How do I perform a for-loop with 2 variables

Daniel Eisentraud

2018 10 30

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I am trying to simulate the heating of a cube. Energy coming only from the top Surface. Seeing the cube as a single mass-point wasnt a Problem, but now I have to "cut " it into 10/20/30 layers. How can I simulate the heating over time, while taking into account that the 10 layers are transferring the heat from each layer. I dont want the 2nd variabel to be time-dependant.

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Daniel Eisentraud 2018-10-31

编辑：Daniel Eisentraud 2018-10-31

在 MATLAB Online 中打开

I think i got the idea. What I am trying (and not managing) to do now is solving the following term with C1 and C2 as a constant value.

 n=Number of timesteps
tMax = 12hours 
h =hight of the block
s= number of layers 
 dt=tMax/n
  dx=h/s
for i=2:n
    for m=2:s   %Want to run to the last layer, 
I would define T(i,s+1)= T(i,s) since the bottom of the block is isolated
 T(1,m)=290 %Starting Temp [K]
T(i,1)= C2*exp(-t(i)*10^(-4.1))+T(i-1,1);
T(i,m)=(T(i,m+1)+T(i,m-1)+C1*T(i-1,m))/(C1+2);
end
end

Thats what I have in mind but cant get to work. M is the number of the current layer and it should write every layer's Temperatur at any point in time into my matrix. In the end i want to sum up the layers at any instance of i and divide them by the number of layers (s) to have an average temperature of the block itself.

I need help to make this work by creating proper matrixes. I am not too sure about the way I loop either. In general working with equations that need 2 variables and therefore matrixes arent something I am used too, so i would be so thankful for any help.

Daniel Eisentraud 2018-10-31

编辑：Daniel Eisentraud 2018-10-31

在 MATLAB Online 中打开

Now i coded this: (T_0 is the starting temp,) It seems to do what it shoudl for the first 10 intervals:

</matlabcentral/answers/uploaded_files/138933/test.JPG> after the 10 intervals it starts doign wierd things

    dt=tTOT/n;
dx=h/l;
C1=(roh*c*dx^2)/(dt*lam);
C2=(q_s*A*dt)/(V*roh*c);
T=T_0*ones(l,n);
for i=2:n
        for m=2:l   
        T(i,1)= C2*exp(-(dt*(i-1))*10^(-4.1))+T(i-1,1);
        T(i,m)=(T(i,m+1)+T(i,m-1)+C1*T(i-1,m))/(C1+2);
    end
end