Plot heat conduction temperature at various radii with Matlab

Question

I have an array in Matlab that is updated for every time step: each row corresponds to a time and each column represents a temperature at a certain radius from the center. It would also be handy if a color gradient could be applied to the plot using the meshgrid and contourf commands. So far, this is the Matlab code that I have, but I am not sure how to get the temperature into the plot and animate the change in temperature.

Tinf = 200;  % ambient temperature

% where r1 = radius1, r2 = radius2, etc.
%        t = time
%        rows = time
%        columns = radius

%    r1   r2    r3    r4    r5
T = [98   105   110   118   128;  % t=1
     109  110   117   124   134;  % t=2
     110  118   120   130   144]; % t=3

r = 0.08;  % radius of circle

rx = -r:0.01:r;
ry = r:-0.01:-r;

[x_coor, y_coor] = meshgrid(rx, ry);

radius = sqrt(x_coor.^2+y_coor.^2);

figure(1)
contourf(radius,'edgecolor','none')

I am trying to create a circular plot in Matlab that would show the temperature (color) at each radius and animate that temperature (change color) as it increases or decreases with time.

An example of such a plot at a certain time would be:

So column 1 in the T array corresponds to node 1 in the picture, column 2 corresponds to node 2, etc. Thus at time = 0 then node1 = 98, node2 = 105, node3 = 110, node4 = 118, node5 = 128; at time = 1 then node1 = 109, node2 = 110, node3 = 117, node4 = 124, node5 = 134; and so on.

Any suggestions to accomplish such a plot would be very helpful.

Answer 1

Same as @Magla's nice answer but draws a single surface (not an overlay) allowing interpolation

T = [98   105   110   118   128;
    109  110   117   124   134;
    114  118   120   130   138];

Rmax = 30;
[x,y,z] = sphere(100);
x=x*Rmax;
y=y*Rmax;

rxy2 = x.^2+y.^2;


r = [0 10 20 30];
r2 = r.^2;

figure('Color', 'w');

for ind_t = 1:size(T,1)
    for ii = 1:length(r2)-1
        ir_find = find(rxy2<=r2(ii+1) & rxy2>r2(ii));
        z(ir_find) = T(ind_t,ii);
    end

    hax = axes('Position',[0 0 1 1]);
    h = surf(x,y,z)  % sphere centered at origin

    shading interp
    set(h, 'EdgeColor', 'None');

    view(0,90);
    axis equal;
    set(hax, 'Visible', 'Off', 'CLim', [min(T(:)) max(T(:))]);
    pause(0.5);
end

edit

Rewrote to use meshgrid and to use the particular radii etc of interest. Make sure to adjust r_res to a value you find adequate.

T = [98   105   110   118   128;
    109  110   117   124   134;
    114  118   120   130   138];

%---------------------------------------
r = 0.08;  % radius of circle

r_res = 0.0005;

rx = -r:r_res:r;
ry = rx;

[x, y] = meshgrid(rx, ry);

rxy2 = x.^2+y.^2;
z=ones(size(rxy2))*NaN;

%---------------------------------------

Nshells = size(T,2);
r = [0:1/Nshells:1]*r;
r2 = r.^2;

figure('Color', 'w');
colormap hot

for ind_t = 1:size(T,1)
    for ii = 1:Nshells
        ir_find = find(rxy2<=r2(ii+1) & rxy2>r2(ii));
        z(ir_find) = T(ind_t,ii);
    end

    hax = axes('Position',[0 0 1 1]);
    h = surf(x,y,z)  % sphere centered at origin

    shading interp
    set(h, 'EdgeColor', 'None');

    view(0,90);
    axis equal;
    set(hax, 'Visible', 'Off', 'CLim', [min(T(:)) max(T(:))]);
    pause(0.5);
end

Answer 2

Here is a solution that makes use of sphere. sphere generates the matrices x and y that are multiply by a decreasing radius r, and matrix z that is reduced to a single value (a sphere becomes a disk). z is multiplied by the temperature and disks are plotted on top of each other. Colors depend on the min and max of the whole input matrix. Animation is done with pause.

T = [98   105   110   118   128;
    109  110   117   124   134;
    114  118   120   130   138];

[x,y,z] = sphere(100);
r = [50 40 30 20 10];

figure('Color', 'w');

for ind_t = 1:size(T,1)

    hax = axes('Position',[0 0 1 1]);

    for ii = 1:length(r)
        h = surf(x*r(ii),y*r(ii),z*0+T(ind_t,ii))  % sphere centered at origin
        set(h, 'EdgeColor', 'None');
        hold on;
    end

    view(0,90);
    axis equal;
    set(hax, 'Visible', 'Off', 'CLim', [min(T(:)) max(T(:))]);
    pause(0.5);

end

This gives