Chapter 2
Heat Conduction Equation
2130
The base plate of an iron is subjected to specified heat flux on the left surface and convection and
radiation on the right surface.
The mathematical formulation, and an expression for the outer surface
temperature and its value 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.
4
Heat loss through the upper part of the iron is negligible.
Properties
The thermal conductivity and emissivity are given to be
k
= 2.3 W/m
⋅
°C and
ε
= 0.7.
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
2
2
4
base
0
0
W/m
000
,
100
m
10
150
W
1500
=
×
=
=
−
A
Q
q
&
&
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
=
and
−=
=
k
dT
dx
q
()
&
,
0
80 000
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Convection, Mass, Heat, Radiation, Heat Transfer, Thermal conductivity, heat conduction equation, base plate, mathematical formulation

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