0 0 0 hy for uy for Uuo = = = = 0 0 sm U / 40 my 001.0

Application Project 1
Section – 3.5 Page – 67
--------------------------------------------------------------------------------------------Consider a fluid bounded by two parallel plates extended to infinity such that no end
effects are encountered. The planar walls and the fluid are initially at rest. Now, the lower wall
is suddenly accelerated in the x-direction, as illustrated in the Figure
A spatial coordinate system is selected such that the lower wall includes x- & z-axis plane to
which the y-axis is perpendicular. The spacing between two plates is denoted by h.
The Navier-Stokes Equation for this problem may be expressed as
u
 2u
 2
t
x
 is the kinematic viscosity of the fluid. It is required to compute the velocity profile
u  ut , y  . The initial and boundary conditions for this problem are stated as follows:
Where
u  Uo
a) Initial condition
b) Boundary conditions
t=0
t 0
u0
u  Uo
u0
for
y0
for 0  y  h
for
for
y0
yh
m 2 / s , and the spacing between plates is
40 mm. The velocity of the lower wall is specified as U 0  40 m / s . A grid system with
y  0.001 m and various values of time steps is to be used to investigate the numerical
The fluid is oil with a kinematic viscosity of 0.000217
schemes and the effect of time step on stability and accuracy. Solve the stated problem by the
Laasonen implicit method with
a) t  0.002
b) t  0.00232