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Chapter 9
Natural Convection
935
An insulated electric wire is exposed to calm air. The temperature at the interface of the wire and the
plastic insulation is to be determined.
Assumptions
1
Steady operating conditions exist.
2
Air is an ideal gas with constant properties.
3
The local
atmospheric pressure is 1 atm.
Properties
The properties of air at 1 atm and the anticipated film
temperature of (
T
s
+
T
∞
)/2 = (50+30)/2 = 40
°
C are (Table A15)
Air
T
∞
= 30
°
C
T
s
ε
= 0.9
L
= 12 m
D
=
6 mm
Resistance
heater
1

2
5
K
003195
.
0
K
)
273
40
(
1
1
7255
.
0
Pr
/s
m
10
702
.
1
C
W/m.
02662
.
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. We
start the solution process by “guessing” the surface temperature to be 50
°
C for the evaluation of the
properties and
h
. We will check the accuracy of this guess later and repeat the calculations if necessary.
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This note was uploaded on 01/24/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.
 Fall '10
 Dr.DanielArenas
 Thermodynamics, Convection, Mass

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