3. The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation, 25°C 25°C If the plate is represented by a series of nodes (Fig.1), centered T12 100°C finite-divided differences can substituted for the second T31 100°C 10°C derivatives, which results in a system of linear algebraic equations as follows: 75°C 75°C
3. The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation, 25°C 25°C If the plate is represented by a series of nodes (Fig.1), centered T12 100°C finite-divided differences can substituted for the second T31 100°C 10°C derivatives, which results in a system of linear algebraic equations as follows: 75°C 75°C
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. The steady-state distribution of temperature on a heated plate can
be modeled by the Laplace equation,
25°C
25°C
If the plate is represented by a
series of nodes (Fig.1), centered
finite-divided
T12
100°C
differences
can
substituted
for
the
second
T31
100°C
derivatives, which results in a
system of linear algebraic equations
as follows:
75°C
76°C
Use the Gauss-Seidel method to
solve for the temperatures of the
in Fig.1.
0 |T,
-1T2
-1T,
4
(175)
|125
75
25
-1 -1
4
1
4
- 1
4
-1 -1
11
nodes
Perform
the
21
computation until ɛ, is less than &s
= 0.5%.
T,
22
%3D
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