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Chapter 2
Heat Conduction Equation
280E
A long homogeneous resistance heater wire with specified convection conditions at the surface is
used to boil water. The mathematical formulation, the variation of temperature in the wire, and the
temperature at the centerline of the wire are to be determined.
Assumptions
1
Heat transfer is steady since there is no indication of any change with time.
2
Heat transfer
is onedimensional since there is thermal symmetry about the center line and no change in the axial
direction.
3
Thermal conductivity is constant.
4
Heat generation in the wire is uniform.
Properties
The thermal conductivity is given to be
k
= 8.6 Btu/h
⋅
ft
⋅
°F.
Analysis
Noting that heat transfer is steady and onedimensional in the radial
r
direction, the mathematical
formulation of this problem can be expressed as
0
1
=
+
⎟
⎠
⎞
⎜
⎝
⎛
k
g
dr
dT
r
dr
d
r
&
and
−=
−
∞
k
dT r
dr
hTr
T
()
[()
]
0
0
(convection at the outer surface)
dT
dr
0
0
=
(thermal symmetry about the centerline)
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This note was uploaded on 01/14/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.
 Fall '10
 Dr.DanielArenas
 Thermodynamics, Resistance, Convection, Mass, Heat

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