How can i get the temperature convergence

I am trying to resolve a 2D heat transfer problem (I am a Matlab starter). I have written the code below, and when I run it it does not stop. I tried to incorporate a convergence condition using the error (err), but whenever I stop the program I always find that my error was 150. Could someone help to adjust this code to get the convergence check. (By the was my project is a 3d project, I am just trying a 2d case then once i get it working I will expand it). Thank you for the help

    %===Solution of the problem of 2D in the bookmarks:Case2a=====

    close all;
    clear all;
    clc;

    DX=3; % step size
    DY=3; 
    Lx= 60; %length along x-axis in cmn
    Ly=30;   %length along y-axis
    m=Lx/DX+1;    %Number of nodes along x-axis
    n=(Ly/DY+1);    %Number of nodes along y-axis
    n=floor(n);

    k=2;
    h=500;
    T_inf=20;

    X=0:DX:Lx;
    Y=0:DY:Ly;
    T=zeros(m,n);

    tol=1;
    s=0; %s=2000 could be set as the maximum number of allowed iteration for example
    err=1; 
    T_old=10;

    while err >=tol && s<2001
    s=s+1;

    %--boundary conditions----------------------------------------------------

    T(1,:)=160;     %west
    T(m,:)=100;    %east

    %===South Boundary "insulation" ==============
    for i=2:m-1
       T(i,1)=0.25*[2*T(i,2)+T(i-1,1)+T(i+1,1)];
    end
    %================North Boundary "Convection" ================
    for i=2:m-1
      T(i,n)=0.5*k/(h*DX+2*k)*[2*T(i,n-1)+T(i-1,n)+T(i+1,n)+2*h*DX*T_inf/k];
    end

    for i = 2:m-1
        for j = 2:n-1
        T(i,j)=0.25*(T(i-1,j)+T(i+1,j)+T(i,j-1)+T(i,j+1));
        end
    end
    err=max(max(abs(T-T_old)));
    end

    %T=rot90(T)

[Roger Stafford]

I see a possible problem in your doubly nested for-loops. At each trip through the 'while' loop you are clearly attempting to make each internal T(i,j) set to the average of the four surrounding T values. However, your method has the disadvantage that after altering T(i,j) you then use this altered value in computing T(i,j+1) rather than its original value. The same trouble is present in the two "boundary" for-loop. You need to retain original values until you have finished operation on the entire matrix by placing the results in a different matrix, and then copy these altered values back into the T values.

Another problem is that you don't update the variable 'T_old' so it will always remain at its original value of 10.

[Rachid]

I appreciate your feed back. I already fixed the second issue you mentioned and i will look into the first one.

Answer 1

[Rachid]

Ok guys. Thank you. I figured the answer.