This preview shows page 1. Sign up to view the full content.
Chapter 5
Numerical Methods in Heat Conduction
528
A plate is subjected to specified heat flux on one side and specified temperature on the other. The
finite difference formulation of this problem is to be obtained, and the unknown surface temperature under
steady conditions is to be determined.
Assumptions
1
Heat transfer through the base plate is given to be steady.
2
Heat transfer is one
dimensional since the plate is large relative to its thickness.
3
There is no heat generation in the plate.
4
Radiation heat transfer is negligible.
5
The entire heat generated by the resistance heaters is transferred
through the plate.
Properties
The thermal conductivity is given to be
k
=
20 W/m
⋅
°C.
Analysis
The nodal spacing is given to be
Δ
x
=0.2 cm.
Then the number of nodes
M
becomes
4
1
cm
2
.
0
cm
6
.
0
1
=
+
=
+
Δ
=
x
L
M
The right surface temperature is given to be
T
3
=85
°
C. This problem
involves 3 unknown nodal temperatures, and thus we need to have 3
equations to determine them uniquely.
Nodes 1, 2, and 3 are interior
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat

Click to edit the document details