I'm having trouble plotting the temperature field for a thin plate with border temperatures known.

Hello everyone, i'm having trouble plotting the temperature distribution for a 2d heat transfer in a thin plate, with border temperatures known. I have to plot the distribution from the equation in the figure. For now I'm using the following code, but It doesn't seem to be working.

X = 5;

Y = 5;

L = 1;

W =1;

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)

X and Y being the number of nodes.

Answer 1

[Torsten]

Write a function

function T = Temp(x,y)
  T = ...;
end

in which you calculate the value of the infinite sum for x-y coordinates (x,y) and call and plot the function like

x = 0:0.1:1;
y = 0:0.1:1.5;
[X,Y] = ndgrid(x,y);
for i = 1:numel(x)
    for j = 1:numel(y)
        T(i,j) = Temp(x(i),y(j));
    end
end
surf(X,Y,T)

Answer 2

[William Rose]

@Lucas Resende,

theta1 has dimensions 5x5.

You define it with a loop over n=1:100. SInce there is no index in the assignment statement, you are assigning a value to all of theta1 on each loop pass. YOu need to do something like

for i=1:5
    for j=1:5
        theta1(i,j)=sin(i/2)+cos(j)/2;    %or whatever
    end
end

Then you must plot it:

surf(1:5,1:5,theta1);  %or similar

Try somehting like that.