2D-Heat propagation in a matrix in Matlab

Question

I want to calculate and visualize a heat propagation in a 24 x 24 matrix. There are two hot-spots in the matrix whose temperature stays constant over the time. The outer edges of the matrix also stay constant over the time. I am new to MATLAB and until now I have written following script:

%declaration and initialization of matrix with
%24 x 24 cells, start temp. = 20°C
PlateOrg (1:24, 1:24) = 20;
% size of matrix
[height, width] = size(PlateOrg);
cells = height * width;
% percent that is given from one cell to its neighbouring cells
prop = 0.2;
%These are the hot-spots, they heat up the neighbouring cells
%but do not heat up themselves any higher -> their
%temperature is constant over the simulation
PlateOrg(4,4:20) = 100;
PlateOrg(5:9,20) = 80;
PlateOrg(11:19,4) = 50;
PlateOrg(20,4:20) = 60;
%First Contourf 2D-Diagram with start temperatures
contourf(PlateOrg);

PlateOld = [];
PlateOld = PlateOrg;
PlateNew = [];
% the amount of cycles 
cycles = 50;
% Calculation of the heat propagation
for k = 1:cycles
    %the outer edges stay constant at temp. = 20°C
    %for the whole simulation
    PlateNew(:,1) = 20;
    PlateNew(1,:) = 20;
    PlateNew(24,:) = 20;
    PlateNew(:,24) = 20;
    %every cell gets 20 percent heat of four neighbouring cells
    for i=2:height-1
        for j=2:width-1
            PlateNew(i,j)=...
            (1-4*prop)*PlateOld(i,j)+prop*...
            (PlateOld(i,j-1)+PlateOld(i,j+1)+...
             PlateOld(i-1,j)+PlateOld(i+1,j));
        end
    end
end

pause(0.2);
contourf(PlateNew)
colorbar
title('Heat propagation in a plate');
PlateOld = PlateNew;

I figured out the calculation for the heat propagation in two dimensions but the simulation still would not work. Do you see any issues?

Answer 1

the part:

pause(0.2);
contourf(PlateNew)
colorbar
title('Heat propagation in a plate');
PlateOld = PlateNew;

has to be in the for k = 1:cycle loop. The rest should be fine. But at the moment the hot spots are not staying constant. You have to do the same as for the edges.

Regards, Michael

Answer 2

As for your code, looks like your forget set

PlateOld = PlateNew;

on the 41'th line (in the end of "for k = 1:cycles" loop).

Also seems your code produces wrong outer edges constant temperature set on the k 1'st iteration. On the first iteration your PlateNew matrix is empty, so setting

PlateNew(:,1) = 20;
PlateNew(1,:) = 20;

produce filling just one (first) element of the matrix. Your code looks like C-style. Instead MATLAB more efficiently can operate with matrices. So your for loop more efficiently can be implemented as (replaces lines 21-41 in your code)

PlateNew = PlateOld;
% the amount of cycles 
cycles = 50;
% Calculation of the heat propagation
for k = 1:cycles
    %every cell gets 20 percent heat of four neighbouring cells
    PlateNew = filter2(prop * [0 1 0; 1 1/prop-4 1; 0 1 0], PlateNew);

    %the outer edges stay constant at temp. = 20°C
    %for the whole simulation
    PlateNew(:,1) = 20;
    PlateNew(1,:) = 20;
    PlateNew(24,:) = 20;
    PlateNew(:,24) = 20;
end