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Chapter 9
Natural Convection
921
A cylindrical resistance heater is placed horizontally in a fluid. The outer surface temperature of the
resistance wire is to be determined for two different fluids.
Assumptions
1
Steady operating conditions exist.
2
Air is an ideal gas with constant properties.
3
The local
atmospheric pressure is 1 atm.
4
Any heat transfer by radiation is ignored.
5
Properties are evaluated at
500
°
C for air and 40
°
C for water.
Properties
The properties of air at 1 atm and 500
°
C are (Table A15)
1

2
5
K
001294
.
0
K
)
273
500
(
1
1
6986
.
0
Pr
/s
m
10
804
.
7
C
W/m.
05572
.
0
=
+
=
=
β
=
×
=
υ
°
=
−
f
T
k
Air
T
∞
= 20
°
C
Resistance
heater,
T
s
400 W
L
=1 m
D
=
0.5 cm
The properties of water at 40
°
C are
1

2
6
K
000377
.
0
32
.
4
Pr
/s
m
10
6582
.
0
/
C
W/m.
631
.
0
=
β
=
×
=
ρ
μ
=
υ
°
=
−
k
Analysis
(
a
) 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
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Resistance, Convection, Mass, Heat

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