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Chapter 2
Heat Conduction Equation
256
A large plane wall is subjected to specified temperature on the left surface and convection on the right
surface.
The mathematical formulation, the variation of temperature, and the rate of heat transfer are 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
= 2.3 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 left
surface, the mathematical formulation of this problem can be expressed as
dT
dx
2
2
0
=
x
T
∞
=15°C
h=
24 W/m
2
.°C
T
1
=80°C
A=
20 m
2
L=
0.4 m
k
and
TT
()
08
0
1
==°
C
−=
−
∞
k
dT L
dx
hT L T
[()
]
(
b
) Integrating the differential equation twice with respect to
x
yields
dT
dx
C
=
1
Tx
Cx C
=+
12
where
C
and
C
1
2
are arbitrary constants.
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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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