1D HEAT TRANSFER EXPLICIT USING FINITE DIFFERENCE METHOD

Hi! Just wanna ask why our code wont reach equilibrium even we already increase the number of tme.

Here is our code:

clear, clc, close all

%finite difference method

% dT/dt = alpha * dT^2/dx^2

% dT = u(x, t) solve for dt

% u(x , t) = u(x, t-1) + alpha * dt / dx^2 * (u(x+1, t-1) - 2 * u(x, t-1) + u(x-1, t-1))

% Parameters

L = input ('What is the length of the rod? (in m): ');

disp('L = ');

disp(L);

T = input ('How long do you want the heat diffusion to take? (in s): ');

disp('T = ');

disp(T);

nx = input ('How many spatial points? ');

disp('nx = ');

disp(nx);

alpha = input ('What is your thermal diffusitivity? ');

disp('alpha = ');

disp(alpha);

%Thermal Diffusivity of different materials m^2/s

x = linspace(0, L, nx);

dx = x(2) - x(1);

dt = 0.5*(dx^2)/(2*alpha);

t = 0:dt:T;

u = zeros(nx, length(t));

% Initial condition (u(x,0) = initial temperature distribution)

u(:, 1) = input ('What is the constant temperature at the rest of the rod? ');

disp('u(:, 1) = ');

disp(u(:, 1));

% Boundary conditions (u(0, t) = u(L, t) = 0 for insulated ends)

u(1, : ) = input ('What is the thermal boundary on the left side? ');

disp('u(1, : ) = ');

disp(u(1, : ));

u(nx, : ) = input ('What is the thermal boundary on the right side? ');

disp('u(nx, : ) = ');

disp(u(nx, : ));

% Finite difference method (explicit)

for i = 2:length(t)

for j = 2:nx-1

u(j, i) = u(j, i-1) + alpha * dt / dx^2 * (u(j+1, i-1) - 2 * u(j, i-1) + u(j-1, i-1));

end

end

for i = 1:length(t)

u(:, i)

end

% Plotting the temperature distribution

figure(1);

[T, X] = meshgrid(t, x);

surf(X, T, u);

zlim([0 100])

xlabel('Distance');

ylabel('Time');

zlabel('Temperature');

title('1D Heat Equation Solution using Finite Differences');

figure(2);

subplot(2,1,1),

contour(X,u,T);,

colormap;

title('Temperature (Steady State)'), xlabel('Distance'),ylabel('Temperature'), colorbar

subplot(2,1,2),

pcolor(X,T,u);,

shading interp;,

title('Temperature (Steady State)'),xlabel('Distance'), ylabel('Time'), colorbar

[Torsten]

Please hardcode the inputs so that we can execute the code and reproduce your problem.