How do I fix this error? (Error using / Matrix dimensions must agree.)

% Non-steady state flow between two parallel plates of water
% Parameters
rho = 1000; % Density of water in kg/m^3
mu = 0.001; % Viscosity of water in Pa*s
V = 2; % Velocity of the upper plate in m/s
h = 0.1; % Distance between the two plates in m
ll=diff(u);

Unrecognized function or variable 'u'.

% Discretize the spatial domain
y = linspace(-h, h, 100);
% Initialize the velocity field
u = zeros(length(y), 1);
% Time step
dt = 0.01;
% Final time
t_final = 10;
% Boundary conditions
u(1) = 0; % No-slip condition at the bottom plate
u(end) = V; % Moving plate condition at the top plate
% Time loop
for t = 0:dt:t_final
    % Calculate the diffusion term
    diffusion = mu * (diff(u))/diff((y));
    % Update the velocity field
    u = u + dt * diffusion;
    % Enforce the boundary conditions
    u(1) = 0;
    u(end) = V;
end
% Plot the velocity field
figure
plot(y, u, 'linewidth', 2)
xlabel('y (m)')
ylabel('u (m/s)')
title('Non-steady state flow between two parallel plates of water')

[Dyuman Joshi]

There seems to be a discrepancy in the code, see above. Is the code snippet ll = diff(u) in the right line?

It's trying to access the variable u before it has been defined.

[Torsten]

You set up the problem

du/dt = mu* du/dy

here.

For this problem, you only need one boundary condition, not two.

And why are you talking about diffusion ? It's the convection equation that you set up in your code.

Answer 1

[SAI SRUJAN]

Hi Adam,

I understand that you are facing an issue with plotting the velocity field for the non-steady state flow between two parallel plates of water.

The error message "Error using / Matrix dimensions must agree" indicates that you are trying to perform division on two matrices or arrays whose dimensions do not agree with the MATLAB '/' operator. For the operation 'A/B' to be executed in MATLAB, the matrices 'A' and 'B' need to have an identical number of columns.

In the code snippet you provided, the error is occurring in the following line:

diffusion = mu * (diff(u))/diff((y));

The 'diff(u)' function computes the difference between adjacent elements of 'u', which results in a vector that is one element shorter than 'u'. The dimensions of 'diff(u)' are 99 x 1 double whereas the dimensions of 'diff(y)' are 1 x 99 double, this mismatch of the number of columns for 'diff(u)' and 'diff(y)' is causing the error.

To fix the error, you should ensure that you are using division and that the dimensions of the vectors you are dividing match.

Finally, the line 'll=diff(u);' is before 'u' is defined and will throw an "Unrecognized function or variable 'u' " error. You should remove or comment out this line.

For a comprehensive understanding of the "/" operator and "diff" function in MATLAB, please refer to the following documentation.

https://www.mathworks.com/help/matlab/ref/mrdivide.html

https://www.mathworks.com/help/matlab/ref/diff.html

I hope this helps.