Using Explicit Finite Difference Method to Determine the Time at which Unsteady State Ends - 1D Heat transfer

I need to find the time at which unsteady state ends and steady state begins by using explicit finite difference method. I tried modifying the fde code by adding a while loop and if statement inside the loop as below but the code keeps running forever. What should I do?

%% Expilict Finite Difference Method 1D Transiet Heat System 

%defining parameters:
    k = 28; %W/mC
    qG = 6*10^5; %W/m^3 
    h = 60; %W/m^2C
    Tair = 30; %C
    Ti = 100; %C
    alpha = 12.5*10^-6; %m^2/s
    th = 1000; %hour
    ts = 300; %second
    
%dicretization:
    a=0;
    b=5; %cm
    n=6; %number of nodes
    dx1 = (b-a)/(n-1);
    dx = dx1/100; %m
    x = (a/100):dx:(b/100);

%calculating dt
    dt1 = (dx^2)/(2*alpha*(1+((h*dx)/k)));
    dt = 100;

%calculating r
    r = alpha*dt/dx;

% Initial temperature
   for i = 1:n
        T(i,1) =Ti ;
   end
   
while 1   
    for t=1:ts/dt %end of time will be found but how :/   
       
        % Temperature at the boundary
        T(1,t+1) = ((1-2*r)*T(1,t))+(2*r*T(2,t))+(r*qG*(dx^2)/k);
        T(n,t+1) = ((1-(2*r)-(2*r*h*dx/k))*T(n,t))+(2*r*T(n-1,t))+(2*r*h*dx*Tair/k) +(r*qG*(dx^2)/k);
        
        % Implementation of the explicit method to interior nodes
        for i=2:n-1  % Space Loop
            T(i,t+1) =T(i,t) + r*(T(i-1,t)+T(i+1,t)-2.*T(i,t)) + r*qG*(dx^2)/k;
        end
       
    end
    
    if T(n,t)==T(n,t+1)
        t_final=ts/3600;
        break
    else
        ts=ts+dt;
    end
   
end
    

   

Answer 1

[SALAH ALRABEEI]

Your dicretization much satisfy the stability condition since the explicit scheme is conditionally stable. Moreover, The error might not be less than 1e-7 which still not 0. Therefore, your breaking condition might to get satisfied.