create a temperature distribution plot for different time intervals of a plane wall under transient heat conduction with cyclic heat flux applied to one side in matlab

Here's a possible approach to create such a plot:

1. Define the geometry of the plane wall and the properties of the material (e.g. thermal conductivity, specific heat, density).

2. Define the time interval for the simulation, discretized into small time steps, and the cyclic heat flux to be applied to one side of the wall (e.g. as a sinusoidal function).

3. Use a numerical method (e.g. finite differences) to solve the heat conduction equation for each time step, using the previous temperature distribution as initial condition.

4. At each time step, store the temperature distribution across the wall. This can be represented as a matrix, with rows corresponding to different positions along the thickness of the wall, and columns corresponding to different time steps.

5. Once the simulation is complete, plot the temperature distribution at different time intervals, using a contour or surface plot. This can be done by selecting the appropriate columns from the matrix created in step 4.

Here's some sample code that implements these steps:

main.m
% Define material properties and geometry of wall
k = 1; % thermal conductivity
rho = 1; % density
Cp = 1; % specific heat
L = 1; % wall thickness

% Define time interval and cyclic heat flux
t_start = 0;
t_end = 10;
dt = 0.1;
t = t_start:dt:t_end;

Q0 = 1; % amplitude of heat flux
w = 2*pi/100; % frequency (100 time steps for one cycle)

% Initialize temperature matrix
n = 100; % number of spatial nodes
T = zeros(n,length(t));

% Apply initial condition (e.g. uniform temperature across wall)
T(:,1) = 20; % initial temperature

% Solve heat conduction equation for each time step
for i=1:length(t)-1
    % Compute heat flux at current time step
    q = Q0*sin(w*t(i));
    
    % Compute temperature profile using forward finite differences
    for j=2:n-1
        T(j,i+1) = T(j,i) + dt/(rho*Cp*L)*(k*(T(j+1,i)-T(j,i)) - k*(T(j,i)-T(j-1,i)) + q*(j==n));
    end
end

% Plot temperature distribution at selected time intervals
figure;
subplot(2,2,1);
contourf(T(:,1:10:end));
colorbar;
title('t=0:1:10');
subplot(2,2,2);
contourf(T(:,11:10:end));
colorbar;
title('t=11:1:20');
subplot(2,2,3);
contourf(T(:,21:10:end));
colorbar;
title('t=21:1:30');
subplot(2,2,4);
contourf(T(:,31:10:end));
colorbar;
title('t=31:1:40');
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This code generates a 2x2 plot with temperature contours for four different time intervals (0:1:10, 11:1:20, 21:1:30, 31:1:40). The contours show the temperature distribution across the wall, with hotter regions shown in red and cooler regions shown in blue. The cyclic heat flux applied to the right side of the wall is not shown explicitly, but its effect is visible as periodic variations in temperature across the wall.