Plotting Temperature profile as a function of x,y and z.

Hello,

I have a temperature function, which is a function of all 3 co-ordinates x,y and z. It is just one equation which iterates in for loops. But I am unable to plot this temperature function in 3D space.

I would really appreciate some help with the plotting aspect. I don't know how exactly to use isosurface or slicing even though I went through a couple of questions posted here.

Thanks in advance!

%Properties of the system
eta = 0.5;
P = 200;
v = 0.1;
k = 42.7; 
d = 0.0038; 
rho = 7850; 
Cp = 477;
T0 = 300;

fileID = fopen('myfile.txt','w');

Q=eta*P/v;
alpha = k/Cp;

for t = 1:1:100
  for x = 1:1:10
    for y = 1:1:10
      for z = 1:1:10
        psi = x - v*t;
        R = sqrt(psi^2 + y^2 + z^2); 
        T(:) = (Q/(2*pi*k*d))*exp(-v*psi/(2*alpha))*exp(-(v*R)/(2*alpha))/R + T0;
        fprintf('%f\n', T)
        fprintf(fileID,'%d\t%d\t%d\t%f\n',x,y,z,T);
      end % z loop end
      fprintf(fileID,'\n');
    end % y loop end
    fprintf(fileID,'\n');
  end % x loop end
  fprintf(fileID,'\n');
end % t loop end

Answer 1

[Boris Blagov]

I think you have many more dimensions than three - you have five dimensions. x,y,z,t and the values (temperature)

You have one T for each (x,y,z) triple and you have hundred triples for t = 1:100.

For example, you have one temperature associated with x=1, y=1 (conditional on z and t), another temperature associated with x = 2 and y = 1 (conditional on z and t) and so forth. You can generate a 3-D plot, conditioning on two of the four variables, i.e. for the temperature as a function of all "x" and all "y", conditional on one z and one t.

Here is the code for that (just for a single t!). Consider preallocating T for speed. I have changed the line T(:) from your code to T(x,y,z) and fixed t = 1.

   %Properties of the system
clc
clear
eta = 0.5;
P = 200;
v = 0.1;
k = 42.7; 
d = 0.0038; 
rho = 7850; 
Cp = 477;
T0 = 300;
fileID = fopen('myfile.txt','w');
Q=eta*P/v;
alpha = k/Cp;
% for t = 1:1:100
t = 1;
  for x = 1:1:10
    for y = 1:1:10
      for z = 1:1:10
        psi = x - v*t;
        R = sqrt(psi^2 + y^2 + z^2); 
        T(x,y,z) = (Q/(2*pi*k*d))*exp(-v*psi/(2*alpha))*exp(-(v*R)/(2*alpha))/R + T0;
      end % z loop end
    end % y loop end
  end % x loop end
% end % t loop end
surf(T(:,:,1))

Edit: consider using "fclose at the end" as a general good practice

[Nihal Acharya]

Thank you, Boris. That was indeed helpful!

[Nihal Acharya]

I also have another question regarding plotting. You said there are 5 dimensions. But if you observe, psi = x - v*t, would remove a dimension, since it is a function of both x and t, and make it 4 dimensions if I wanted to plot it.

Is there any way I can make a plot of (psi,y,z,T)? Or should I use a slice function here to plot if I wanted to eliminate another dimension (so that it becomes just a function of 2 axes and T i.e. x,y,T or y,z,T or x,z,T)?

Thanks in advance!

[Walter Roberson]

slice() or isosurface()

[Nihal Acharya]

But with slice() or isosurface(), I will only be able to view the volume when I plot i.e. the x, y and z- axes, not the temperature profile. How can I plot the aforementioned (in the code) temperature function in the figure using the slice function?

[Walter Roberson]

isosurface() several representative T values, getting "shells" of equal temperature in 3 space.

[Nihal Acharya]

Hi Walter, Is the use of isosurface() here something similar to the following attached post? -

https://in.mathworks.com/matlabcentral/answers/110977-3d-density-plot-multiple-isosurfaces-on-the-same-plot

Thanks!