create a for loop that accounts for cyclic transient heat conduction in a plane wall in matlab

Here is an example of a for loop that accounts for cyclic transient heat conduction in a plane wall using Matlab:

main.m
% Define inputs
Tm = 20;
Ta = 5;
k = 0.5;
h = 10;
L = 0.2;
t = 0:1:3600;
alpha = k/(p*c);

% Preallocate memory for temperature matrix
T = NaN(numel(t), 2);

% Set initial conditions
T(1,:) = [Tm, Tm];

% Calculate temperature for each time step using for loop
for i = 2:numel(t)
    % Calculate temperature difference between inner and outer wall
    dT = T(i-1,1) - T(i-1,2);
    
    % Use cyclic boundary condition to update temperature matrix
    T(i,1) = T(i-1,1) - ((h*L)/(p*c))*(T(i-1,1) - Ta)*dt + ((k*L)/(p*c))*(dT/L)*dt;
    T(i,2) = T(i-1,2) + ((h*L)/(p*c))*(T(i-1,1) - Ta)*dt - ((k*L)/(p*c))*(dT/L)*dt;
end

% Plot results
plot(t, T(:,1), 'r', t, T(:,2), 'b');
xlabel('Time (s)');
ylabel('Temperature (°C)');
legend('Inner wall', 'Outer wall');
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In this example, we define the relevant parameters (Tm, Ta, k, h, L) and set up a time vector (t) for the simulation. We then preallocate memory for the temperature matrix (T) and set the initial conditions (the walls start at temperature Tm).

The for loop then iterates through each time step and calculates the temperature at each wall using the cyclic boundary condition. The temperature matrix is updated with each iteration, and we can plot the results at the end.

Note that in this example, we assume constant values for the parameters. If any of the parameters change over time, you would need to modify the for loop accordingly.

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