The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation, a²T ²T + a²x a²y 0= If the plate is represented by a series of nodes as illustrated in Figure, centered finite-divided differences can be substituted for the second derivatives, which results in a system of linear algebraic equations. Use the Gauss-Seidel method to solve for the temperatures of the nodes in Figure.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation,
a²T ²T
+
a²x a²y
If the plate is represented by a series of nodes as illustrated in Figure, centered finite-divided differences
can be substituted for the second derivatives, which results in a system of linear algebraic equations.
Use the Gauss-Seidel method to solve for the temperatures of the nodes in Figure.
0=
Submission date: 09/01/2024
25°C
T12
T₂2
250°C
#
T₁1
T₂1
250 CO
75°C
25°C
75°C
0°C
0°C
Transcribed Image Text:The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation, a²T ²T + a²x a²y If the plate is represented by a series of nodes as illustrated in Figure, centered finite-divided differences can be substituted for the second derivatives, which results in a system of linear algebraic equations. Use the Gauss-Seidel method to solve for the temperatures of the nodes in Figure. 0= Submission date: 09/01/2024 25°C T12 T₂2 250°C # T₁1 T₂1 250 CO 75°C 25°C 75°C 0°C 0°C
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