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Chapter 2
Heat Conduction Equation
259
The base plate of a household iron is subjected to specified heat flux on the left surface and to
specified temperature on the right surface.
The mathematical formulation, the variation of temperature in
the plate, and the inner surface temperature are to be determined for steady onedimensional heat transfer.
Assumptions
1
Heat conduction is steady and onedimensional since the surface area of the base 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.
4
Heat loss through the upper part of
the iron is negligible.
Properties
The thermal conductivity is given to be
k
= 20 W/m
⋅
°C.
Analysis
(
a
) Noting that the upper part of the iron is well insulated and thus the entire heat generated in the
resistance wires is transferred to the base plate, the heat flux through the inner surface is determined to be
&
&
,
q
Q
A
0
0
4
800
50 000
==
×
=
−
base
2
2
W
160 10
m
W/m
Taking the direction normal to the surface of the wall to be the
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat

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