2D Temperature Distribution

Question

Jonathan Bird 2020-2-18

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https://ww2.mathworks.cn/matlabcentral/answers/506276-2d-temperature-distribution

评论： darova 2020-2-21

I need to plot the temperature distribution for the square cross-section of a bar, 3 sides are fixed at a temperature of 283 K, the fourth side at 508 K and the initial temperature of the interior is 307 K everwhere. The analytical solution is as follows:

L and W are both equal to 1, and the summation is done from n =1 to n =100. Here is what I have done so far, I've tried to make 100 10 x 10 grids and populate each element with values for theta and then sum all the grids to give a final 10 x 10 grid for the temperature distribution. I don't really understand how to execute this with for loops, thanks for any help.

X = 10;

Y = 10;

theta1 = zeros (X,Y);

for n =1:100

for X1 = 1:X

for Y1 = 1:Y

theta1(n,X1,Y1)=(2/pi)*(((-1)^(n+1)+1)/(n))*sin(n*pi*X1/L)*(sinh(n*pi*Y1/L))/(sinh(n*pi*W/L));

end

theta1sum = sum(theta1);

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darova 2020-2-18

I found a mistake

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Answer 1

darova 2020-2-18

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https://ww2.mathworks.cn/matlabcentral/answers/506276-2d-temperature-distribution#answer_416248

在 MATLAB Online 中打开

I made some changes in your code

X = 10;
Y = 10;
theta1 = zeros(X,Y);
for n =1:100
    theta1 = theta1 + (2/pi)*(((-1)^(n+1)+1)/(n))*sin(n*pi*X1/L).*(sinh(n*pi*Y1/L))./(sinh(n*pi*W/L));
end
surf(X,Y,theta1)

Pay attention to bit-wise operators (i highlighted in red)

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Jonathan Bird 2020-2-21

Thanks for your help, unfortunately I get the following error message.

Error using surf (line 71)

Data dimensions must agree.

Error in HEAT_TRANSFER_CW (line 40)

surf(X,Y,theta1)

darova 2020-2-21

在 MATLAB Online 中打开

Try

X = 10;
Y = 10;
[X1,Y1] = meshgrid(1:X,1:Y);
theta1 = zeros(X,Y);
for n =1:100
    theta1 = theta1 + (2/pi)*(((-1)^(n+1)+1)/(n))*sin(n*pi*X1/L).*(sinh(n*pi*Y1/L))./(sinh(n*pi*W/L));
end
surf(X,Y,theta1)