THERMOPHYSICAL PROPERTIES OF TROPICAL FRUIT JUICESl

THERMOPHYSICAL PROPERTIES OF TROPICAL FRUIT JUICESl
Sílvia Cristina Sobottka Rolim de MOURA2, Silvia Pimentel Marconi GERMER3, Denise Calil Pereira
JARDIM4, Mitie Sônia SADAHlRAs
SUMMARY
Precise knowledge of the thermal and rheological properties of foods is of fundamental importance to establish the
design of process equipment. However, for tropical fruit products such as juices, there is a complete lack of this information in the literature, seriously hindering processing procedures. Thermophysical properties of tropical fruit juices:
thermal diffusivity, specific heat and density, were experimentally determined, and the values obtained compared with
those predicted by mathematical models already existent in the literature, based on the chemical composition. The juices
studied were prepared from pulps of cupuaçu (Theobroma grandiflorum), açai (Euterpe oleracea, Mart.) and graviola (Annona
muricata), and the determinations were made in the temperature range from 10 to BO°e. The thermal conductivity was
deduced from the knowledge of the other properties. The viscosity of the filtered juices was also determined using a
capillary viscometer.
KEY WüRDS: Thermal properties; Tropical fruit juices; Viscosity; Thermal diffusivity; Specific heat.
RESUMO
PROPRIEDADES TERMOFÍSICAS DE SUCOS DE FRUTAS
TROPICAIS
o conhecimento preciso das propriedades térmicas e reológicas dos alimentos é de fundamental importância no dimensionamento de equipamentos. Porém, para produtos de frutas tropicais, como sucos, não existe na literatura referências destas
propriedades, o que dificulta seriamente o processamento dos mesmos. Propriedades termofísicas: difusividade térmica,
calor específico e densidade, de sucos de frutas tropicais, foram determinadas experimentalmente e comparadas a valores
preditos por modelos matemáticos, já existentes na literatura, em função da sua composição química. Os sucos estudados
foram preparados com polpas de cupuaçu (Theobroma grandiflorum), açaí (Euterpe oleracea, Mart.) e graviola (Annona muricata)
e as determinações foram realizadas na faixa de temperatura de 10 a BO°e. A condutividade térmica foi obtida através do
conhecimento das demais propriedades. Determinou-se, também, a viscosidade dos sucos filtrados em um viscosímetro
capilar.
PALAVRAS-CHAVE: Propriedades térmicas; Sucos de frutas tropicais; Viscosidade; Difusividade térmica; Calor específico.
1 Recebido para publicação em 21/09/1998. Aprovado para publicação em 30/12/1998.
2.3.4.sPesquisadores do Instituto de Tecnologia de Alimentos - FRUTHOTEC/ITAL. Av. Brasil, 2880 - Campinas/SP - CEP 13073-001
emails:[email protected]@[email protected]@ital.org.br
70
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Braz. J. Food Technol., Campinas, 1(1,2): 70-76, janldez.1998
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1.INTRODUCTION
ln order to determine the dimensions of food processing equipment, especially heat exchangers and
other equipment requiring pumping of the product, it
is essential to know the precise values of the thermal
properties of the products (thermal conductivity, thermal diffusivity and specific heat) and how these properties react during processing as a function of temperature.
The need for precise knowledge of the thermal properties has led to studies on the influence of composition and temperature on these properties.
POLLEY et aI. (1980), have published a collection
of tables of the thermal properties of various foods,
including meats, fruits, vegetables, milk and cereaIs.
Some, but not all, of the thermal properties of the following fruit juices can be found in these tables: appIe, cherry, grape, orange and pear.
CONSTENLA et aI. (1989) published more specific
data on the thermophysical properties of clarified
apple juice at various temperatures and concentrations. This paper presents the experimental results of
the determinations of density, viscosity, specific heat
and thermal conductivity. The results show the great
influence of concentration and temperature on the
determination of these properties, and model the data
as a function of these variables. VIRENDRA et aI.
(1989) studied the prediction of the thermal conductivity of various juices (apple, cherry, grape, orange
and strawberry), using several mathematical models,
and a comparison of the theoretical values with the
experimental values showed an error of less than 10%.
Experimental values for the thermal diffusivity of
apple, cherry, grape, orange and tomato juices can be
found in GEORGE (1990). Once again, the majority of
the data are for sub-tropical fruit juices.
A knowledge of the rheological properties of foods
becomes necessary in a series of applications such
as: quality control, knowledge of the physical structure and principally the control and sizing of industrial processes.
The effect of temperature and concentration on the
density and viscosity of apple juice was studied by
BAYINDIRLI (1992). Mathematical models were obtained from the experimental data, showing excellent correlation (r>0.99). The influence of temperature and viscosity on filtered fruit juices and sugar cane juice can be
found inALVARADO (1993). The results show that the
viscosity of the fruit juices follows Arrhenius' law, showing activation energies of the order of 20kJ / g.mo!.
A more recent prediction of the thermophysical
properties, applied to clarified fruit juices as a function of concentration and temperature, can be found in
PEACOCK (1995). The paper presents mathematical
models to predict rise in boiling point, density, enthalpy, specific heat, sucrose solubility, surface tension, thermal conductivity and viscosity. The study
shows that good correlation exists between the thermophysical properties and the concentration and
temperature of fluid products.
It is important to emphasize the increasing demand
for processed food in the country (Brazil), bringing,
as a consequence, the demand for industrial modernization, technological adequation and improved
quality. These demands can only be met if more scientific information on food processing becomes available, requiring knowledge of the physical properties
in order to calculate the processes. Currently, the countless data available in the literature on similar products are inadequate, in the majority of cases, for brazilian products. For the majority of brazilian products, the thermophysical properties are not available in the literature.
The objective of this research was to experimentally determine the density, viscosity, specific heat and
- thermal diffusivity as well as calculate the thermal
conductivity of cupuaçu, açaí and graviola juices in the
temperature range from 10 to 80°e. ln addition, the
paper presents a comparison between the experimental data and values obtained from mathematical modeIs found in the literature.
2. METHODOLOGY
2.1 MateriaIs
Juices prepared from commercial pulps of cupuaçu
(Theobroma grandiflorum), açaí (Euterpe oleracea, Mart.)
and graviola (Annona muricata), chemically analysing
using official methods (WILLIAMS, 1990).
2.2 Methods
Viscosity (/l)
Determined at three temperatures using a capillary glass viscometer, after filtering through cotton wool
(VAN WAZER et aI., 1972).
Density (p)
Determined at three temperatures by fluid displacement using a pycnometer, according to AOAC method n°. 985.19 (WILLIANS, 1990).
Specific heat (Cp)
Specific heat was determined using an adaptation
of the method of mixtures of HWANG, HAYAKAWA
Braz. J. Food Technol., Campinas, 1(1,2): 70-76, jan/dez.1998
71
H k = thermal capacity of the calorimeter (cal;oC)
C w = specific heat of distilled water (cal/g.°C)
v( = mass of distilled water (g)
T fw = temperature corresponding to the start of
the straight part of the time' temperature curve
for distilled water (0C)
Tow = initial temperature of the distilled water (0C)
dT / dt = slope of the time' temperature curve for
distilled water (OC/min)
te = time corresponding to Tfw of the time' temperature curve for distilled water (min)
C s = specific heat of the polyethylene bag (cal! g.0C)
= mass of the polyethylene bag (g)
s
Wc = sample mass (g)
Toe = initial temperature of sample (0C)
(1979). The calorimeter used for the measurement of
the specific heat consisted of a ane liter thermos flask.
Before starting the tests, the thermal capacity of the
calorimeter was obtained, by calibrating it in the temperature range to be used (10 to 70°C). 100 to 150g
samples of juice, packaged in polyethylene bags, were
placed in a cold chamber (S°C) for 24 hours to stabilize the temperature.
Approximately 500g distilled water at 90°C were
introduced into the calorimeter, and after stabilizing
the temperature, a sample package was placed in the
calorimeter after initially determining its internal temperature.
Using a calibrated T-type needle thermocouple,
passing through the lid of the thermos flask, the temperature inside the calorimeter was recorded every
30 seconds. The equipment was shaken constantly in
a shaker, as shown in Figure 1.
W
Assay for Specific Heat
74
(c)
(a)
\.
§: 72
~
J \
...GI
...GI
-
70
68
Q. 66
E
GI
64
~
62
j
lO
I \.
o
J
50
time (min)
FIGURE 1. Design of the apparatus constructed to
measure specific heat: (a) calorimeter (b) digital thermometer (c) thermocouple lead (d) shaker.
Readings were taken until thermal equilibrium was
reached, and the data used to construct a graph of the
temperatures (duly corrected using a calibration equation) as a function of time (Figure 2). The linear regression was determined from the linear part of the
curve. The specific heat of the sample was calculated
using equation (1), which was derived as a function
of the energy balance.
la, - To) - IdTldtlt).±...C,.•. W.,U,. -
Toe - IdTldtlt)
W, «Toe -TIw) + (dT/dt)t.)
Where:
Cp = specific heat of the sample (cal/ g.0C)
72
_1
Carrected
Temperature
FIGURE 2. Example of a time' temperature curve obtained using the calorimeter, for the determination of
specific heat in tropical fruit juices.
(d)
Cp =~ •. w).
100
(1)
Thermal diffusivity (a)
Thermal diffusivity was determined based on the
method of DICKERSON (1965) using the apparatus
shown in Figure 3. The Scm (diameter) by 29.8cm (height) celI, constructed in stainless steel, was connected to two calibrated thermocouples: one at the surface to measure the temperature of the medium, and the
other in the central plane, to measure the temperature
of the product. To avoid the formation of convection
currents, which would hamper the analysis, the sampIes were partialIy solidified by adding 1% agar. The
measuring system was placed in a thermal bath containing ethylene glycol at O°C and alIowed to reach
thermal equilibrium. Heating was then started at a
rate of 0.7°C/min, and stopped when the temperature
reached approximately 8S°C. During the experiment,
the temperatures were registered every minute using the
Dianachart (16 bits) data aquisition system.
Braz. J. Food Technol., Campinas, 1(1,2): 70-76, jan/dez.1998
The evolution of the internal and external temperature profiles were drawn (see example in Figure 4)
and the thermal diffusivity calculated for each value
registered using equation (2):
(2)
where:
A = rate of temperature rise of the bath (OC/min)
R = radius of the cell (m)
(Text-Tint) = temperature difference between the
inside and outside of the cell (0C)
The value for A is a constant, since it is the rate of
temperature rise of the bath. The value (T ext-T int ) decreases as the temperature of the bath increases. Therefore the diffusivity was calculated for each registered temperature and the average value obtained in
the range under study.
Thermal conductivity (k)
This was determined using equation 3, after determining the other properties.
2.3 Analysis of the results
The experimentally obtained values (assays carried
out in triplicate) were compared with those obtained
using mathematical modeIs available in the literature.
For Specific heat
Model I:
HWANG and HAYAKAWA (1979)
Cp = 4.184. (Cpw·Ww+ Cpc,Wc+ CpfWr)I 100
I g.0C) (4)
a
Where: C pc = C.....p carbo h y d ra te = 0.41 cal/gOC
C pw = L p water = 1 cal/gOC
C r = C rat = 0.53 call gOC
Ww = % water
Wc = % carbohydrate
Wr=%fat
HEATERJ
STIRRER
IJ
~
__-l~+=~
THERMOCOUPLES
(3)
k=r.C p .u
Model II: SIEBEL (1982)
(J Ig.°C)
C p = 0.837 + 3.349 . Xw
(5)
Where: Xw= sample moisture (in decimal form)
For Thermal Diffusivity
FIGURE 3. Design of the apparatus for measuring
thermal diffusivity.
T
100
m
p
80
e
60
r
a
40
t
u
20
(6)
Where: a w= diffusivity of water (m 2 I s)
X w= sample moisture (in decimal form)
Assay for Thermal Diffusivity
e
Model I:
RIEDEL (1982)
= 0.088.10-6 + (a w - 0.088 x 10-6 ). X w (m 2 /s)
a
Model II: MARTENS (1982)
a = [0.057363. X w + 0.000288 (T + 273)].10-6 (m 2 /s) (7)
Where: X w= sample moisture (in decimal form)
T = sample temperature (0C)
- - T ex!. temp
For Thermal Conductivity
--Tint.temp
r
e
ICI
O
O
50
100
time (min)
FIGURE 4. Example of a time' temperature curve registered in an experimental assay to determine thermal diffusivity in tropical fruit juices.
Model I:
KOLAROV and GROMOV (1989)
k = 0.140 + 0.42. Xw(forjuices)
(W Im.°C) (8)
Where: w = water
Model II:
SWEAT (1989)
k = 0.58. X w + 0.25. Xc + 0.16. Xr (W Im.°C) (9)
Where: w = water c = carbohydrate f = fat
Braz. J. Food Technol., Campinas, 1(1,2): 70-76, jan/dez.1998
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73
3. RESULTS AND DISCUSSION
Table 1 shows the compositions of the pulps and Table 2 the formulations used in the study. Table 3 presents the values obtained for the proximate composition of the formulated juices. These values were used in
the mathematical models for the theoretical calculation
of the properties.
Table 4 shows the data obtained in the experimental
assays for density, viscosity, specific heat, thermal diffusivity and the calculated values for thermal conductivity.
TABLE 1. Physico-chemical characterization of the cupuaçu, açaí and graviola pulps.
TYPE
Moisture
(%)
Carbohydrate
(%)
Fat
(%)
Brix
(o)
pH
(21°C)
Cupuaçu
Açaí
89.83
93.80
10.17
2.84
3.36
8.9
3.5
3.74
4.75
Graviola
88.96
11.04
8.0
3.50
TABLE 2. Formulation of the cupuaçu, açaí and graviola juices.
TYPE
Cupuaçu
Açaí
Graviola
Pulp (%)
21.0
44.7
31.6
Water (%)
69.0
44.7
63.6
Sugar (%)
9.4
10.6
4.9
Milk (%)
0.6
TABLE 3. Physico-chemical characterization of the formulated cupuaçu, açaí and graviola juices.
TYPE
Carbohydrate
(%)
11.54
Fat
(%)
Cupuaçu
Moisture
(%)
87.86
Açaí
86.63
11.87
1.50
Graviola
91.70
8.39
Protein
(%)
0.6
Brix
(0)
11.5
pH
(21°C)
4.02
11.9
4.95
8.40
4.50
TABLE 4. Experimental results for the thermophysical properties of cupuaçu, açaí and graviola juices.
Cupuaçu
Juices
Açaí
Graviola
1.049
1.047 (1.036)
1.012
1.047
1.042 (1.032)
1.008
1.034
1.030 (1.013)
0.974
12.71
4.00
1.14
1.46 x 10. 7
2.14
1.20
0.35
1.51 x 10. 7
2.48
1.145
0.34
1.50x10·7
0.91184/3.82
0.88246/3.69
0.94821 /3.97
0.578
0.575
0.603
Properties
Density (g/cm
3
)
5°C
25°C (average)
87°C
Viscosity (cP)
5°C
25°C
87°e
2
Thermal diffusivity (m /s)
AverageT=55°e
Specific heat
(cal/g .oe )/(J/g. oe)
AverageT=40oe
T h erm a I C ond u ctivity*
(w/m.oe)
*Result calculated from other experimental data.
74
Braz. J. Food Technol., Campinas, 1(1,2): 70-76, janldez.1998
------------_.....
ln order to compare the experimental data for specific heat, thermal conductivity and thermal diffusivity with the calculated data, the mathematical modeIs, specific for each property, presented in equati-
ons 4 to 9, were used.
The results can be seen in Table 5 (for specific heat),
Tables 6, 7 and 8 (for thermal diffusivity) and Table 9
(for thermal conductivity).
TABLE 5. A comparison between the values calculated for specific heat (Cp) using modeIs I and II and the
experimental data for cupuaçu, açaí and graviola juices.
Juices
Cpmodell
Cpmodelll
Cpexperimental
Cupuaçu
3.88
3.78
3.82
Açaí
3.86
3.74
3.69
Graviola
3.98
3.91
3.97
%errar = (thearetical vai ue-experimental value)/(experimental value) x 100.
(%)
(%)
errarmodel I
1.55
4.61
0.25
errarmodelll
1.05
1.35
1.51
TABLE 6. Comparison between the values calculated using models I and II and the experimental data, for the
thermal diffusivity (a) of cupuaçu juice.
(%)
(%)
Temperature (0C)
40
50
60
70
amodell
1.43 X 10-7
1.47 X 10-7
1.50 X 10-7
1.52 X 10'7
amodelll
1.41 x
1.43 X
1.46 X
1.49 x
Uexperimental
10'7
10'7
10'7
10'7
1.42 X 10'7
1.38 X 10'7
1.43 X 10'7
1.62 X 10-7
errarmodel I
0.70
6.52
4.90
6.17
errarmodel II
0.70
3.62
2.10
8.02
%errar = (thearetical value-experimental value)/(experimental value) x 100.
TABLE 7_ Comparison between the values calculated using modeIs I and II and the experimental data, for the
thermal diffusivity (a) of açaí juice.
Temperature (oC)
40
50
60
70
%error
amodell
1.43 X 10'7
1.46 X 10-7
1.49 X 10-7
1.51 X 10-7
amodelll
1.40 X 10'7
1.43 X 10'7
1.46 X 10'7
1.48 X 10-7
aexperimental
1.38 X 10'7
1.43 X 10-7
1.53 x 10'7
1.69 X 10-7
= (thearetical vai ue-experimental value)/(experimental vai ue)
An analysis of Tables 5 to 9 shows that the greatest
error was obtained for the prediction of thermal conductivity (13% error). This is due to the fact that this
property is calculated from the values for the other
properties, and so the individual error for each property contributes to that of thermal conductivity. The
error in the prediction of the other properties was
within the expected value and that obtained by other
authors (approximately 10%). It can also be seen that
(%)
(%)
errarmodell
errarmodel II
3.50
2.10
2.61
10.65
1.45
4.58
12.43
x 100
the error between the values for thermal diffusivity
increases with increase in temperature, which may
be due to the dissolution of the agar added to the juice, consequently increasing the convection of the system. For each property, the values obtained for the
three juices were very similar, with the exception of
viscosity (Table 4) which showed very distinct values. It was also shown that the variation in viscosity
with temperature was considerable, within the range
'--------------Braz. J. Food Technol., Campinas,
1(1,2): 70-76, jan/dez.1998
75
studied, especially for cupuaçu juice. On the other
hand, thermal diffusivity (Tables 6 to 8) showed little
variation with temperature within the sarne range.
4. CONCLUSIONS
It was conduded that the experimental results were
very dose to the calculated ones, based on the composition and temperature (error of approximately
10%). Thus the methodologies used here can be safely applied to determining the thermal properties of
this type of product. It is important to emphasize that
if these properties were not adequately determined, .
this could result in under-processing or an incorrect
calculation of equipment dimensions.
ACKNOWLEDGEMENTS
The authors would like to thank Cia. Ciali. Amazonense for their authorization to publish the results
obtained in this joint projecto We would also like to
thank the trainee Áurea Maria Castelo Branco Leal
for her collaboration in the assays and in the evaluation of the results.
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with temperature and Concentration, Journal
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CONSTENLA, D.T., LOZANO, J.E., CRAPISTE,
G.H. Thermophysical Properties of Clarified
Apple Juice as a Function of Concentration and
Temperature, Journal of Food Science,
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Braz. J. Food Technol., Campinas, 1(1,2): 70-76, Jan eZ.1998
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