Why do I have a never ending loop ?

Not sure why my loop continues? Solving a diffusion equation for context. Continues to print out time but should stop when conditions are met.

% Define constraints 
alpha = 0.001; % cm^2/s
height = 2; % cm 
dx = 0.1; % cm 
dt = 0.1; % s

% Boundary conditions 
Tbottom = 130; % C degrees
Tcondition=60; %degrees C 

% Grid spacing 
npoints = int32(height/dx)+1;

% Mesh 
T=ones(1,npoints)*4.0; %initial temp is 4
disp(T)

time=0;

condition=true;
while condition 
    time=time+dt;
    fprintf('Current Time is: %f\n', time);
    Tnew=ones(1,npoints);

    T(1)=Tbottom;

    for i=2:npoints-1
        Tnew(i)=(T(i))+alpha*dt/dx/dx * (T(i+1)+T(i-1)-2*T(i)); 
    end
    
    i=npoints-1;
    Tnew(i)=T(i)-alpha*dt/dx/dx * (T(i)-T(i-1));

    Tmin=inf;
    for i=1:npoints
        T(i)=Tnew(i);

        if T(i)<Tmin
            Tmin=T(i);
        end
    end

    if Tmin>Tcondition
        condition=false;
    end
end
disp(T);

[Torsten]

Which boundary condition did you try to set at x = height ?

In your code, your work with T = 4, and you set a strange update at x = height - dx:

i=npoints-1;
Tnew(i)=T(i)-alpha*dt/dx/dx * (T(i)-T(i-1)); 

And note that you never set Tnew(1) to a reasonable value in the while-loop.

[Jalyn-Rose]

I used the x=height for my grid spacing not for the boundary. My only boundaries are the T=130 and 60. T=4 is the initial temp across right side of my diffusion.

[Torsten]

To answer your question:

Your while loop never stops because Tnew(1) is always 1 from the setting Tnew=ones(1,npoints);, thus < Tcondition.

Answer 1

[Torsten]

The initial condition at t = 0 seems to be T = 4 for all x in your code.

But you must set boundary conditions for T at x = 0 and x = 2.

At x = 0, this seems to be T = 130 for all t. But what about x = 2 ?

% Define constraints 
alpha = 0.001; % cm^2/s
height = 2; % cm 
dx = 0.1; % cm 
nx = height/dx+1;
% Boundary conditions 
Tbottom = 130; % C degrees
Tcondition=60; %degrees C 
dt = 0.1; % s
nt = 5000;
T = 4*ones(nx,1);
T(1) = Tbottom;
Tnew = zeros(size(T));
condition = true;
counter = 0;
hold on
while condition
  counter = counter + 1;
  Tnew(1) = T(1);         % T = 130 at x = 0
  Tnew(2:nx-1) = T(2:nx-1)+dt*alpha/dx^2*(T(1:nx-2)-2*T(2:nx-1)+T(3:nx));
  Tnew(nx) = Tnew(nx-1);  %dT/dx = 0 at x = 2
  T = Tnew;
  condition = min(T) < Tcondition;
  if counter == 500
    counter = 0;
    plot((0:nx-1)*dx,T) 
  end
end
hold off
grid on

[Jalyn-Rose]

ok i meant to have At x=2 I want the T=4

[Torsten]

But then 4=Tmin < Tcondition for all t, and you will never quit the while loop...

[Jalyn-Rose]

Hmmm I want the while loop to continue until the Tcondition is met so I think i have my sign switched. Starting at x=0,T=130 until x=2, T=60 and and display the time it takes to get there from x=2, T=4.

[Torsten]

Starting at x=0,T=130 until x=2, T=60 and and display the time it takes to get there from x=2, T=4.

That's what my code does. The only thing you have to do is add the dt's in the while loop.

[Jalyn-Rose]

I see, thank you for the help!

[Jalyn-Rose]

Im uncertain of how I would see the time?

[Torsten]

time = 0;
while ...
    time = time + dt;
    ...
end