Example 192
Heat is transferred across an infinite plane wall. The left side
is held at
T
1
and the right side is cooled by convection. Find
T
(
x
) and
q
x.
,
f
hT
x = 0
x = L
L
k
T = T
1
Solution:
The conduction equation for this steady, onedimensional
case with no heat generation is
2
2
0
T
x
∂
=
∂
12
TC
x
C
=+
At
x
= 0
T=T
1
x = L
()
f
dT
kh
T
T
dx
−=
−
At
x
= 0,
T=T
1
C
2
=
T
1
x = L
f
T
T
−
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11
2
f
kC
h C L C
T
−=
+
−
( )
1
f
h C L T T
+
−
( )
1
f
hC L h T T
−−
=
−
( )
1
1
f
hT T
C
kh
L
−
=
+
1
1
f
TT
C
k
L
h
−
=
+
1
12
1
()
f
Tx Cx C
x T
k
L
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 Spring '08
 Kaminski

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