simulate a nutsche filter dryer in matlab

main.m
% Example parameters for a Nutsche filter dryer simulation
cake_height = 0.2; % [m]
cake_diameter = 0.5; % [m]
cake_porosity = 0.6; % [-]
heat_transfer_coeff = 200; % [W/(m^2*K)]
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main.m
% Define the differential equation system for the Nutsche filter dryer
function dydt = nutsche_filter_dryer(t, y)
    % Unpack the state variables (y)
    cake_mass = y(1);
    cake_temperature = y(2);

    % Define the input variables (Q_in, f_vac, T_in, P_in)

    % Define the filtration model to calculate the filtration rate (dM/dt)
    dMdt = ...

    % Define the heat transfer model to calculate the temperature change (dT/dt)
    dTdt = ...

    % Define the derivatives of the state variables (dy/dt)
    dydt(1, :) = dMdt; % Mass balance
    dydt(2, :) = dTdt; % Energy balance
end
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main.m
% Set the initial conditions and simulation time span
y0 = [cake_mass_initial, cake_temperature_initial];
tspan = [0, t_final];

% Solve the differential equation system using ODE45
[t, y] = ode45(@nutsche_filter_dryer, tspan, y0);
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main.m
% Plot the results of the Nutsche filter dryer simulation
figure;
subplot(2, 1, 1);
plot(t, y(:, 1)); % Mass profile over time
xlabel('Time [s]');
ylabel('Mass [kg]');

subplot(2, 1, 2);
plot(t, y(:, 2)); % Temperature profile over time
xlabel('Time [s]');
ylabel('Temperature [K]');
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