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Chapter 2
Heat Conduction Equation
2128
A large plane wall is subjected to convection, radiation, and specified temperature on the right
surface and no conditions on the left surface.
The mathematical formulation, the variation of temperature
in the wall, and the left surface temperature are to be determined for steady onedimensional heat transfer.
Assumptions
1
Heat conduction is steady and onedimensional since the wall is large relative to its
thickness, and the thermal conditions on both sides of the wall are uniform.
2
Thermal conductivity is
constant.
3
There is no heat generation in the wall.
Properties
The thermal conductivity and emissivity are given to be
k
= 8.4 W/m
⋅
°C and
ε
= 0.7.
Analysis
(
a
) Taking the direction normal to the surface of the wall to be the
x
direction with
x
= 0 at the left
surface, and the mathematical formulation of this problem can be expressed as
dT
dx
2
2
0
=
and
−
=
−+
−
=
+
−
∞∞
k
dT L
dx
hT L
T
T L
T
hT T
T
T
()
[
(
)][
(
)
]
[
][
(
)
εσ
4
22
4
273
surr
4
surr
4
]
TL T
==°
2
45 C
(
b
)
Integrating the differential equation twice with respect to
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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, Radiation

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