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Chapter 9
Natural Convection
926
A printed circuit board (PCB) is placed in a room. The average temperature of the hot surface of the
board is to be determined for different orientations.
Assumptions
1
Steady operating conditions exist.
2
Air is an ideal gas with
constant properties.
3
The local atmospheric pressure is 1 atm.
3
The heat
loss from the back surface of the board is negligible.
Properties
The properties of air at 1 atm and the anticipated film
temperature of (
T
s
+
T
∞
)/2 = (45+20)/2 = 32.5
°
C are (Table A15)
1

2
5
K
003273
.
0
K
)
273
5
.
32
(
1
1
7275
.
0
Pr
/s
m
10
631
.
1
C
W/m.
02607
.
0
=
+
=
=
=
×
=
°
=
−
f
T
k
β
υ
Analysis
The solution of this problem requires a trialanderror approach since the determination of the
Rayleigh number and thus the Nusselt number depends on the surface temperature which is unknown
L
= 0.2 m
Insulation
Air
T
∞
= 20
°
C
PCB,
T
s
8 W
(
a
)
Vertical PCB
. We start the solution process by “guessing” the surface temperature to be 45
°
C for the
evaluation of the properties and
h
. We will check the accuracy of this guess later and repeat the calculations
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Convection, Mass

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