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Chapter 2
Heat Conduction Equation
2135
A large plane wall is subjected to convection on the inner and outer surfaces. The mathematical
formulation, the variation of temperature, and the temperatures at the inner and outer surfaces to be
determined for steady onedimensional heat transfer.
Assumptions
1
Heat conduction is steady and onedimensional.
2
Thermal conductivity is constant.
3
There is no heat generation.
Properties
The thermal conductivity is given to be
k
= 0.77 W/m
⋅
°C.
Analysis
(
a
) Taking the direction normal to the surface of the wall to be the
x
direction with
x
= 0 at the
inner surface, the mathematical formulation of this problem can be expressed as
dT
dx
2
2
0
=
and
dx
dT
k
T
T
h
)
0
(
)]
0
(
[
1
1
−
=
−
∞
]
)
(
[
)
(
2
2
∞
−
=
−
T
L
T
h
dx
L
dT
k
(
b
)
Integrating the differential equation twice with respect to
x
yields
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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, Convection, Mass, Heat

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