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Chapter 5
Numerical Methods in Heat Conduction
562
A rectangular block is subjected to uniform heat flux at the top, and iced water at 0
°
C at the sides.
The steady finite difference formulation of the problem is to be obtained, and the unknown nodal
temperatures as well as the rate of heat transfer to the iced water are to be determined.
Assumptions
1
Heat transfer through the body is given to be steady and twodimensional.
2
There is no
heat generation within the block.
3
The heat transfer coefficient is very high so that the temperatures on
both sides of the block can be taken to be 0°C.
4
Heat transfer through the bottom surface is negligible.
Properties
The thermal conductivity is given to
be
k
= 23 W/m
⋅
°C.
Analysis
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 2D heat conduction is expressed as
0
4
0
4
node
bottom
right
top
left
2
node
node
bottom
right
top
left
=
−
+
+
+
=
+
−
+
+
+
T
T
T
T
T
k
l
g
T
T
T
T
T
&
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat

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