Chapter 5
Numerical Methods in Heat Conduction
550
A long solid body is subjected to steady twodimensional heat transfer. The unknown nodal
temperatures and the rate of heat loss from the top surface are to be determined.
Assumptions
1
Heat transfer through the body is given to be steady and twodimensional.
2
Heat is
generated uniformly in the body.
Properties
The thermal conductivity is given to be
k
= 180 W/m
⋅
°C.
Analysis
(
a
) The nodal spacing is given to be
Δ
x
=
Δ
x
=
l
=0.1 m, and the general finite difference form of an
interior node equation for steady twodimensional heat conduction for the case of constant heat generation
is expressed as
0
4
2
node
node
bottom
right
top
left
=
+
−
+
+
+
k
l
g
T
T
T
T
T
There is symmetry about a vertical line passing through the middle of the region, and thus we need to
consider only half of the region. Then,
4
3
2
1
and
T
T
T
T
=
=
Therefore, there are there are only 2 unknown nodal temperatures,
T
1
and
T
3
, and thus we need only 2
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat, Heat Transfer, Harshad number, Thermal conductivity, steady twodimensional heat

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