solve drying model in matlab

To solve a drying model in MATLAB, one can follow the following steps:

1. Set up the drying model and formulate it as a partial differential equation (PDE) system. This may involve specifying the governing equations, initial/boundary conditions, and material properties.

2. Discretize the PDE system in space and time. This can be done using finite difference, finite volume, or finite element methods.

3. Set up the numerical scheme to solve the discretized PDE system. This may involve choosing an appropriate time-stepping method, such as explicit or implicit schemes, and solving linear/nonlinear equations.

4. Implement the numerical scheme in MATLAB. This can be done using built-in ODE/PDE solvers or by coding the solver from scratch.

5. Run simulations and analyze the results. This can involve plotting the time evolution of the drying process and comparing it against experimental data.

Here's an example code that solves a simple 1D drying model using the finite difference method in MATLAB:

main.m
% Parameters
L = 1;          % Length of material (m)
T0 = 293;       % Initial temperature (K)
H0 = 0.1;       % Initial moisture content (kg/kg dry solid)
rho = 1000;     % Density of material (kg/m^3)
cp = 2000;      % Specific heat capacity of material (J/kg-K)
D = 1e-7;       % Moisture diffusivity (m^2/s)
k = 0.1;        % Thermal conductivity (W/m-K)

% Discretization
nx = 101;       % Number of grid points
dx = L/(nx-1);  % Grid spacing
x = linspace(0,L,nx);   % Grid

% Time stepping
dt = 0.5;       % Time step (s)
t = 0:dt:1800;  % Simulation time
nt = length(t);

% Initial conditions
T = ones(nx,1)*T0;
H = ones(nx,1)*H0;

% Boundary conditions
T(1) = 373;     % Temperature at surface (K)
T(end) = 293;   % Temperature at core (K)

% Finite difference scheme
for i = 1:nt-1
    % Temperature equation
    T(2:end-1) = T(2:end-1) + dt*(k/(rho*cp*dx^2))*(T(1:end-2) - 2*T(2:end-1) + T(3:end));
    
    % Moisture equation
    H(2:end-1) = H(2:end-1) + dt*(D/dx^2)*(H(1:end-2) - 2*H(2:end-1) + H(3:end));
end

% Plotting
figure;
plot(x,T,'-','LineWidth',2); hold on;
plot(x,H,'--','LineWidth',2);
xlabel('Length (m)');
ylabel('Temperature (K) / Moisture content (kg/kg dry solid)');
legend('Temperature','Moisture content');
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This code simulates the drying process of a material with initial moisture content of 0.1 kg/kg dry solid at a constant temperature of 293 K. The material is heated at the surface to a temperature of 373 K and cooled at the core to the initial temperature. The results are plotted as a function of length, showing the evolution of temperature and moisture content over time.