Chapter 5
Numerical Methods in Heat Conduction
524
A uranium plate is subjected to insulation on one side and convection on the other. The finite
difference formulation of this problem is to be obtained, and the nodal temperatures under steady
conditions are to be determined.
Assumptions
1
Heat transfer through the wall is steady since there is no indication of change with time.
2
Heat transfer is onedimensional since the plate is large relative to its thickness.
3
Thermal conductivity is
constant.
4
Radiation heat transfer is negligible.
Properties
The thermal conductivity is given to be
k
= 28 W/m
⋅
°C.
Analysis
The number of nodes is specified to be
M
= 6. Then the nodal spacing
Δ
x
becomes
m
01
.
0
1

6
m
05
.
0
1
=
=
−
=
Δ
M
L
x
This problem involves 6 unknown nodal temperatures, and thus we need to have 6 equations to determine
them uniquely.
Node 0 is on insulated boundary, and thus we can treat it as an interior note by using the
mirror image concept. Nodes 1, 2, 3, and 4 are interior nodes, and thus for them we can use the general
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Convection, Mass, Heat, Heat Transfer, Δx, nodal temperatures

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