Matrix Size Mismatch for Heat Conduction - 1x1 vs 50x100x101

I am looking to calculte the heat transfer across an axysymmetric 2D cylinder. I've discreteised the governing equations using the explicit control-volume finite difference method. Howeever, for one of my surfaces, there seems to be a matrix mismatch because when I run the code I get the error message

"Unable to perform assignment because the size of the left side is 1-by-1 and the size of the right side is 50-by-100-by-101."

Here is the portion of the code with the T(i,j,step+1) portion that has been flagged

% Create grids
dr = R / Nr;
dz = L / Nz;
r = linspace(dr/2, R-dr/2, Nr);
z = linspace(dz/2, L-dz/2, Nz);

% Initialize 3D arrays for temperature and concentration
T = ones(Nr, Nz, num_steps+1); % Temperature array
rho = ones(Nr, Nz, num_steps+1) * rho_initial; % Concentration array
%Initial conditions
T(i,j,step) = Tint;

for step = 1:num_steps
    t = step * dt;
    for i = 2:Nr-1
        for j = 2:Nz-1

At least one END is missing. The statement beginning here does not have a matching end.

            
            T(i,j,step+1) = (dt*k*(r(i) - 1/2))/(rho*Cpg*dr^2*r(i))*T(i-1,j,step) + (dt*k*(r(i) + 1/2))/(rho*Cpg*dr^2*r(i))*T(i+1,j,step) + ...
                (2*dt*k)/(rho*Cpg*dz^2)*T(i,j,step) + (2*h*dt)/(rho*Cpg*dz)*Tinf + (1 - (dt*k*(r(i) - 1/2))/(rho*Cpg*dr^2*r(i)) - ...
                (dt*k*(r(i) + 1/2)/(rho*Cpg*dr^2*r(i)) - (2*dt*k)/(rho*Cpg*dz^2) - (2*h*dt)/(rho*Cpg*dz)))*T(i,j,step) + Q_gen*(dt/rho*Cpg);

Answer 1

[Walter Roberson]

T and rho are both 3D matrices.

            T(i,j,step+1) = (dt*k*(r(i) - 1/2))/(rho*Cpg*dr^2*r(i))*T(i-1,j,step) + (dt*k*(r(i) + 1/2))/(rho*Cpg*dr^2*r(i))*T(i+1,j,step) + ...
                (2*dt*k)/(rho*Cpg*dz^2)*T(i,j,step) + (2*h*dt)/(rho*Cpg*dz)*Tinf + (1 - (dt*k*(r(i) - 1/2))/(rho*Cpg*dr^2*r(i)) - ...
                (dt*k*(r(i) + 1/2)/(rho*Cpg*dr^2*r(i)) - (2*dt*k)/(rho*Cpg*dz^2) - (2*h*dt)/(rho*Cpg*dz)))*T(i,j,step) + Q_gen*(dt/rho*Cpg);

This code uses all of rho in multiple places, instead of indexing rho similar to the way that you index T

[Chizembi Sakulanda]

I see, yes! Thank you!