
194 Heat Transfer: Thermal Management of Electronics
where λ
n
is the solution of the equation λ
n
W tan λ
n
W = hW/k for n = 1, 2, 3, …
Figure 8.16 shows a thin rectangular plate or a long rectangular rod with uniform
internal heat generation. The sides at x = 0 and y = 0 are adiabatic and the sides at
x = L and y = W are at T = T
1
. The solution of two-dimensional heat conduction equa-
tion for this domain is [1,2]
TxyT
gL
k
x
L
g
Lk
n
n
(,)
()
=+ −
()
−
−
1
2
2
3
2
1
21
λ
ccoscosh
cosh
()
λλ
λ
λ
π
nn
n
n
n
xy
W
n
L
=
∑
=
+
0
21
2
∞
where..
(8.61)
8.5 TRANSIENT HEAT CONDUCTION
Consider a section of a thin plane wall shown in Figure 8.17. Let’s assume that the ini-
tial temperature distr ...