
184 Heat Transfer: Thermal Management of Electronics
Radiation boundary conditions for both sides of the thin plane wall shown in
Figure 8.8 can be written as
surr,1
4
−
∂
∂
=−
[]
−
∂
∂
k
T
x
TTt
k
T
x
t(,)
(
(,),
0
1
4
0εσ
LLt
TLtT
,)
(,).=−
[]
εσ
2
4
2
4
surr,
(8.40)
Example 8.4
Let’s consider the silicon die of Example 8.2 and assume that the back side of this
die has an emissivity of 0.7 and is exposed to a surrounding at 25°C. Obtain an
expression for temperature distribution inside this die.
Solution
The differential equation and the boundary conditions are
dT
dx
k
dT
dx
x
2
2
0
0
2
=
−=
=
,
()
Boundary Conditions:
00000
0 0007
0 0007
4
W/m.
m
2
m
−=
=
k
dT
dx
T
x(. )
((.)εσ −−
298
4
).
The genera ...