find the temperature distribution along a plane wall with large heat flux applied to the inner surface for short intervals in matlab

main.m
% Define parameters
L = 1; % length of wall in meters
dx = 0.01; % distance between nodes in meters
x = 0:dx:L; % vector of node locations
k = 0.5; % thermal conductivity in W/(m*K)
rho = 100; % density in kg/m^3
cp = 500; % specific heat capacity in J/(kg*K)
Q = 1e5; % heat flux in W/m^2
t = 1; % time in seconds
dt = 0.1; % time step in seconds
nt = t/dt; % number of time steps

% Initialize temperature vector
T = zeros(size(x));

% Apply boundary conditions
T(1) = 273; % temperature at left end of wall
T(end) = 273; % temperature at right end of wall

% Perform time loop
for i = 1:nt
    % Compute heat flux at each node
    q = zeros(size(x));
    q(1) = Q; % heat flux at left end of wall
    q(end) = 0; % heat flux at right end of wall
    q(2:end-1) = -k/dx*(T(3:end)-T(1:end-2));
    
    % Compute temperature at each node
    T = T + dt/(rho*cp*dx)*q;
end

% Plot temperature distribution
plot(x,T)
xlabel('Distance (m)')
ylabel('Temperature (K)')
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