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ME 608
Numerical Methods in Heat, Mass, and Momentum Transfer
Final Examination
Date: April 30, 2008
8:0010:00 AM
Instructor: J. Murthy
Open Book, Open Notes
Total: 50 points
Use the finite volume method in all problems.
NAME:
Problem
Points
Score
1
25
2
25
TOTAL
50
1
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View Full Document1. Consider onedimensional steady laminar incompressible flow in a porous medium in the domain shown in Fig. 1.
The flow is described by the following governing equations:
∂
u
x
=
0
0
=

μ
u
κ

p
x
+
x
p
u
x
P
All properties may be considered constant, with
=
10

3
kg
/
(
m

s
)
and the permeability
= 10

2
m
2
. The length
of the domain,
L
, is 0
.
3
m
. The inlet velocity is given as
u
1
=
0
.
5
m
/
s
and the outlet velocity is
u
4
=
0
.
5
m
/
s
.
You are asked to solve for the velocity and pressure field in the 3cell computational domain shown in Figure 1 using the
finite volume method and the SIMPLE algorithm.
Use a staggered mesh, and perform only one iteration of SIMPLE
.
Start with an initial guess of
p
=
0
Pa
everywhere. Use underrelaxation factors of
α
u
=
1
.
0 and
p
=
1
.
0.
(a) Develop the appropriate discrete momentum equations, first showing the analytical expressions for the various
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