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Chapter 7
External Forced Convection
729
A fan blows air parallel to the passages between the fins of a heat sink attached to a transformer. The
minimum freestream velocity that the fan should provide to avoid overheating is to be determined.
Assumptions
1
Steady operating conditions exist.
2
The critical Reynolds number is Re
cr
= 5
×
10
5
.
3
The
fins and the base plate are nearly isothermal (fin efficiency is equal to 1)
4
Air is an ideal gas with constant
properties.
5
The local atmospheric pressure is 1 atm.
Properties
The properties of air at the film temperature of
(T
s
+ T
∞
)/2 = (60+25)/2 = 42.5
°
C are (Table A15)
7248
.
0
Pr
/s
m
10
726
.
1
C
W/m.
02681
.
0
2
5

=
×
=
°
=
υ
k
Analysis
We first need to determine radiation heat transfer rate. Note that we
will use the base area and we assume the temperature of the surrounding
surfaces are at the same temperature with the air (
T
surr
=
°
25 C )
Air
V
∞
T
∞
= 25
°
C
L
= 10 cm
T
s
= 60
°
C
20 W
W
1.4
]
K)
273
25
(
K)
273
60
)[(
C
.
W/m
10
67
.
5
(
m)]
m)(0.062
1
.
0
)[(
90
.
0
(
)
(
4
4
2
8
4
4
=
+
−
+
°
×
=
−
=
−
surr
s
s
rad
T
T
A
Q
σε
&
The heat transfer rate by convection will be 1.4 W less than total rate of heat transfer from the transformer.
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Convection, Force, Mass, Heat

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