ME 410
Fall 2007
Homework 3
Due:
September 11, 2007
1. Consider a large plane wall of thickness L = 0.06 m.
The wall surface at x = 0
is insulated while the surface at x = L is maintained at a temperature of 25
°
C.
The thermal conductivity of the wall is k = 26 W/m
°
C, and heat is generated in
the wall at a rate of
3
5
.
0
/
m
W
e
q
q
L
x
o
−
=
where
3
6
/
10
5
.
7
m
W
x
q
o
=
.
Assuming
steady onedimensional heat transfer (a) express the differential equation and
the boundary conditions for the heat conduction through the wall, (b) obtain a
relation for the variation of temperature in the wall by solving the differential
equation and (c) determine the temperature of the insulated surface of the wall.
k, thermal conductivity, is given for isotropic media
Reduced form of the energy equation for isotropic media with heat generation
and boundary conditions
()
s
x
L
x
o
T
L
T
x
T
e
k
q
k
x
q
x
T
=
=
∂
∂
−
=
−
=
∂
∂
=
−
0
)
(
0
5
.
0
2
2
Separate and integrate twice, recalling that heat generation is a function of x
2
1
5
.
0
2
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 Spring '08
 BENARD
 Heat, Heat Transfer, Thermal conductivity, Boundary conditions, Qin, isotropic media

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