I need this question done in Matlab please. Show the code you used for the scrip

Question

I need this question done in Matlab please. Show the code you used for the script file. Thanks a lot. QUESTION 3: (Problem 12.11) The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation: If the plate is represented by a series of nodes (Fig. P12.11), centered finite differences can be substituted for the second derivatives, which result in a system of linear algebraic equations. Use the Gauss-Seidel method to solve for the temperatures of the nodes in Fig. P12.11. (Take a unit square plate) leo . 10oC toot

Explanation / Answer

clear all

clc

L= input('Enter Length:');

H= input('Enter Width:');

T1=input('Enter temperature of the bottom side:');

T2=input('Enter temperature of the right side:');

T3=input('Enter temperature of the top side:');

T4=input('Enter temperature of the left side:');

m= input('Enter the number of horizontal grid points:');

n= input('Enter the number of vertical grid points:');

dx= round(L/m);

dy= round(H/n);

T = zeros(n,m);

for i = 1 : n

for j = 1 : m

T(i,m) = T2;

T(i,1) = T4;

T(n,j) = T3;

T(1,j) = T1;

end

end

T(1,1)= (T1+T4)/2;

T(1,m)= (T1+T2)/2;

T(n,m)= (T2+T3)/2;

T(n,1)= (T3+T4)/2;

A=0;

while isequal(A,T) == 0

A=T;

for i = 2 : n-1

for j = 2 : m-1

T(i,j) = .25*( T(i+1,j)+ T(i-1,j) + T(i,j+1) + T(i,j-1) );

end

end

end

disp(T)

[C,h] = contour(T,[50:1:300]);

clabel(C,h)

colorbar

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