12-31
12-59
Air is blown over an aluminum plate mounted on an array of power transistors. The number of transistors that can be placed on this plate is to be determined.
Assumptions 1
Steady operating conditions exist.
2
The critical Reynolds number is Re ideal gas with constant properties.
6
The local atmospheric pressure is 1 atm. cr
= 5 u
10
5
.
3
Radiation effects are negligible
4
Heat transfer from the back side of the plate is negligible.
5
Air is an
Properties
The properties of air at the film temperature of
(
T s
+
T f
)/2 = (65+35)/2 = 50 q
C are (Table A-22)
Transistors
Q k
Pr
0 .
02735 W/m.
q
C
1 .
798 u
10
5
0 .
7228 m
2
/s
T
Air
V
= 4 m/s f
= 35 q C
T s
=65 q
C
Analysis
The Reynolds number is
Re
L
VL
Q
(4 m/s)(0.25
1 .
798 u 10
5 m) m
2
/s
55 , 617
L
=25 cm which is less than the critical Reynolds number. Thus the flow is laminar. Using the proper relation in laminar flow for Nusselt number, heat transfer coefficient and the heat transfer rate are determined to be
Nu h hL k k
L
Nu
0 .
664
0 .
Re
L
02735
0 .
5
Pr
W/m.
0 .
25 m
1 / 3 q
C
0 .
664
( 140 .
5 )
( 55 , 617 )
15 .
37
0 .
5
( 0
W/m
.
7228
2
.
q
C
)
1 / 3
140 .
5
A s
Q conv wL
( 0 .
25 hA s
(
T f
T s m)(0.25
m)
)
= 0.0625
m
2
( 15 .
37 W/m
2
.
q
C)(0.0625
m
2
)(65 35) q
C = 28.83
W
Considering that each transistor dissipates 6 W of power, the number of transistors that can be placed on this plate becomes n
28 .
8 W
6 W
4 .
8
4
This result is conservative since the transistors will cause the flow to be turbulent, and the rate of heat transfer to be higher.
PROPRIETARY MATERIAL
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