generating a graph of velocity profiles for flow between parallel plates with bottom injection and top suction for different values of re. in matlab

To generate a graph of velocity profiles for flow between parallel plates with bottom injection and top suction for different values of Reynolds number (Re) in MATLAB, you can follow these steps:

1. Define the problem parameters:

   • Channel height (H): distance between the parallel plates
   • Channel width (W): width of the channel
   • Viscosity (mu): fluid viscosity
   • Bottom injection flow rate (Q_inj): flow rate for the bottom injection
   • Top suction flow rate (Q_suc): flow rate for the top suction

2. Set the range of Reynolds numbers (Re) for which you want to plot the profiles.

3. Create a MATLAB script to calculate and plot the velocity profiles:

   • Use the governing equations for flow between parallel plates (incompressible and steady-state) to calculate the velocity distribution along the height of the channel.
   • Iterate through the range of Reynolds numbers, and for each value, calculate the velocity profile.
   • Plot the velocity profiles for each Reynolds number using the plot function in MATLAB.

Here's an example MATLAB code snippet to help you get started:

main.m
% Problem parameters
H = 0.1;                % Channel height (m)
W = 0.1;                % Channel width (m)
mu = 0.001;             % Viscosity (Pa.s)
Q_inj = 1e-4;           % Bottom injection flow rate (m^3/s)
Q_suc = 1e-4;           % Top suction flow rate (m^3/s)

% Range of Reynolds numbers
Re_range = [1000, 2000, 3000, 4000, 5000];

% Calculate and plot velocity profiles
figure;
hold on;
for i = 1:length(Re_range)
    Re = Re_range(i);
    
    % Calculate velocity profile
    y = linspace(0, H, 100);                 % Height range
    v = (Q_inj - Q_suc) / (mu * H / W);      % Average velocity
    delta_v = (Re * mu / (W * H)) * (y - H/2);  % Velocity difference from the average
    
    % Plot the velocity profile
    plot(v + delta_v, y);
end
hold off;

% Add labels and titles
xlabel('Velocity (m/s)');
ylabel('Height (m)');
title('Velocity Profiles for Flow between Parallel Plates');
legend('Re = 1000', 'Re = 2000', 'Re = 3000', 'Re = 4000', 'Re = 5000');
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Make sure to adjust the problem parameters, Reynolds number range, and plot configurations according to your specific needs.

This code generates a graph of velocity profiles for different values of Reynolds numbers (Re) between the parallel plates, with bottom injection and top suction. The velocity profiles are plotted along the vertical height of the channel.

Note: This example assumes a simplified flow model without considering the effects of pressure gradient and other factors. It is for illustrative purposes only and may need modification for more complex flow scenarios.

Hope this helps!