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.

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.

ChapterMA: Math Assessment

Section: Chapter Questions

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Concept explainers

Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.

Question

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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