how to incorporate heat flux into a plane wall undergoing transient heat conduction in matlab

main.m
L = length of the wall
tmax = maximum time to be simulated
dx = spatial step size
dt = time step size
k = thermal conductivity of the wall
rho = density of the wall
cp = specific heat of the wall
T_initial = initial temperature at each point
q0 = heat flux at t = 0
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main.m
alpha = k / (rho * cp)
Fo = alpha * dt / dx^2
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main.m
T = ones((L/dx)+1, (tmax/dt)+1) * T_initial
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main.m
for i = 2:(L/dx)
    T(i,1) = T(i,1) + q0 * dt / (k * dx)
end
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main.m
for j = 1:(tmax/dt)
    for i = 2:(L/dx)
        T(i,j+1) = T(i,j) + Fo * (T(i+1,j) - 2*T(i,j) + T(i-1,j))
    end
end
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main.m
[X, Y] = meshgrid(0:dx:L, 0:dt:tmax);
surf(X, Y, T');
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