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

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Kumaresh Kumaresh on 27 Sep 2022
Commented: Kumaresh on 30 Sep 2022
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

Torsten on 27 Sep 2022
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 on 30 Sep 2022
Thank you. Its clear now