model temperature as a function of position in a plane wall undergoing transient heat conduction with cyclic heat flux applied to one side in matlab

main.m
function temperature_in_wall()

    % Define the parameters of the problem
    k = 1;      % Thermal conductivity
    rho = 1;    % Density
    c = 1;      % Specific heat
    L = 1;      % Thickness of the wall
    Q0 = 1;     % Magnitude of the heat flux
    T0 = 0;     % Initial temperature
    h = 0.05;   % Convective heat transfer coefficient
    Ta = 0;     % Ambient temperature
    tspan = [0 10];  % Time interval to solve over
    x = linspace(0,L,101);  % Spatial grid

    % Define the heat flux function
    function q = heat_flux(x,t)
        q = Q0 * (1 - 2*abs(mod(t,1)-0.5));
    end

    % Define the PDE system
    function [c,f,s] = heat_eqn(x,t,u,DuDx)
        c = rho*c;
        f = k*DuDx;
        s = heat_flux(x,t) + h*(Ta - u);
    end

    % Set the initial and boundary conditions
    function [pl,ql,pr,qr] = heat_bc(xl,ul,xr,ur,t)
        pl = ul - T0;
        ql = 0;
        pr = ur - T0;
        qr = k*(h/c)*ur - h*Ta;
    end

    % Solve the PDE
    sol = pdepe(0,@heat_eqn,@heat_bc,@initial_condition,x,tspan);

    % Plot the results
    surf(x,t,sol);
    title('Temperature distribution in the wall');
    xlabel('Location in wall');
    ylabel('Time');
    zlabel('Temperature')

    % Define the initial condition
    function u0 = initial_condition(x)
        u0 = T0 * ones(size(x));
    end
end
1342 chars
50 lines