Verifying my code for this problem, are these the right solution and graphs?

clc; clear; close all;
% Parameters
L = 10;  % mm
W = 4;   % mm
dx = 1;  % mm
dy = 1;  % mm
T_inf = 22; % Ambient temperature (°C)
Tb = 50;    % Base plate temperature (°C)
h = 630;    % Convective heat transfer coefficient (W/m^2.K)
k = 20;     % Thermal conductivity (W/m.K)
% Grid size
Nx = L/dx + 1;
Ny = W/dy + 1;
% Initialize temperature field
T = ones(Nx, Ny) * T_inf;  % Start with ambient temperature
% Set bottom boundary condition
T(:,1) = Tb;
% Convection boundary condition coefficient
conv_coeff = h * dy / k;
% Iteration parameters
tol = 1e-4;
max_iter = 5000;
error = 1;
iter = 0;
% Jacobi Iteration
while error > tol && iter < max_iter
    T_old = T;
    
    for i = 2:Nx-1
        for j = 2:Ny-1
            T(i,j) = (T_old(i+1,j) + T_old(i-1,j) + T_old(i,j+1) + T_old(i,j-1)) / 4;
        end
    end
    
    % Apply convective boundary conditions
    T(1, :) = (conv_coeff * T_inf + T_old(2, :)) / (1 + conv_coeff); % Left boundary
    T(Nx, :) = (conv_coeff * T_inf + T_old(Nx-1, :)) / (1 + conv_coeff); % Right boundary
    T(:, Ny) = (conv_coeff * T_inf + T_old(:, Ny-1)) / (1 + conv_coeff); % Top boundary
    % Compute error
    error = max(max(abs(T - T_old)));
    iter = iter + 1;
end
fprintf('Converged in %d iterations\n', iter);

Converged in 57 iterations

% (b) Plot temperature profile along vertical lines at x=1mm, x=4mm, x=6mm
x_positions = [2, 5, 7]; % Corresponding to x=1mm, x=4mm, x=6mm
figure;
hold on;
for x_index = x_positions
    plot(T(x_index, :), 'LineWidth', 2);
end
xlabel('Vertical position (y-axis)');
ylabel('Temperature (°C)');
legend('x=1mm', 'x=4mm', 'x=6mm');
title('Temperature Profile along Vertical Lines');
grid on;
hold off;

% (c) Plot temperature contour
figure;
contourf(T', 20);
colorbar;
xlabel('x (mm)');
ylabel('y (mm)');
title('Temperature Contour of the Rib');

% (d) Refine the grid with dx=dy=0.5mm
dx = 0.5; dy = 0.5;
Nx = L/dx + 1;
Ny = W/dy + 1;
T_fine = ones(Nx, Ny) * T_inf;
T_fine(:,1) = Tb;
conv_coeff = h * dy / k;
error = 1;
iter = 0;
while error > tol && iter < max_iter
    T_old = T_fine;
    
    for i = 2:Nx-1
        for j = 2:Ny-1
            T_fine(i,j) = (T_old(i+1,j) + T_old(i-1,j) + T_old(i,j+1) + T_old(i,j-1)) / 4;
        end
    end
    
    T_fine(1, :) = (conv_coeff * T_inf + T_old(2, :)) / (1 + conv_coeff);
    T_fine(Nx, :) = (conv_coeff * T_inf + T_old(Nx-1, :)) / (1 + conv_coeff);
    T_fine(:, Ny) = (conv_coeff * T_inf + T_old(:, Ny-1)) / (1 + conv_coeff);
    error = max(max(abs(T_fine - T_old)));
    iter = iter + 1;
end
fprintf('Refined grid converged in %d iterations\n', iter);

Refined grid converged in 204 iterations

% Compare temperature profile at x=4mm for both grids
x_index_coarse = 5; % Corresponding to x=4mm in the coarse grid
x_index_fine = 9;   % Corresponding to x=4mm in the fine grid
figure;
plot(T(x_index_coarse, :), 'r--', 'LineWidth', 2);
hold on;
plot(T_fine(x_index_fine, :), 'b-', 'LineWidth', 2);
xlabel('Vertical position (y-axis)');
ylabel('Temperature (°C)');
legend('Coarse grid (1mm)', 'Fine grid (0.5mm)');
title('Comparison of Temperature Profiles at x=4mm');
grid on;
hold off;

[Saif]

% I will go and check, thanks for noticing , someone else in my team wrote another code, any chance someone can take a look at that pls, thanks

clc;
clear;
close all;
% Define Parameters
k = 20;                % Thermal conductivity (W/m.K)
h = 630;               % Convective heat transfer coefficient (W/m^2.K)
T_inf = 295.15;        % Ambient temperature (Kelvin)
T_base = 323.15;       % Base temperature (Kelvin)
L = 10e-3;             % Length of the rib (m)
W = 4e-3;              % Width of the rib (m)
% Define grid spacing (Δx = Δy = 1mm)
dx = 1e-3;           
dy = 1e-3;            
% Compute number of grid points
nx = L/dx + 1;      
ny = W/dy + 1;      
% Initialize matrices
T = ones(nx, ny) * T_inf; % Initial guess
T(1, :) = T_base;         % Bottom boundary at base temperature
% Jacobi Method Parameters
max_iter = 10000;       % Maximum iterations
MinError = 1e-6;       % Convergence criteria
error = inf;
iter = 0;
% Coefficient for convective boundary
beta = h * dx / k;
% Solve using Jacobi method
while error > MinError && iter < max_iter
    T_old = T;
    
    % Update interior points using Jacobi iteration
    for i = 2:nx-1
        for j = 2:ny-1
            T(i, j) = (T_old(i+1, j) + T_old(i-1, j) + T_old(i, j+1) + T_old(i, j-1)) / 4;
        end
    end
    % Apply convective boundary conditions (top, left, and right)
    for j = 2:ny-1
        T(nx, j) = (T_old(nx-1, j) + 2 * beta * T_inf) / (1 + 2 * beta); % Right
    end
    for i = 2:nx-1
        T(i, ny) = (T_old(i, ny-1) + 2 * beta * T_inf) / (1 + 2 * beta); % Top
        T(i, 1) = (T_old(i, 2) + 2 * beta * T_inf) / (1 + 2 * beta); % Left
    end
    
    % Apply convective boundary to top-right and top-left corners
    T(nx, ny) = (T_old(nx-1, ny) + T_old(nx, ny-1) + 2 * beta * T_inf) / (2 + 2 * beta);
    T(nx, 1) = (T_old(nx-1, 1) + T_old(nx, 2) + 2 * beta * T_inf) / (2 + 2 * beta);
    % Compute error for convergence
    error = max(max(abs(T - T_old)));
    iter = iter + 1;
end
% Part B: Temperature Profile at Selected x Locations
x_values = [1, 4, 6] * 1e-3; % In meters
figure;
hold on;
for i = 1:length(x_values)
    x_idx = round(x_values(i) / dx) + 1;
    plot(linspace(0, W, ny), T(x_idx, :), 'LineWidth', 2);
end
legend('x = 1 mm', 'x = 4 mm', 'x = 6 mm');
xlabel('Distance along y (m)');
ylabel('Temperature (K)');
title('Temperature Profile at Selected x Locations');
grid on;

% Part C: Temperature Contour Plot
figure;
contourf(linspace(0, L, nx), linspace(0, W, ny), T', 20, 'LineWidth', 0.5);
colorbar;
xlabel('X (m)');
ylabel('Y (m)');
title('Temperature Contour Plot');
axis equal;

% Part D: Solve for Δx = Δy = 0.5 mm
dx2 = 0.5e-3;           
dy2 = 0.5e-3;            
% Compute number of grid points
nx2 = L/dx2 + 1;      
ny2 = W/dy2 + 1;      
% Initialize matrices
T2 = ones(nx2, ny2) * T_inf; % Initial guess
T2(1, :) = T_base;           % Bottom boundary at base temperature
% Reset error and iteration count
error = inf;
iter = 0;
beta2 = h * dx2 / k;
% Solve using Jacobi method
while error > MinError && iter < max_iter
    T_old = T2;
    
    for i = 2:nx2-1
        for j = 2:ny2-1
            T2(i, j) = (T_old(i+1, j) + T_old(i-1, j) + T_old(i, j+1) + T_old(i, j-1)) / 4;
        end
    end
    
    for j = 2:ny2-1
        T2(nx2, j) = (T_old(nx2-1, j) + 2 * beta2 * T_inf) / (1 + 2 * beta2); % Right
    end
    for i = 2:nx2-1
        T2(i, ny2) = (T_old(i, ny2-1) + 2 * beta2 * T_inf) / (1 + 2 * beta2); % Top
        T2(i, 1) = (T_old(i, 2) + 2 * beta2 * T_inf) / (1 + 2 * beta2); % Left
    end
    
    T2(nx2, ny2) = (T_old(nx2-1, ny2) + T_old(nx2, ny2-1) + 2 * beta2 * T_inf) / (2 + 2 * beta2);
    T2(nx2, 1) = (T_old(nx2-1, 1) + T_old(nx2, 2) + 2 * beta2 * T_inf) / (2 + 2 * beta2);
    error = max(max(abs(T2 - T_old)));
    iter = iter + 1;
end
% Compare Temperature Profile at x = 4mm for Δx=1mm and Δx=0.5mm
x_position = 4e-3;
x_idx1 = round(x_position / dx) + 1;
x_idx2 = round(x_position / dx2) + 1;
figure;
plot(linspace(0, W, ny), T(x_idx1, :), 'r-', 'LineWidth', 2);
hold on;
plot(linspace(0, W, ny2), T2(x_idx2, :), 'b--', 'LineWidth', 2);
legend('Δx=1mm', 'Δx=0.5mm');
xlabel('Distance along y (m)');
ylabel('Temperature (K)');
title('Comparison of Temperature Profile at x=4mm');
grid on;

Answer 1

[Torsten]

Look at the contour plot. The temperature at x = 0 should be at T_b = 50°C. This is not the case in your graphics. Maybe you interchanged the axes ?

And why do the temperature profiles in your last plot start at 1 and end at 9 ? And why does the red curve end at 5 ? Both curves should start at 0 and end at 4.

I suggest creating

x = linspace(0,L,Nx)
y = linspace(0,W,Ny)

in both cases (coarse and fine) so that you can make plots over the correct x- and y-grids.