PROBLEM 4.28
KNOWN:
Dimensions and surface temperatures of a square channel.
Number of chips mounted on
outer surface and chip thermal contact resistance.
F
IND:
Heat dissipation per chip and chip temperature.
SCHEMATIC:
ASSUMPTIONS:
(1) Steady state, (2) Approximately uniform channel inner and outer surface
temperatures, (3) Twodimensional conduction through channel wall (negligible endwall effects), (4)
Constant thermal conductivity.
ANALYSIS:
The total heat rate is determined by the twodimensional conduction resistance of the
channel wall, q = (T
2
– T
1
)/R
t,cond(2D)
, with the resistance determined by using Equation 4.21 with Case
1 of Table 4.1.
For W/w = 1.6 > 1.4
1
()
t,cond(2D)
0.930 ln W / w
0.050
0.387
R
0.00160 K / W
2
L k
2
0.160m 240 W / m K
ππ
−
==
=
⋅
T
he heat rate per chip is then
( )
21
c
t,cond 2D
50 20 C
TT
q
156.3 W
N R
120 0.0016 K / W
−°
−
=
<
a
nd, with q
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This note was uploaded on 12/07/2010 for the course MAE Heat Trans taught by Professor Lee,j.s. during the Spring '10 term at Seoul National.
 Spring '10
 LEE,J.S.
 Heat Transfer

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