2D Temperature distribution from 1D temperature distribution T(x)

Hello all,

Hope everyone is doing good.

I have got 1D temperature distribution T(x) along axial distance. Based on a convention below, I need to extract 2D temperature distribution based on 1D. The convention is based on the figure attached here.

In my hand, I have data related to x-position and 1D temperature distribution + convention data to extract 2D temperature distribution.

% Position along x-direction
x_position = [0.05; 0.0625; 0.075; 0.0875; 0.10; 0.1125; 0.125; 0.1375; 0.15; 0.1625; 0.175; 0.1875; 0.2; 0.2125; 0.225;  0.2375;  0.25;  0.2625; 0.2750; 0.2875; 0.3];
% 1D temperature 
desired_temperatures = [100; 100; 55.39; 30.383; 23.047; 20.894; 20.26; 20.077; 20.023; 20.007; 20.002; 20; 20; 20; 20; 20; 20; 20; 20; 20; 20];
% Introduced y-distance for 2D
y = [0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0]; % j //26 points

% 2D temperature distribution
if 0 < y < 0.25 - x
    Theta(x, y) = T(0.25 – y);
else if 5 > y > 4.75 +x
    Theta(x, y) = T(y - 4.75);
else
    Theta(x, y) = T(x);
end
end

Lets say, when T(0.25 - y) returns T(0.25), MATLAB couldn't understand/return the variable from T(0.25) because I believe the temperature variable are stored in indices as, T(1) T(2) T(3) T(4) .... so so on.

So how to make Matlab understand the above (if) - (else if) loops works ?

Can someone share your ideas on above context ?

Thank you

Answer 1

[Torsten]

x_position = [0.05; 0.0625; 0.075; 0.0875; 0.10; 0.1125; 0.125; 0.1375; 0.15; 0.1625; 0.175; 0.1875; 0.2; 0.2125; 0.225;  0.2375;  0.25;  0.2625; 0.2750; 0.2875; 0.3];
% 1D temperature 
desired_temperatures = [100; 100; 55.39; 30.383; 23.047; 20.894; 20.26; 20.077; 20.023; 20.007; 20.002; 20; 20; 20; 20; 20; 20; 20; 20; 20; 20];
% Introduced y-distance for 2D
y = [0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0]; % j //26 points
f = @(xq) interp1(x_position,desired_temperatures,xq);
[X,Y] = ndgrid(x_position,y);
for i = 1:numel(x_position)
    for j = 1:numel(y)
        THETA(i,j) = T(x_position(i),y(j),f);
    end
end
contourf(X,Y,THETA)
colorbar

function Theta = T(x,y,f)
  if 0 < y && y < 0.25 - x
    Theta = f(0.25-y);
  elseif 5 > y && y> 4.75 + x
    Theta = f(y-4.75);
  else
    Theta = f(x);
  end
end

[Kumaresh Kumaresh]

Thank you for your response and efforts to write the above code.

In my code, I have extracted THETA(i,j) for 1D temperature distribution in different manner, but your code looks super smart :-)

However, I couldn't able to understand the function (Theta = T(x,y,f)) for 2D temperature distribution. Could you please explain it ?

Thanks again

[Torsten]

However, I couldn't able to understand the function (Theta = T(x,y,f)) for 2D temperature distribution. Could you please explain it ?

What exactly don't you understand in the function ? It's in principle a copy of your code :

if 0 < y < 0.25 - x
    Theta(x, y) = T(0.25 – y);
else if 5 > y > 4.75 +x
        Theta(x, y) = T(y - 4.75);
else
    Theta(x, y) = T(x);
end

The function f is an interpolating function that returns an approximation for desired_temperatures(x) if x is not in the list of the x_positions.

[Kumaresh]

Thank you. Its clear now