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
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 01/19/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.
 Fall '10
 Dr.DanielArenas
 Thermodynamics, Convection, Mass, Heat

Click to edit the document details