36.6 560.0 2.82 5.25
1.74
95.0% 5.90 104.5 7.42 950.8 11.4 118.6
46.9 560.1 2.82 4.98
1.79
94.8% 6.16 104.7 7.60 996.5 11.4 119.3
59.7 559.2 2.81 4.70
1.88
94.9% 6.03 104.6 7.94 1047.8 11.4 119.0
72.5 559.6 2.82 4.45
1.97
95.1% 5.87 104.7 8.24 1100.4 11.4 119.7
85.5 560.6 2.82 4.17
2.03
94.8% 6.25 104.7 8.48 1166.7 11.4 119.8
96.7 562.6 2.83 4.00
2.05
94.9% 6.09 104.6 8.51 1216.8 11.4 119.3
110.9 561.0 2.82 3.79
2.12
94.8% 6.18 104.8 8.74 1271.3 11.4 119.8
120.1 560.2 2.82 3.65
2.15
95.0% 5.95 104.7 8.86 1312.6 11.4 119.5
126.4 560.0 2.82 3.55
2.15
95.0% 6.00 104.6 8.80 1344.3 11.4 118.9
175.9 561.2 2.82 3.00
2.24
94.6% 6.42 104.8 9.06 1565.2 11.4 119.8
201.1 559.7 2.82 2.79
2.29
95.0% 5.96 104.7 9.19 1663.0 11.4 119.4
227.6 557.6 2.80 2.56
2.32
94.8% 6.19 104.8 9.25 1789.5 11.4 119.8
270.5 561.5 2.82 2.26
2.31
94.7% 6.31 104.7 9.13 2014.0 11.4 119.7
329.5 560.3 2.82 2.13
2.63
94.7% 6.36 104.8 10.35 2115.1 11.4 119.8
375.0 559.0 2.81 2.12
2.98
94.8% 6.18 104.8 11.71 2123.3 11.4 119.8
430.0 556.8 2.80 2.09
3.36
95.1% 5.87 104.8 13.18 2135.2 11.4 119.9
477.8 561.4 2.82 2.09
3.75
94.7% 6.32 104.8 14.72 2157.7 11.4 119.9
523.2 562.5 2.83 2.10
4.13
94.9% 6.11 104.8 16.22 2150.9 11.4 119.8
Table C.39
199
dn
μm
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
z
s Tjets Tboxavg
o
mm mm oC
C
10
3 21.1 35.2
10
3 21.1 35.8
10
3 21.2 35.5
10
3 21.5 35.4
10
3 21.7 35.7
10
3 21.6 35.8
10
3 21.2 35.7
10
3 21.7 36.1
10
3 21.4 34.8
10
3 21.7 35.9
10
3 21.6 35.5
10
3 21.7 36.5
10
3 21.8 35.6
10
3 21.7 36.5
10
3 21.7 36.3
10
3 21.6 34.7
10
3 21.8 35.2
10
3 21.6 35.1
10
3 21.5 36.1
10
3 21.5 35.6
10
3 21.5 35.9
10
3 21.6 35.6
10
3 21.8 36.6
10
3 21.6 35.0
10
3 21.8 34.7
10
3 21.2 35.2
10
3 22.1 35.1
Pjets
kPa
214.9
216.1
215.0
214.9
215.1
215.0
214.3
214.7
213.9
214.6
213.9
215.1
214.9
214.3
213.7
213.1
213.7
215.2
214.5
213.8
214.6
214.2
215.5
213.6
213.4
214.9
214.1
Tw
C
29.5
31.5
34.6
38.2
42.3
47.1
51.2
55.1
59.1
63.2
66.7
67.2
84.0
91.1
97.2
104.9
111.3
120.4
133.3
145.2
148.4
148.8
148.6
149.1
150.4
151.8
153.3
o
qw
W/cm2
14.5
20.1
27.3
37.2
48.9
61.8
73.5
86.4
97.1
110.2
122.5
119.4
169.4
191.0
218.6
250.2
271.9
303.7
346.7
397.1
435.7
489.2
515.8
522.9
580.3
618.8
662.3
Vflow
ml/min
871.5
872.0
871.7
870.1
869.9
869.1
868.3
868.6
867.8
868.3
867.1
869.5
868.5
866.3
862.6
862.6
862.7
870.0
866.0
863.4
865.7
862.0
868.8
865.6
861.6
866.3
863.7
vjets
m/s
4.38
4.39
4.39
4.38
4.38
4.37
4.37
4.37
4.37
4.37
4.36
4.37
4.37
4.36
4.34
4.34
4.34
4.38
4.36
4.34
4.35
4.34
4.37
4.35
4.33
4.36
4.34
Pr
6.08
5.93
5.70
5.44
5.17
4.90
4.71
4.49
4.32
4.13
3.99
3.97
3.39
3.19
3.03
2.85
2.71
2.53
2.31
2.14
2.10
2.09
2.09
2.08
2.07
2.06
2.02
h
W/cm2 oC
1.75
1.93
2.05
2.22
2.36
2.43
2.45
2.59
2.57
2.65
2.71
2.63
2.72
2.75
2.90
3.00
3.04
3.07
3.10
3.21
3.43
3.85
4.07
4.10
4.51
4.74
5.05
Xair
95.2%
95.1%
95.2%
95.2%
95.1%
95.1%
95.1%
95.0%
95.3%
95.1%
95.2%
94.9%
95.2%
94.9%
94.9%
95.4%
95.2%
95.3%
95.0%
95.2%
95.1%
95.2%
94.8%
95.3%
95.4%
95.2%
95.3%
Psat
kPa
5.68
5.89
5.76
5.76
5.83
5.87
5.83
5.99
5.57
5.92
5.78
6.10
5.80
6.10
6.05
5.53
5.69
5.65
5.98
5.80
5.90
5.80
6.15
5.62
5.53
5.69
5.64
Tsat
o
C
104.6
104.7
104.6
104.5
104.7
104.7
104.7
104.7
104.5
104.7
104.6
104.6
104.8
104.8
104.8
104.6
104.7
104.7
104.7
104.7
104.7
104.7
104.7
104.8
104.8
104.7
104.8
Nu
Re
7.55
8.31
8.81
9.51
10.06
10.28
10.33
10.87
10.75
11.05
11.25
10.89
11.11
11.18
11.72
12.08
12.18
12.24
12.27
12.62
13.47
15.09
15.98
16.10
17.69
18.57
19.77
1299.2
1329.0
1376.4
1431.7
1497.4
1568.1
1624.2
1694.6
1753.0
1823.3
1877.2
1893.0
2173.3
2288.5
2383.6
2516.9
2634.4
2819.3
3040.3
3250.4
3319.1
3314.7
3340.6
3333.9
3346.4
3379.5
3416.1
s/dn Pamb
kPa
11.4 119.1
11.4 119.6
11.4 119.1
11.4 118.9
11.4 119.5
11.4 119.6
11.4 119.4
11.4 119.7
11.4 118.9
11.4 119.6
11.4 119.3
11.4 119.3
11.4 119.8
11.4 119.9
11.4 119.8
11.4 119.3
11.4 119.6
11.4 119.6
11.4 119.6
11.4 119.7
11.4 119.6
11.4 119.7
11.4 119.4
11.4 119.9
11.4 120.0
11.4 119.7
11.4 119.9
Table C.40
200
dn
μm
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
z
s Tjets Tboxavg
o
mm mm oC
C
10
3 21.7 34.8
10
3 22.0 34.5
10
3 21.5 35.4
10
3 22.0 34.5
10
3 21.6 35.0
10
3 21.6 34.5
10
3 21.8 35.1
10
3 21.7 34.7
10
3 21.5 34.7
10
3 21.5 33.9
10
3 21.6 34.9
10
3 21.6 35.8
10
3 21.6 36.3
10
3 21.5 36.1
10
3 22.2 35.2
10
3 21.6 34.8
10
3 22.3 35.2
10
3 22.4 35.4
10
3 22.5 36.1
Pjets
kPa
274.5
274.8
275.4
275.2
275.1
275.0
276.2
275.6
275.8
275.1
275.5
277.8
276.9
276.3
275.7
276.7
276.0
276.5
276.6
Tw
C
28.2
29.0
32.0
35.3
38.5
41.7
45.8
49.4
51.8
55.5
58.7
73.6
86.8
97.2
106.4
117.1
128.4
134.0
124.6
o
qw
W/cm2
14.7
16.4
25.0
35.7
45.3
55.5
70.3
81.2
90.8
104.4
115.1
171.0
220.2
263.0
298.7
342.3
385.8
408.5
369.8
Vflow
ml/min
1125.7
1126.4
1127.2
1128.1
1128.5
1128.2
1128.6
1129.0
1128.2
1129.7
1131.3
1134.2
1133.1
1130.6
1127.2
1135.2
1129.5
1131.8
1133.1
vjets
m/s
5.66
5.67
5.67
5.67
5.68
5.68
5.68
5.68
5.68
5.68
5.69
5.71
5.70
5.69
5.67
5.71
5.68
5.69
5.70
Pr
6.13
6.05
5.86
5.60
5.41
5.22
4.96
4.78
4.66
4.48
4.33
3.73
3.31
3.04
2.80
2.59
2.38
2.29
2.44
Table C.41
h
W/cm2 oC
2.25
2.33
2.40
2.68
2.67
2.76
2.92
2.93
2.99
3.08
3.11
3.29
3.37
3.48
3.54
3.58
3.64
3.66
3.62
Xair
95.3%
95.4%
95.2%
95.4%
95.3%
95.4%
95.3%
95.4%
95.4%
95.6%
95.3%
95.1%
95.0%
95.0%
95.3%
95.4%
95.2%
95.2%
95.0%
Psat
kPa
5.56
5.47
5.74
5.46
5.62
5.46
5.65
5.53
5.53
5.30
5.60
5.86
6.03
5.97
5.68
5.56
5.70
5.75
5.96
Tsat
o
C
104.6
104.4
104.6
104.6
104.6
104.6
104.7
104.6
104.7
104.7
104.7
104.8
104.8
104.8
104.7
104.8
104.6
104.7
104.6
Nu
Re
9.74
10.05
10.34
11.50
11.43
11.75
12.39
12.37
12.59
12.90
12.99
13.56
13.76
14.06
14.24
14.30
14.42
14.46
14.38
1665.4
1686.5
1735.7
1809.1
1866.0
1926.8
2015.4
2084.0
2128.8
2208.3
2280.6
2605.2
2895.0
3119.3
3338.4
3601.3
3865.2
4014.0
3792.4
s/dn Pamb
kPa
11.4 119.2
11.4 118.5
11.4 119.2
11.4 119.0
11.4 119.0
11.4 119.0
11.4 119.7
11.4 119.0
11.4 119.4
11.4 119.5
11.4 119.6
11.4 119.8
11.4 119.8
11.4 119.8
11.4 119.7
11.4 119.8
11.4 118.9
11.4 119.5
11.4 119.2
dn
z
s
Tjets Tboxavg
o
Pjets
o
Tw
qw
o
Vflow
2
μm mm mm C
C
kPa
C W/cm ml/min
69.3 10 1 16.9 20.0 163.9 63.5 103.2 299.2
69.3 10 1 16.5 23.8 162.6 94.5 188.4 291.4
69.3 10 1 16.3 27.6 166.8 113.7 264.6 302.5
69.3 10 1 16.5 35.1 166.0 126.7 362.6 300.4
69.3 10 1 16.6 41.9 169.3 131.6 407.9 314.4
69.3 10 1 16.7 45.8 167.8 133.0 412.8 307.4
vjets
m/s
3.33
3.24
3.36
3.34
3.50
3.42
Pr
h
Xair
Psat
2o
4.32
3.24
2.77
2.51
2.42
2.40
W/cm C
kPa
2.21
97.7% 2.33
2.42
97.1% 2.94
2.72
96.3% 3.69
3.29
94.3% 5.66
3.55
91.9% 8.15
3.55
89.9% 9.98
Tsat
Nu
Re
s/dn Pamb
o
C
99.6
99.6
99.6
99.6
99.6
99.4
2.44
2.59
2.88
3.45
3.71
3.71
351.8
442.5
527.5
571.9
617.7
609.6
Tsat
Nu
Re
14.4
14.4
14.4
14.4
14.4
14.4
kPa
99.9
99.9
99.9
100.0
100.0
99.3
Table C.42
dn
z
s
Tjets Tboxavg
201
o
o
Pjets
Tw
o
qw
Vflow
2
μm mm mm C
C
kPa
C W/cm
69.3 10 1 17.1 23.8 580.3 31.5 86.0
69.3 10 1 17.1 23.1 585.5 48.6 207.9
69.3 10 1 17.2 23.5 593.3 68.9 370.2
ml/min
934.7
913.2
893.5
vjets
Pr
h
Xair
2o
Psat
m/s
W/cm C
kPa
10.40 6.24
5.97
97.0% 2.95
10.16 5.07
6.59
97.2% 2.82
9.94 4.08
7.15
97.1% 2.89
o
C
99.5
99.6
99.6
s/dn Pamb
kPa
6.82 793.9 14.4 99.6
7.38 932.0 14.4 99.9
7.84 1106.0 14.4 99.9
Table C.43
dn
z
s
Tjets Tboxavg
o
Pjets
o
Tw
o
μm mm mm C
C
kPa
C
69.3 10 1 16.8 22.9 324.1 42.2
69.3 10 1 16.6 22.4 323.6 61.0
69.3 10 1 16.5 23.0 323.0 74.7
69.3 10 1 16.5 26.1 320.3 92.7
69.3 10 1 16.8 27.5 326.6 100.2
69.3 10 1 16.9 32.9 321.8 113.3
69.3 10 1 17.2 42.3 317.2 123.8
69.3 10 1 17.5 48.4 316.5 129.8
qw
Vflow
2
W/cm
101.7
196.2
275.5
373.1
419.5
498.7
587.3
666.9
ml/min
514.2
512.0
508.9
503.1
503.6
495.9
488.4
487.6
vjets
m/s
5.72
5.69
5.66
5.60
5.60
5.52
5.43
5.42
Pr
h
Xair
PsatA TsatA
2o
5.48
4.45
3.88
3.29
3.08
2.77
2.55
2.44
W/cm C
kPa
3.99
97.2% 2.79
4.42
97.3% 2.71
4.73
97.2% 2.81
4.90
96.6% 3.38
5.03
96.3% 3.68
5.17
95.0% 4.99
5.51
91.7% 8.32
5.94
88.6% 11.36
202
Nu
Re
4.50
4.89
5.17
5.26
5.37
5.47
5.79
6.22
489.9
586.6
658.6
753.6
800.4
865.5
916.4
953.1
Nu
Re
s/dn Pamb
o
C
99.6
99.6
99.6
99.6
99.6
99.6
99.6
99.6
14.4
14.4
14.4
14.4
14.4
14.4
14.4
14.4
kPa
99.9
99.9
99.9
99.9
100.0
100.0
100.0
100.0
Table C.44
dn
z
s
Tjets Tboxavg
o
o
Pjets
Tw
o
μm mm mm C
C
kPa
C
69.3 10 1 16.8 18.5 597.8 34.0
69.3 10 1 16.5 18.9 597.1 49.8
69.3 10 1 16.6 21.6 587.9 75.0
69.3 10 1 17.2 25.3 587.3 92.4
69.3 10 1 17.8 32.6 586.1 108.4
qw
Vflow
2
W/cm
102.2
215.4
405.4
557.6
713.5
ml/min
811.4
808.7
800.7
796.9
789.5
vjets
m/s
9.02
9.00
8.91
8.86
8.78
Pr
h
Xair
2o
6.06
5.04
3.87
3.28
2.85
PsatA TsatA
W/cm C
kPa
5.96
97.9% 2.13
6.48
97.8% 2.18
6.94
97.4% 2.57
7.42
96.8% 3.23
7.88
95.1% 4.92
s/dn Pamb
o
C
99.5
99.6
99.6
99.6
99.6
6.79 706.8 14.4
7.25 830.4 14.4
7.57 1039.1 14.4
7.97 1197.5 14.4
8.36 1340.8 14.4
kPa
99.4
99.9
100.0
100.0
100.0
Table C.45
dn
z
s
Tjets Tboxavg
o
Pjets
o
Tw
qw
o
Vflow
2
μm mm mm C
C
kPa
C W/cm
69.3 10 1 16.1 20.0 530.3 54.6 281.7
69.3 10 1 15.8 20.7 565.1 67.4 390.6
69.3 10 1 16.3 21.1 567.9 74.1 437.0
69.3 10 1 16.4 24.2 567.3 83.5 528.2
69.3 10 1 16.9 25.5 591.0 91.1 600.3
69.3 10 1 16.0 26.7 627.4 98.9 680.6
ml/min
963.2
929.3
910.0
881.1
888.2
876.4
vjets
m/s
10.71
10.34
10.12
9.80
9.88
9.75
Pr
h
Xair
PsatA TsatA
2o
4.79
4.20
3.91
3.58
3.32
3.13
Nu
Re
s/dn Pamb
o
W/cm C
kPa
C
7.31
97.7% 2.34 100.0 8.14 1033.4 14.4
7.56
97.6% 2.43 100.2 8.31 1120.6 14.4
7.55
97.6% 2.50 100.3 8.24 1169.6 14.4
7.88
97.1% 3.01 100.7 8.53 1226.0 14.4
8.09
96.9% 3.26 101.0 8.70 1317.9 14.4
8.21
96.7% 3.50 101.0 8.78 1371.2 14.4
kPa
101.2
102.0
102.4
104.0
105.0
105.2
Table C.46
203
dn
z
s
Tjets Tboxavg
Pjets
Tw
qw
Vflow
o
o
μm mm mm oC
C
kPa
C W/cm2 ml/min
69.3 10 1 16.0 19.5 191.9 55.1 97.9 303.9
69.3 10 1 15.8 21.6 192.8 85.5 191.0 301.1
69.3 10 1 15.8 26.2 193.1 108.9 264.5 297.1
69.3 10 1 15.9 27.7 196.3 122.7 326.1 299.9
69.3 10 1 15.8 38.7 199.5 131.2 427.7 302.9
69.3 10 1 15.7 53.0 200.6 137.6 532.8 306.1
vjets
m/s
3.38
3.35
3.30
3.34
3.37
3.40
Pr
h
4.77
3.53
2.89
2.60
2.44
2.34
W/cm2 oC
2.50
2.74
2.84
3.05
3.71
4.37
Xair
97.8%
97.5%
96.7%
96.5%
93.7%
87.9%
PsatA TsatA
kPa
2.27
2.57
3.40
3.71
6.90
14.30
Nu
Re
s/dn Pamb
o
C
99.9
100.2
100.8
100.9
102.0
104.3
2.78
2.97
3.02
3.21
3.88
4.56
327.4
423.8
499.4
554.0
590.4
620.8
14.4
14.4
14.4
14.4
14.4
14.4
kPa
100.9
102.2
104.3
104.6
108.9
117.8
Table C.47
dn
μm
182.1
182.1
182.1
182.1
182.1
z
s
Tjets Tboxavg
o
Pjets
o
Tw
qw
o
Vflow
2
mm mm C
C
kPa
C W/cm
10 1 15.7 19.0 102.4 67.9 98.9
10 1 16.1 19.0 102.2 87.8 144.1
10 1 16.4 19.1 102.8 100.8 178.2
10 1 16.2 19.3 102.5 110.9 207.8
10 1 16.3 20.1 103.9 131.9 311.8
ml/min
1083.8
1082.6
1080.2
1083.4
1080.3
vjets
m/s
1.75
1.75
1.74
1.75
1.74
Pr
h
Xair
2o
4.18
3.44
3.07
2.84
2.42
PsatA TsatA
Nu
Re
5.47
5.69
5.92
6.11
7.41
499.5
592.6
654.6
704.3
808.1
Nu
Re
s/dn Pamb
o
W/cm C
kPa
C
1.90
97.8% 2.19 99.6
2.01
97.8% 2.20 99.7
2.11
97.8% 2.21 99.8
2.19
97.8% 2.24 99.8
2.70
97.7% 2.35 100.0
5.5
5.5
5.5
5.5
5.5
kPa
99.8
100.1
100.4
100.6
101.3
Table C.48
204
dn
μm
182.1
182.1
182.1
182.1
182.1
z
s
Tjets Tboxavg
o
o
Pjets
Tw
o
qw
Vflow
2
mm mm C
C
kPa
C W/cm
10 1 16.2 19.5 108.2 50.8 104.7
10 1 16.3 19.4 107.9 58.6 130.8
10 1 16.2 19.5 108.3 85.6 234.6
10 1 16.8 19.6 108.6 108.4 316.1
10 1 17.1 20.6 109.0 131.5 405.5
ml/min
1563.6
1565.7
1566.3
1557.2
1556.0
vjets
m/s
2.52
2.52
2.53
2.51
2.51
Pr
h
Xair
2o
4.99
4.58
3.51
2.88
2.41
PsatA TsatA
s/dn Pamb
o
W/cm C
kPa
C
3.03
97.7% 2.26 99.7
3.09
97.7% 2.26 99.7
3.38
97.7% 2.26 99.7
3.45
97.7% 2.28 99.9
3.54
97.6% 2.42 100.0
8.90 616.0
8.99 665.6
9.60 842.8
9.62 999.7
9.74 1166.9
5.5
5.5
5.5
5.5
5.5
kPa
100.2
100.1
100.4
100.8
101.4
Table C.49
205
dn
μm
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
z
s Tjets Tboxavg
o
mm mm oC
C
10
3 22.4 60.7
10
3 23.2 60.7
10
3 22.3 61.3
10
3 23.1 61.7
10
3 22.8 62.1
10
3 22.7 63.3
10
3 23.0 63.2
10
3 22.5 64.7
10
3 23.0 67.8
10
3 22.4 69.1
10
3 23.1 70.0
10
3 22.8 67.8
10
3 23.1 66.0
10
3 22.5 65.4
10
3 23.4 60.8
10
3 22.5 63.3
Pjets
kPa
90.9
89.6
90.1
89.4
89.2
89.0
88.6
89.1
89.1
89.7
88.7
89.0
88.3
89.9
89.0
89.9
Tw
C
51.0
58.3
68.9
80.1
90.4
99.3
107.8
115.1
116.8
117.3
118.4
119.0
128.5
134.7
141.8
146.5
o
qw
W/cm2
15.5
16.9
27.8
38.5
48.1
61.2
70.0
84.9
95.4
113.2
122.2
129.3
185.2
245.4
295.9
357.9
Vflow
ml/min
202.0
202.8
202.7
203.1
201.2
200.8
199.4
198.9
198.5
198.5
197.4
202.3
201.2
200.2
198.6
199.8
vjets
m/s
1.02
1.02
1.02
1.02
1.01
1.01
1.00
1.00
1.00
1.00
0.99
1.02
1.01
1.01
1.00
1.01
Pr
4.66
4.27
3.88
3.47
3.18
2.95
2.76
2.62
2.57
2.58
2.54
2.54
2.37
2.28
2.16
2.11
h
W/cm2 oC
0.54
0.48
0.60
0.68
0.71
0.80
0.83
0.92
1.02
1.19
1.28
1.34
1.76
2.19
2.50
2.89
Xair
75.7%
75.6%
75.0%
74.5%
74.0%
72.4%
72.5%
70.7%
66.5%
64.6%
63.0%
66.5%
69.1%
69.8%
75.6%
72.4%
Psat
kPa
20.56
20.60
21.14
21.55
21.97
23.20
23.11
24.66
28.32
29.91
31.18
28.33
26.20
25.48
20.64
23.21
Tsat
o
C
95.0
95.0
95.0
95.0
95.0
94.9
94.8
94.9
95.0
95.0
95.0
95.0
95.0
94.9
95.0
94.9
Nu
Re
2.28
2.01
2.47
2.77
2.89
3.23
3.31
3.66
4.05
4.76
5.11
5.36
6.96
8.64
9.83
11.34
381.6
413.2
450.0
498.0
533.1
567.6
599.6
626.1
634.2
633.2
637.3
654.6
692.4
713.2
741.5
762.3
s/dn Pamb
kPa
11.4 84.5
11.4 84.6
11.4 84.5
11.4 84.5
11.4 84.6
11.4 84.2
11.4 84.1
11.4 84.3
11.4 84.4
11.4 84.4
11.4 84.4
11.4 84.5
11.4 84.7
11.4 84.2
11.4 84.5
11.4 84.2
Table C.50
206
dn
μm
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
z
s Tjets Tboxavg
o
mm mm oC
C
10
3 23.1 85.4
10
3 23.5 84.5
10
3 24.1 83.7
10
3 23.4 83.1
10
3 24.2 82.2
10
3 23.8 81.0
10
3 24.2 80.1
10
3 24.0 79.4
10
3 23.7 79.3
10
3 24.3 78.7
10
3 23.5 78.7
10
3 24.0 79.3
10
3 23.7 77.7
10
3 23.7 78.0
10
3 23.5 81.4
10
3 23.4 82.3
Pjets
kPa
90.6
91.4
91.5
91.5
91.3
90.0
90.5
92.3
92.5
91.7
92.5
92.1
92.2
92.1
91.7
92.4
Tw
C
61.6
64.5
72.1
80.0
89.3
95.5
104.7
111.3
116.6
117.2
118.9
119.9
128.7
137.2
142.6
145.8
o
qw
W/cm2
18.3
22.8
30.4
41.8
48.8
52.8
74.5
88.5
102.4
115.6
124.7
135.5
194.3
251.2
306.3
359.1
Vflow
ml/min
197.9
197.9
198.5
200.6
199.3
201.0
199.4
202.1
201.7
201.0
200.1
200.0
201.6
201.3
202.3
199.7
vjets
m/s
1.00
1.00
1.00
1.01
1.00
1.01
1.00
1.02
1.01
1.01
1.01
1.01
1.01
1.01
1.02
1.00
Pr
4.14
4.00
3.70
3.46
3.17
3.02
2.80
2.66
2.56
2.54
2.52
2.50
2.35
2.22
2.15
2.11
h
W/cm2 oC
0.47
0.56
0.63
0.74
0.75
0.74
0.93
1.01
1.10
1.24
1.31
1.41
1.85
2.21
2.57
2.93
Xair
29.9%
32.5%
34.9%
36.4%
38.8%
41.7%
43.6%
45.4%
45.7%
47.1%
47.2%
45.8%
48.9%
48.6%
40.7%
38.5%
Psat
kPa
58.81
56.72
54.82
53.68
51.83
49.33
47.65
46.24
46.05
44.91
44.91
46.00
43.17
43.64
50.07
52.02
Tsat
o
C
94.8
94.8
94.9
95.0
95.1
95.1
95.0
95.0
95.1
95.1
95.2
95.1
95.0
95.1
95.0
95.0
Nu
Re
1.98
2.31
2.61
3.02
3.05
2.98
3.72
4.05
4.40
4.96
5.21
5.62
7.32
8.72
10.12
11.52
415.0
427.5
459.7
492.6
529.5
557.2
591.7
626.4
646.4
649.3
649.9
656.2
697.5
733.2
759.2
762.4
s/dn Pamb
kPa
11.4 83.9
11.4 84.0
11.4 84.1
11.4 84.4
11.4 84.7
11.4 84.7
11.4 84.5
11.4 84.6
11.4 84.7
11.4 85.0
11.4 85.1
11.4 84.9
11.4 84.5
11.4 84.9
11.4 84.4
11.4 84.6
Table C.51
207
dn
μm
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
z
s Tjets Tboxavg
o
mm mm oC
C
10
3 26.0 90.9
10
3 26.4 90.0
10
3 26.5 89.9
10
3 25.7 90.3
10
3 25.6 90.0
10
3 25.7 89.8
10
3 25.7 89.6
10
3 25.2 89.9
10
3 25.1 89.8
10
3 25.9 89.2
10
3 25.1 89.6
10
3 24.8 89.4
10
3 25.5 88.9
10
3 24.8 89.2
10
3 25.4 87.4
Pjets
kPa
89.8
89.3
89.1
90.6
90.3
91.5
89.8
90.4
89.8
89.8
89.4
90.7
89.7
90.6
89.9
Tw
C
69.1
72.3
82.8
92.1
102.7
109.7
114.4
114.7
117.0
119.4
122.0
123.5
133.0
140.7
144.2
o
qw
W/cm2
16.1
21.1
29.7
42.2
53.4
71.0
76.1
93.1
105.1
117.9
130.4
134.4
196.9
272.5
313.3
Vflow
ml/min
196.0
195.4
194.2
193.7
192.8
191.4
191.8
191.2
190.7
190.4
190.1
189.6
189.9
189.5
189.4
vjets
m/s
0.99
0.98
0.98
0.97
0.97
0.96
0.96
0.96
0.96
0.96
0.96
0.95
0.96
0.95
0.95
Pr
3.74
3.61
3.29
3.06
2.81
2.66
2.57
2.57
2.53
2.47
2.44
2.42
2.26
2.16
2.10
h
W/cm2 oC
0.37
0.46
0.53
0.63
0.69
0.85
0.86
1.04
1.14
1.26
1.35
1.36
1.83
2.35
2.64
Xair
13.3%
16.3%
16.5%
15.3%
16.1%
16.4%
17.4%
16.3%
17.0%
18.6%
17.6%
18.1%
19.5%
18.9%
24.8%
Psat
kPa
72.46
70.20
69.74
70.91
70.22
69.69
69.08
69.79
69.47
68.07
68.92
68.58
67.31
68.11
63.45
Tsat
o
C
94.7
94.8
94.7
94.7
94.7
94.6
94.7
94.6
94.7
94.7
94.7
94.8
94.7
94.8
94.9
Nu
Re
1.54
1.89
2.15
2.57
2.78
3.38
3.42
4.15
4.55
5.01
5.35
5.40
7.23
9.25
10.36
449.9
461.9
499.4
531.2
569.5
593.8
613.6
610.9
617.9
629.9
636.0
639.6
681.5
708.6
725.2
s/dn Pamb
kPa
11.4 83.5
11.4 83.8
11.4 83.5
11.4 83.7
11.4 83.7
11.4 83.4
11.4 83.6
11.4 83.4
11.4 83.7
11.4 83.6
11.4 83.7
11.4 83.8
11.4 83.6
11.4 83.9
11.4 84.3
Table C.52
208
dn
μm
263
263
263
263
263
263
263
263
263
263
263
263
263
263
z
s Tjets Tboxavg
o
mm mm oC
C
10
3 53.4 86.1
10
3 53.4 86.6
10
3 53.4 86.1
10
3 53.9 86.0
10
3 53.6 87.6
10
3 53.6 87.1
10
3 54.3 87.6
10
3 54.5 87.9
10
3 53.5 88.8
10
3 54.5 89.1
10
3 54.5 89.5
10
3 53.9 90.2
10
3 54.0 90.4
10
3 54.6 91.8
Pjets
kPa
87.0
86.4
86.2
86.6
86.5
87.4
86.7
85.6
86.8
85.0
84.4
85.8
86.7
85.0
Tw
C
88.3
93.8
102.9
109.4
112.3
114.8
117.3
120.2
123.2
125.4
127.3
129.1
135.1
142.2
o
qw
W/cm2
12.5
15.2
23.0
33.6
48.4
65.0
81.7
91.2
98.0
117.1
122.8
135.9
199.9
255.3
Vflow
ml/min
117.2
117.7
117.5
117.4
116.8
116.5
116.8
117.0
116.2
115.6
115.6
115.4
115.1
115.4
vjets
m/s
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.58
0.58
0.58
0.58
0.58
0.58
Pr
2.54
2.44
2.29
2.19
2.15
2.12
2.07
2.03
2.01
1.97
1.95
1.93
1.87
1.79
h
W/cm2 oC
0.36
0.38
0.46
0.60
0.82
1.06
1.30
1.39
1.41
1.65
1.69
1.81
2.47
2.91
Xair
28.4%
27.2%
28.5%
28.5%
24.2%
25.7%
23.8%
22.8%
20.2%
19.3%
17.8%
15.6%
14.6%
10.2%
Psat
kPa
60.26
61.41
60.34
60.12
63.85
62.69
63.96
64.66
66.99
67.67
68.71
70.63
71.25
74.94
Tsat
o
C
94.9
94.9
94.9
94.9
94.9
95.0
94.8
94.7
94.8
94.8
94.7
94.7
94.6
94.6
Nu
Re
1.43
1.50
1.84
2.38
3.24
4.17
5.08
5.43
5.50
6.46
6.59
7.06
9.62
11.32
378.8
393.9
416.1
433.5
437.6
442.8
452.2
460.8
462.8
468.6
473.0
475.3
489.7
510.4
s/dn Pamb
kPa
11.4 84.2
11.4 84.4
11.4 84.3
11.4 84.1
11.4 84.2
11.4 84.4
11.4 83.9
11.4 83.7
11.4 83.9
11.4 83.8
11.4 83.6
11.4 83.7
11.4 83.4
11.4 83.4
Table C.53
209
dn
μm
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
263
z
s Tjets Tboxavg
o
mm mm oC
C
10
3 45.8 85.6
10
3 45.9 86.4
10
3 46.2 87.1
10
3 46.6 87.3
10
3 46.2 88.3
10
3 46.7 88.5
10
3 46.8 90.0
10
3 46.9 91.1
10
3 46.0 90.5
10
3 46.8 90.1
10
3 47.0 92.2
10
3 47.1 92.9
10
3 47.1 94.3
10
3 46.7 94.8
10
3 46.8 98.3
10
3 46.6 95.6
Pjets
kPa
91.4
91.5
91.2
90.6
90.8
90.1
90.2
90.2
90.3
89.8
89.4
90.0
89.2
88.8
88.8
89.0
Tw
C
75.1
80.6
89.3
99.1
108.5
111.1
112.7
115.2
118.8
121.3
122.8
124.2
132.0
138.1
142.1
145.2
o
qw
W/cm2
14.4
20.2
30.6
46.2
55.5
69.3
84.1
95.4
101.5
114.8
127.0
139.0
197.1
249.5
305.6
332.5
Vflow
ml/min
198.6
198.1
196.5
196.8
196.3
196.5
196.0
196.2
195.7
195.7
195.4
194.9
195.5
194.9
194.8
194.3
vjets
m/s
1.00
1.00
0.99
0.99
0.99
0.99
0.99
0.99
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
Pr
2.98
2.85
2.66
2.47
2.31
2.27
2.24
2.20
2.16
2.12
2.10
2.08
1.98
1.91
1.87
1.84
h
W/cm2 oC
0.49
0.58
0.71
0.88
0.89
1.08
1.28
1.40
1.39
1.54
1.68
1.80
2.32
2.73
3.21
3.37
Xair
29.5%
27.3%
25.1%
24.4%
21.5%
20.7%
16.1%
12.5%
14.5%
15.9%
8.7%
6.5%
1.0%
-0.8%
-14.2%
-3.8%
Psat
kPa
59.10
60.97
62.84
63.24
65.61
66.21
69.99
73.02
71.49
70.45
76.32
78.17
82.47
83.91
95.44
86.34
Tsat
o
C
94.8
94.8
94.8
94.7
94.7
94.7
94.7
94.6
94.7
94.7
94.7
94.7
94.6
94.6
94.7
94.6
Nu
Re
1.98
2.34
2.84
3.50
3.53
4.25
5.04
5.50
5.49
6.06
6.58
7.07
9.07
10.66
12.50
13.13
556.8
578.1
610.0
652.6
688.8
702.5
707.7
719.4
729.1
742.8
749.1
753.4
788.4
810.5
827.4
837.9
s/dn Pamb
kPa
11.4 83.8
11.4 83.8
11.4 83.9
11.4 83.7
11.4 83.5
11.4 83.5
11.4 83.5
11.4 83.4
11.4 83.6
11.4 83.7
11.4 83.6
11.4 83.6
11.4 83.3
11.4 83.2
11.4 83.6
11.4 83.2
Table C.54 Calibration data (T1-T4 are the thermocouples in the copper block, 1 being the closest to the free surface and 4 the
farthest away).
Tref
o
C
0.05
24
99.85
T1
o
C
-0.06
24.03
100.04
T2
o
C
-0.16
24.00
100.03
T3
o
C
-0.32
23.55
99.70
T4
o
C
-0.42
23.65
99.72
Tjets
o
C
-0.18
19.35
99.70
Tbox
o
C
-0.10
19.38
99.57
Tflowmeter
o
C
-0.08
19.43
100.00
Pbox
Pa
Pjets
Pa
99662
97072
A
AP
PP
PE
EN
ND
DIIX
XD
D
This section deals with the uncertainty associated to the experimental variables.
The uncertainties mentioned in the previous chapters have been calculated according to
the procedure described by Kline and McClintock [35]. The uncertainty δ of a function f
of n variables can be calculated as
⎛
∂f ⎞
δ f = ∑ ⎜ δ xi
⎟
∂xi ⎠
1 ⎝
n
2
(D.1)
where δ xi is the uncertainty associated to the variable xi.
A sample calculation of the heat flux removed through the copper block as
described in Chapters 3 and 4 is presented in section D.2.
D.1 Uncertainty on the cooling module data
The minimum and maximum uncertainties for the data used in Chapter 2 and
listed in appendix A were: for the power ±4.16% and ±8.13% of the measured value, for
the heat flux ±4.16% and ±8.13%, for the thermal resistances ±4.16 % and ±8.72%, and
for the heat transfer coefficient ±4.17% and ±8.58%. The minimum values occurred when
the power was the highest and consequently the temperature differences were also close
to their highest values. On the other side, the maximum uncertainty occurred when the
power level was low, and the temperature differences were also low. In that situation, the
uncertainty on the individual measurement had higher impact on the calculated quantities.
210
D.2 Uncertainty on the open system data
The heat flux (q) mentioned in Chapter 3 is calculated according to the procedure
described below.
A linear least-squares regression on the temperature readings for the 4
thermocoples embedded in the copper block and their distance from the impinged surface
is performed yielding the slope and intercept values. The intercept corresponds to the
surface temperature. The slope multiplied by the thermal conductivity of copper,
evaluated at the block’s mean temperature, yields the heat flux. A plot of the temperature
profile for the case presented in Table B.1, in the copper block is shown in Figure D.1.
The cooling fluid used is water, s = 1 mm, and dn = 69.3 μm. The thermocouples
locations are 1.78 mm, 6.78, 11.78, and 16.78 mm from the free surface of the copper
block.
A linear best fit gives an intercept, Tw, of 24.74 oC and a slope of 156.88 oC/m.
The thermal conductivity for copper is 434.18 W/moC. The heat flux, q, then is 6.8
W/cm2. The uncertainties on Tw and q are 0.12 oC and 0.5 W/cm2, respectively.
211
30
Temperatures
Linear Fit Y=Ax+b
o
o
a = 156.88 C/m; b = 24.74 C
29
28
27
25
o
T [ C]
26
24
23
22
21
20
0
2
4
6
8
10
12
14
16
18
20
x [mm]
distance from free surface
Figure D.1 Temperature profile in the copper block. Values taken from Table B1.
The uncertainties are calculated using Eq.(D.1). Twice the value of the standard
deviations is added to the estimate of the possible “bias” error using again Eq.(D.1).
The maximum and minimum uncertainties on the main parameters which have
been calculated according to Eq.(D.1), using the uncertainties on the individual
measurement specified in Chapter 3 are listed in Table D.1.
Table D.1 Max and min uncertainties for the open system configuration
δq/q
δh/h
δNu/Nu δRe/Re
Max 305% 305%
306%
22.7
Min
6.7%
7.2%
2.7%
2.9%
212
The high value of 305 % of uncertainty on the heat flux occurred for an FC40
case for which the heat flux was only 0.15 W/cm2 and it was caused by the small
temperature difference between the 4 thermocouples installed in the copper block. Only a
few other points had an uncertainty above 30% because usually the heat flux was above
1.54 W/cm2 for which the uncertainty would be 29.7%. At a heat flux of 3.1 W/cm2 the
error is only 14.6% and at 6.6 W/cm2 it is only 7.3%.
An example of the application of this procedure is shown below. The numbers
used in the example are taken from the first line of Table B.1.
Given the values shown in Table D.2:
Table D.2 Variable values and their uncertainty
q
Units W/cm2
Tw
o
C
Tjets
o
C
dn
μm
k
W/m oC kg/m3
Value
6.8
24.7 21.1 69.3
0.6
δ
0.5
0.12
n.a.
0.1
3.0
ρ
μ
V
Njets
kg/ms
ml/min
n.a.
278.5
397
1.74
n.a.
997.7 9.34·10-4
n.a.
n.a.
Using Eq.(3.1) and Eq.(D.1), with the values of Tw, q, and Tjets and their
uncertainties, it is found that h = 18.9 W/cm2, and δh = 0.17 W/cm2. Now, using Eq.(3.2)
and Eq. (D.1), Nu and δNu can be calculated and they are equal to 2.17 and 0.21,
respectively. Proceeding in the same way, using Eq.(3.4), (3.3), and (D.1) Vn = 3.1 m/s,
δVn = 0.27 m/s, Redn = 229.3 and δ Redn = 22.1. Thus, the error on Nu is 9.7% and on Re
it is equal to 9.6%.
213
D.3 Uncertainty on the closed system and high heat flux data
The maximum and minimum uncertainties on the main parameters which have
been calculated according to Eq.(D.1), using the uncertainties on the individual
measurement specified in Chapter 4, are listed in Table D.3 and Table D.4
Table D.3 Max and min uncertainties for the closed system configuration.
δq/q
δh/h
δNu/Nu δRe/Re δXair/Xair
Max 20.6% 24.9%
26.1%
29.9%
144.9%
Min
6.6%
12.6%
0.04%
2.7%
3.1%
The high uncertainty on Xair occurs when Xair is close to zero and it is caused by
the relatively high uncertainty on the pressure and temperature measurement.
A small bias error in the measurement of the temperature of the box, but more
likely the roughness of the control of the temperature of the chamber, by means of the
two electrical ring heaters, caused the chamber temperature to be about 0.5 oC higher than
the saturation value, which generated the unrealistic negative value of Xair. However, then
uncertainty on both pressure and temperature measurement are such that the measured
Pbox +δPbox and Psat(Tbox) + δPsat(Tbox) overlap. As an example, the values of the first line
of Table C.1 are used. Pbox = 100.7 kPa, δPbox =2.1 kPa, Tbox = 100.5 oC, Psat(Tbox) =
103.3 kPa, and δPsat(Tbox) = 1.15 kPa.
214
Table D.4 Max and min uncertainties for the high heat flux data.
δq/q
δh/h
14%
14.1%
16.1%
23.6%
1.6%
Min 3.5%
3.8%
6.9%
12.6%
0.06%
Max
δNu/Nu δRe/Re δXair/Xair
215
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221

Cooling of electronic components using arrays of microjets

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