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Chapter 2
Heat Conduction Equation
266E
A large plate is subjected to convection, radiation, and specified temperature on the top surface and
no conditions on the bottom surface.
The mathematical formulation, the variation of temperature in the
plate, and the bottom surface temperature are to be determined for steady onedimensional heat transfer.
Assumptions
1
Heat conduction is steady and onedimensional since the plate is large relative to its
thickness, and the thermal conditions on both sides of the plate are uniform.
2
Thermal conductivity is
constant.
3
There is no heat generation in the plate.
Properties
The thermal conductivity and emissivity are given to be
k
=7.2 Btu/h
⋅
ft
⋅
°F and
ε
= 0.6.
Analysis
(
a
) Taking the direction normal to the surface of the plate to be the
x
direction with
x
= 0 at the
bottom surface, and the mathematical formulation of this problem can be expressed as
dT
dx
2
2
0
=
and
]
)
460
[(
]
[
]
)
(
[
]
)
(
[
)
(
4
sky
4
2
2
4
sky
4
T
T
T
T
h
T
L
T
T
L
T
h
dx
L
dT
k
−
+
+
−
=
−
+
−
=
−
∞
∞
εσ
TL T
()
==°
2
75 F
(
b
)
Integrating the differential equation twice with
respect to
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Convection, Mass, Heat, Radiation

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