Errors in coding and discretization have been corrected, I guess.
Why did you delete your previous question ? Quite impolite in my opinion.
clc
clear all
close all
%Geometry definition
L=0.3; %Length of the The rectangular bar in meter
W=0.4; %Width of the The rectangular bar in meter
%Material properties
alpha=11.234E-05; %theraml diffusivity
% computional mesh
nx=31; %max divisions in x-direction
ny=41; %max divisions in y-direction
nt=100; %number of time step for transient simulation
dt=20; %time step size
x=linspace(0,L,nx);
y=linspace(0,W,ny);
dx=x(2)-x(1);
dy=y(2)-y(1);
convergence_criteria = 1e-4; %Tolerance limitto stop the iteration at some point
error = 1e9;
%Temperature at boundary nodes
T = zeros(nx,ny); % initialize temperature at all nodes
% Boundary conditions
T_top = 10;
T_bottom = 40;
T_right = 0;
T_left = 0;
T(1,:) = T_left;
T(end,:) = T_right;
T(:,1) = T_bottom;
T(:,end) = T_top;
T(1,1) = (T_bottom+T_left)/2;
T(end,1) = (T_bottom+T_right)/2;
T(1,end) = (T_left+T_top)/2;
T(end,end) = (T_top+T_right)/2;
%method details
T_old = T; %previous iteration temperature
T_prev = T; %previous time step temperature
CFL_x = ((2*alpha*dt)/dx^2); %CFL along x
CFL_y = ((2*alpha*dt)/dy^2); %CFL along y
term_1 = (1 + CFL_x + CFL_y)^(-1);
term_2 = term_1*CFL_x/2;
term_3 = term_1*CFL_y/2;
solution_time = dt; %tracking the solution time
jacobi_iteration = 1;
for k = 1:nt %time marching
while (error > convergence_criteria) %Jacobi Iterative Method
for i = 2:nx-1 %space marching along x
for j = 2:ny-1 %space marching along y
H = (T_old(i+1,j) + T_old(i-1,j));
V = (T_old(i,j+1) + T_old(i,j-1));
T(i,j) = ((T_prev(i,j)*term_1) + (term_2*H) + (term_3*V));
end
end
error = max(max(abs(T_old - T))); %calculating the error
T_old = T; %updating the temperature for next iteration
jacobi_iteration = 1 + jacobi_iteration;
end
error = 1; %re-assigning the error
T_prev = T; %updating the temperature for the next time step
solution_time = dt + solution_time;
end
%ploting temperature contour
figure(1)
contourf(x,y,T.');
colorbar
colormap(jet);
xlabel('X-Axis');
ylabel('Y-Axis');
title_text = sprintf('2D Implicit Unsteady Heat Diffusion, Jacobi, Solution Time: %.3f s',solution_time);
title(title_text);
