clearclcn=100;n1=30;n3=60;P=100;a=002;r=006;v=600;qmidu=7800;c=450;K=32;n2=026;time=1av;c1=timea0001^3qmiduc;c2=Pn2a^2pir^2;T=zerosnnn1n3;T1=zerosnnn1;X=zeros1n3;Y=zeros1n3;Z=zeros1n3;t1=zeros1n3;file

The following MATLAB code simulates the temperature distribution in a cylindrical rod subjected to a moving heat source. The rod has a radius of 0.06 m, length of 0.3 m, and is made of a material with density of 7800 kg/m^3 and specific heat of 450 J/(kg*K). The heat source moves at a constant velocity of 600 m/s along the axis of the rod, with a heat output of 32 W. The simulation runs for a total time of 1 second, with time steps of 0.02 seconds. The temperature distribution is visualized through a 3D plot of temperature slices at different times, and the animation is saved as a GIF file.

clear
clc

% Define parameters
n = 100;        % Number of grid points in each direction
n1 = 30;        % Number of grid points along the length of the rod
n3 = 60;        % Number of time steps
P = 100;        % Heat output of the source (W)
a = 0.02;       % Time step (s)
r = 0.06;       % Radius of the rod (m)
v = 600;        % Velocity of the heat source (m/s)
qmidu = 7800;   % Density of the material (kg/m^3)
c = 450;        % Specific heat of the material (J/(kg*K))
K = 32;         % Thermal conductivity of the material (W/(m*K))
n2 = K/(qmidu*c);   % Thermal diffusivity

% Calculate constants
time = 1*a/v;
c1 = time/((a*0.001)^3*(qmidu*c));
c2 = P*n2*a^2/(pi*r^2);

% Initialize temperature matrix
T = zeros(n,n,n1,n3);

% Initialize position and time arrays for visualization
X = zeros(1,n3);
Y = zeros(1,n3);
Z = zeros(1,n3);
t1 = zeros(1,n3);

% Set initial position and time values
for t = 1:n3
    X(:) = 50;
    Y(t) = 25+v*time*(t-1)/a;
    Z(:) = n1;
    t1(t) = t*0.9+0.1;
end

% Loop over time steps
for t = 1:n3
    % Initialize temperature matrix for current time step
    T1 = zeros(n,n,n1);

    % Loop over past time steps and calculate temperature distribution
    for o = 1:t
        for i = 1:n
            for j = 1:n
                for k = 1:n1
                    if j >= Y(o)
                        T(i,j,k,o) = c1*c2/t1(t-o+1)*exp(-2*((i-X(o))^2+(j-Y(o))^2+(k-Z(o))^2)/((t-o+1)*(r/a)^2));
                    else
                        T(i,j,k,o) = c1*c2/t1(t-o+1)*exp(-2*((i-X(o))^2+(j-Y(o))^2/4+(k-Z(o))^2)/((t-o+1)*(r/a)^2));
                    end
                end
            end
        end
        % Sum up temperature contributions from past time steps
        T1 = T(:,:,:,o)+T1;
    end

    % Add ambient temperature
    T1 = T1+300;

    % Visualize temperature distribution
    h = figure(1);
    xs = 1:1:n;
    ys = 1:1:n;
    zs = 1:1:n1;
    hi = slice(T1,xs,ys,zs);
    axis equal
    set(hi,'FaceColor','interp','EdgeColor','none');
    colormap("jet")
    colorbar

    % Save animation frame to GIF file
    frame = getframe(h);
    im = frame2im(frame);
    [A,map] = rgb2ind(im,jet);
    if t == 1
        imwrite(A,map,'testAnimated3.gif','gif','LoopCount',Inf,'DelayTime',0.1);
    else
        imwrite(A,map,'testAnimated3.gif','gif','WriteMode','append','DelayTime',0.1);
    end
end
``