2D Heat Equation

Harish
/
2D Heat Equation
on 10 Oct 2024
Cite your audio source here (if applicable):
drawframe(1);
Write your drawframe function below
function drawframe(f)
    % Parameters
    Nx = 100; % Number of grid points in the x direction
    Ny = 100; % Number of grid points in the y direction
    Lx = 1;  % Length of the plate in the x direction
    Ly = 1;  % Length of the plate in the y direction
    dx = Lx / (Nx - 1); % Grid spacing in the x direction
    dy = Ly / (Ny - 1); % Grid spacing in the y direction
    alpha = 0.01; % Thermal diffusivity constant
    dt = 0.001; % Time step
    numFrames = 96; % Total number of frames
    stepsPerFrame = 100; % Number of time steps per frame
    % Initialize the temperature field
    persistent T X Y
    if isempty(T)
        T = 50 * ones(Nx, Ny); % Temperature field (50K initially everywhere)
        
        % Set up grid for plotting
        [X, Y] = meshgrid(linspace(0, Lx, Nx), linspace(0, Ly, Ny));
        % Boundary conditions
        T(1, :) = 300; % Top wall heated to 300K
    end
    % Simulate heat diffusion for a number of time steps per frame
    for t = 1:stepsPerFrame
        T_new = T; % New temperature field
        % Update interior points using finite difference scheme
        for i = 2:Nx-1
            for j = 2:Ny-1
                T_new(i, j) = T(i, j) + alpha * dt * ( ...
                    (T(i+1, j) - 2*T(i, j) + T(i-1, j)) / dx^2 + ...
                    (T(i, j+1) - 2*T(i, j) + T(i, j-1)) / dy^2 );
            end
        end
        % Update the temperature field
        T = T_new;
    end
    % Create a figure if it doesn't exist
    persistent fig h
    if isempty(fig)
        fig = figure('Color', 'white');
        ax = axes('Parent', fig);
        h = imagesc(ax, T, [50 300]); % Initialize the 2D plot (temperature values between 50K and 300K)
        colorbar; % Add a colorbar to show temperature
        title('2D Heat Equation Simulation');
        axis off; % Remove axes for cleaner visualization
        colormap('hot'); % Use 'hot' colormap for heat visualization
        axis equal;
    end
    % Update the plot with the new temperature data
    h.CData = T; % Update temperature field data for visualization
    drawnow; % Refresh the plot
end
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