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Chapter 2
Heat Conduction Equation
267E
A large plate is subjected to convection 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 is given to be
k
=7.2 Btu/h
⋅
ft
⋅
°F.
Analysis
(
a
) Taking the direction normal to the surface of the plate to be the
x
direction with
x
= 0
at the bottom surface, the mathematical formulation of this problem can be expressed as
dT
dx
2
2
0
=
and
−=
−
=
−
∞∞
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Convection, Mass, Heat

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