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Chapter 2
Heat Conduction Equation
Assumptions
1
Heat transfer is given to be transient and onedimensional.
2
Thermal conductivity is given
to be variable.
3
There is no heat generation in the medium.
4
The outer surface at
r
=
r
0
is subjected to
convection and radiation.
Analysis
Noting that there is thermal symmetry about the midpoint and convection and radiation at the
outer surface and expressing all temperatures in Rankine, the differential equation and the boundary
conditions for this heat conduction problem can be expressed as
t
T
C
r
T
kr
r
r
∂
ρ
=
⎟
⎠
⎞
⎜
⎝
⎛
2
2
1
T
i
r
2
T
∞
h
k
ε
T
surr
surr
4
εσ
Tt
r
k
Tr t
r
hTr
T
Tr
T
T
i
(,)
(,
)
[()
]
]
0
0
0
0
00
4
=
−=
−
+−
=
∞
251
The outer surface of the North wall of a house exchanges heat with both convection and radiation.,
while the interior surface is subjected to convection only.
Assuming the heat transfer through the wall to
be steady and onedimensional, the mathematical formulation (the differential equation and the boundary
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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, Conductivity, Mass, Heat

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