Heat Transfer: Solve using "relaxation" method while storing residuals and temperatures in arrays

Hello all,

I must write a MATLAB code for my thermal design (Mechanical Engineering) course which must solve four nodal temperatures using "relaxation method". I have written a code according to my professor's guidelines in his lecture, but I cannot find a way to get MATLAB to perform multiple iterations without being thrown into an infinite loop (one in which there are no new calculations taking place; MATLAB will simply count iterations to infinity). I have gotten the first iteration to recalculate T(1) from 300 to 325, but the code stops there. I tried a few different methods using a while or for loop, but every attempt has resulted in an infinite loop. Disclaimer: I am not good at MATLAB whatsoever; please be detailed with any explaination you may offer.

Notes:

-Initial temperature guess must be 300

-Residual tolerance must be 0.1

-Dimensions of element are not specified; we are tasked to solve for three generic interior nodes, and one central-height node on the right wall (which is insulated)

-"Relaxation method" must be used

Thank you in advance.

Code:

close all

clear all

clc

%Set temperature of surfaces

Tt=500; %Top surface temperature

Tl=400; %Left surface temperature

Tb=100; %Bottom surface temperature

%Tr=n/a; %Right surface temperature (insulated)

%Define array for temperatures A through D

T(1,1:4)=300;

%Define arrray for residuals A through D

R(1,1:4)=1;

%Equations for residuals

R(1) = abs(Tt + Tl + Tb + T(2) - 4*T(1)); %Equation for residual A

R(2) = abs(Tt + T(1) + Tb + T(3) - 4*T(2)); %Equation for residual B

R(3) = abs(Tt + T(2) + Tb + T(4) - 4*T(3)); %Equation for residual C

R(4) = abs(Tt + Tb + 2*T(3) - 4*T(4)); %Equation for residual D

Rt = 0.1; %Tolerance for residual

It = 0; %Initial iteration

if max(R) > Rt

It = It + 1; %Iteration series

disp(It);

if (find(max(R)) == 1)

T(1) = (Tt + Tl + Tb + T(2))/4

if (find(max(R)) == 2)

T(2) = (Tt + T(1) + Tb + T(3))/4

if (find(max(R)) == 3)

T(3) = (Tt + T(2) + Tb + T(4))/4

if (find(max(R)) == 4)

T(4) = (Tt + Tb + 2*T(3))/4

disp(max(R));

print(T)

else max(R) <= Rt

print(T)

end

end

end

end

end

Answer 1

[Walter Roberson]

    if (find(max(R)) == 1)

R is a vector. max® is a scalar value. find() of a scalar will be 1 if the scalar is non-nan and non-zero. And that is an odd test if that is your intention.

Your if are all nested. If the first find test is true then since you do not change R before the second test the second must be false.

If you are trying to find the index of the maximum then use the second output of max()

[Julian Saninocencio]

Walter,

Thank you for your input. Your comments lead me in the right direction, and my code is now working properly.

Others, see adjusted code below for reference:

clc

close all

clear all

clc

%Set temperature of surfaces

Tt=500; %Top surface temperature

Tl=400; %Left surface temperature

Tb=100; %Bottom surface temperature

%Tr=n/a; %Right surface temperature (insulated)

%Define array for temperatures A through D

T(1,1:4)=300;

%Define arrray for residuals A through D

R(1,1:4)=1;

%Equations for residuals

R(1) = abs(Tt + Tl + Tb + T(2) - 4*T(1)); %Equation for residual A

R(2) = abs(Tt + T(1) + Tb + T(3) - 4*T(2)); %Equation for residual B

R(3) = abs(Tt + T(2) + Tb + T(4) - 4*T(3)); %Equation for residual C

R(4) = abs(Tt + Tb + 2*T(3) - 4*T(4)); %Equation for residual D

Rt = 0.1; %Tolerance for residual

It = 0; %Initial iteration

while max(R) > Rt

It = It + 1; %Iteration series

It

if (R(1) > Rt)

T(1) = (Tt + Tl + Tb + T(2))/4;

R(1) = abs(Tt + Tl + Tb + T(2) - 4*T(1));

R(2) = abs(Tt + T(1) + Tb + T(3) - 4*T(2));

R(3) = abs(Tt + T(2) + Tb + T(4) - 4*T(3));

R(4) = abs(Tt + Tb + 2*T(3) - 4*T(4));

end

if (R(2) > Rt)

T(2) = (Tt + T(1) + Tb + T(3))/4;

R(1) = abs(Tt + Tl + Tb + T(2) - 4*T(1));

R(2) = abs(Tt + T(1) + Tb + T(3) - 4*T(2));

R(3) = abs(Tt + T(2) + Tb + T(4) - 4*T(3));

R(4) = abs(Tt + Tb + 2*T(3) - 4*T(4));

end

if (R(3) > Rt)

T(3) = (Tt + T(2) + Tb + T(4))/4;

R(1) = abs(Tt + Tl + Tb + T(2) - 4*T(1));

R(2) = abs(Tt + T(1) + Tb + T(3) - 4*T(2));

R(3) = abs(Tt + T(2) + Tb + T(4) - 4*T(3));

R(4) = abs(Tt + Tb + 2*T(3) - 4*T(4));

end

if (R(4) > Rt)

T(4) = (Tt + Tb + 2*T(3))/4;

R(1) = abs(Tt + Tl + Tb + T(2) - 4*T(1));

R(2) = abs(Tt + T(1) + Tb + T(3) - 4*T(2));

R(3) = abs(Tt + T(2) + Tb + T(4) - 4*T(3));

R(4) = abs(Tt + Tb + 2*T(3) - 4*T(4));

end

if max(R) <= Rt

T

end

end