ME 608
Numerical Methods in Heat, Mass, and Momentum Transfer
MidTerm Examination
Date: March 5, 2008
6:00 – 7:30 PM
Instructor: J. Murthy
Open Book, Open Notes
Total: 50 points
Use the finite volume method in all problems.
NAME:
Problem
Points
Score
1
30
2
20
TOTAL
50
1
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1. Consider laminar hydrodynamically and thermally fullydeveloped flow in a 2D parallel plate channel, as shown in
Fig. 1. There is a constant heat generation S in the channel. Neglecting axial diffusion, the energy equation may be
written as:
∂
∂
x
(
ρ
C
p
u
(
y
)
T
) =
∂
∂
y
parenleftbigg
k
∂
T
∂
y
parenrightbigg
+
S
The walls of the channel are perfectly insulated. The velocity field
u
(
y
)
is the classical parabolic profile, given by:
u
(
y
)
u
m
=
3
2
parenleftbigg
1

parenleftBig
y
D
parenrightBig
2
parenrightbigg
Here
u
m
is the mean velocity at any x location.
All properties are assumed constant in keeping with the concept of fullydeveloped flow and heat transfer. You are
given the following information:
ρ
=
1
kg
/
m
3
,
C
p
=
1000
J
/
kgK
,
u
m
=
0
.
1
m
/
s
,
k
=
0
.
5
W
/
mK
,
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 Fall '10
 NA
 Thermodynamics, Numerical Analysis, Heat, finite volume method, axial diffusion

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