Chapter 2
Heat Conduction Equation
268
A compressed air pipe is subjected to uniform heat flux on the outer surface and convection on the
inner surface.
The mathematical formulation, the variation of temperature in the pipe, and the surface
temperatures are to be determined for steady onedimensional heat transfer.
Assumptions
1
Heat conduction is steady and onedimensional since the pipe is long relative to its
thickness, and there is thermal symmetry about the center line.
2
Thermal conductivity is constant.
3
There
is no heat generation in the pipe.
Properties
The thermal conductivity is given to be
k
= 14 W/m
⋅
°C.
Analysis
(
a
) Noting that the 85% of the 300 W generated by the strip heater is transferred to the pipe, the
heat flux through the outer surface is determined to be
2
2
2
W/m
1
.
169
m)
m)(6
(0.04
2
W
300
85
.
0
2
=
×
=
=
=
ππ
L
r
Q
A
Q
q
s
s
s
&
&
&
Noting that heat transfer is onedimensional in the radial
r
direction and heat flux is in the negative
r
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Convection, Mass, Heat, Heat Transfer, ln r1

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