December 2009
Intermediate to advanced
523 pages
18h 30m
English
Content preview from Heat Transfer
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Heat Conduction Equation 189
Conduction heat transfer rate to the left and right sides of this wall are
cond,1cond
QQ kA
dT
dx
kA
TT
L
g
x
== =
−
+
=
()0
0
21
22k
L
QQLkA
dT
dx
k
xL
==−=−
=
,
()
cond,2cond
AA
TT
L
g
k
L
21
2
−
−
.
(8.49)
Note that
QQ gALG
cond,1cond,2
+==
is the total heat generated inside this wall.
Next, let’s consider the same thin plane wall with convection boundary conditions
on both sides as shown in Figure 8.12. The steady-state heat conduction equation and
the boundary conditions for this case are
dT
dx
g
k
k
dT
dx
h
x
2
2
0
0+=
=
=
,Boundary Conditions:
111
22
0(())
(())
,
,
TT
k
dT
dx
hTLT
xL
−
−=−
=
∞
∞
(8.50)
h
1
T
∞, 1
T
∞, 2
h
2
x
L0
g
Q
cond, 2
Q
cond, 1
FIGURE 8. ...
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