12.42 The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation, 0= FT T + 200°C 25°C 25°C T22 0°C T₁ T21 200°C FIGURE P12.42 75°C 75°C 00°C If the plate is represented by a series of nodes (Fig. P12.42), cen- tered 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 Fig. P12.42.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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12.42 The steady-state distribution of temperature on a heated
plate can be modeled by the Laplace equation,
0=
FT T
+
200°C
25°C
25°C
T22
0°C
T₁
T21
200°C
FIGURE P12.42
75°C
75°C
00°C
If the plate is represented by a series of nodes (Fig. P12.42), cen-
tered 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 Fig. P12.42.
Transcribed Image Text:12.42 The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation, 0= FT T + 200°C 25°C 25°C T22 0°C T₁ T21 200°C FIGURE P12.42 75°C 75°C 00°C If the plate is represented by a series of nodes (Fig. P12.42), cen- tered 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 Fig. P12.42.
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