Chapter 2
Heat Conduction Equation
246E
A 1.5kW resistance heater wire is used for space heating. Assuming constant thermal conductivity
and onedimensional heat transfer, the mathematical formulation (the differential equation and the
boundary conditions) of this heat conduction problem is to be obtained for steady operation.
Assumptions
1
Heat transfer is given to be steady and onedimensional.
2
Thermal conductivity is given to
be constant.
3
Heat is generated uniformly in the wire.
Analysis
The heat flux at the surface of the wire is
&
&
&
(.
q
Q
A
G
rL
s
s
==
=
=
s
2
W
in)(15 in)
.2 W / in
2
1200
20
0
6
212
0
ππ
Noting that there is thermal symmetry about the center line and there is uniform heat flux at the outer
surface, the differential equation and the boundary conditions for this heat conduction problem can be
expressed as
0
1
=
+
⎟
⎠
⎞
⎜
⎝
⎛
k
g
dr
dT
r
dr
d
r
&
2 kW
L
= 15 in
D
= 0.12 in
dT
dr
k
dT r
dr
q
s
()
&
0
0
212
0
=
−=
=
.2 W / in
2
247
Heat conduction through the bottom section of an aluminum pan that is used to cook stew on top of
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Conductivity, Resistance, Mass, Heat, Heat Transfer, Trigraph, heat conduction problem

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