3. The steady-state distribution of temperature on a heated plate canbe modeled by the Laplace equation,25°C25°CIf the plate is represented by aseries of nodes (Fig.1), centeredfinite-dividedT12100°CdifferencescansubstitutedforthesecondT31100°Cderivatives, which results in asystem of linear algebraic equationsas follows:75°C76°CUse the Gauss-Seidel method tosolve for the temperatures of thein Fig.1.0 |T,-1T2-1T,4(175)|1257525-1 -1414- 14-1 -111nodesPerformthe21computation until ɛ, is less than &s= 0.5%.T,22%3D

Answered: Image /qna-images/answer/2c665071-b526-4fdc-96b9-f54f71284247.jpg

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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Question

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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