Need help with loop for a heat transfer question

Hello, I worked on a code to calculate the temperature of the slab from a given initial temperature and a given slab thickness after some time t. Now lets say that the slab thickness wasn't given, and the question is asking to calculate the minimum thickness of a slab to satisfy a final temperature after some time t, how can i adjust my code so that it calculates the minimum thickness? im new to matlab so any help would be appreciated. Please let me know if theres something that is not clear about the code, thanks in advance for your help.

%this code calculates the temperature of the slab surface after time t
clear
clc
close

L=0.2; %slab thickness 
Ti=600; %initial surface temp
Tinf=22; %surrounding temp
h=240; %convection coefficient 
k=80.2; %thermal conductivity
alpha=3.31e-5;
dx=0.01;
dt=1.5;
Fo=(alpha*dt)/dx^2; %forier number
Bii=(h*dx)/k;
Bio=(h*dx)/k;
t=1800;
x=[0:dx:L];
n=length(x);
t=[0:dt:t];

T = zeros(numel(t), numel(x));  %temperature of the slab at time t (rows) and position x (columns)
T(1, :) = Ti;  %temperature at t = t0;

for k = 2:numel(t)
 T(k, 1) = T(k-1, 1)*(1-2*Fo-2*Bio*Fo)+2*Fo*T(k-1, 2)+2*Bio*Fo*Tinf; %node1
   for i = 2:numel(x)-1
    T(k, i) = T(k-1, i)*(1-2*Fo)+Fo*(T(k-1, i+1)+T(k-1, i-1)); %interior nodes
   end
 T(k, n) = T(k-1, n)*(1-2*Fo-2*Bii*Fo)+2*Fo*T(k-1, n-1)+2*Bii*Fo*Tinf; %exterior node
end
T(k,n)
%plot temperature for all t at a different x
plot(t, T(:, end));

[KALYAN ACHARJYA]

Which term represents the final temp, is this t?

t=1800;

And your question is find L, when t reaches 1800?

[Guillaume]

For some context, previous question on this topic is error-message-vectors-must-be-the-same-length

[KALYAN ACHARJYA]

Oh

Answer 1

[Bob Thompson]

Since your code already calculates the temperature based on a thickness I think the most minimal change would be to turn L into a variable and "guess" your way to the proper L.

TIdeal = input('Enter the ideal final temperature: ');
T = [];  % Initialization
dL = 0.5; % Initialization
while T(end,end)~= TIdeal;
 L = 1.0; % Just a generic starting value
 % Rest of your code here
 ......
 % End of existing code
 if T(end,end)>TIdeal % Temperature is high, too thin
  L = L+dL; % Increase thickness
  dL = dL/2; % Reduce size of dL
 elseif T(end,end)<TIdeal % Temperature is low, too thick
  L = L-dL; % Reduce thickness
  dL = dL/2; % Reduce size of dL
 else % T = TIdeal or something is broken
  break
 end % Temp check if
end % While loop

There are a number of things that could go wrong with this, but it's a first cut. You may need to change how dL changes, or may need to change the starting value of L as each loop reduces the amount of change possible. Also, you will probably need to adjust the T you are specifically looking at since I assumed you wanted final temp at the furthest thickness.

As a side note, I would strongly advise against using k as your index, since it is also defined as thermal conductivity, and you are currently erasing your thermal conductivity variable in order to index the loop.

[salem alnaqbi]

Thank you very much, very helpful