please help me modify the code i want to simulate the temperature profile distributed along the height of the adsorption column

% Constants

L = 0.050; % Column height (m)

N = 100; % Number of grid points

dz = L / (N-1); % Grid spacing (Note: modified to include boundary points)

tFinal = 100.0; % Final time (s)

dt = 1.0; % Time step size

% Physical properties

lambda_L = 1.0; % Thermal conductivity of liquid phase (W/mK)

rho_p = 1000.0; % Particle density (kg/m^3)

C_g = 1000.0; % Heat capacity of gas phase (J/kgK)

epsilon = 0.4; % Void fraction

h_f = 100.0; % Heat transfer coefficient between gas and solid phases (W/m^2K)

a_s = 0.01; % Surface area per unit volume of solid phase (m^2/m^3)

h_w = 5000.0; % Heat transfer coefficient between gas phase and wall (W/m^2K)

d_int = 0.1; % Internal diameter of the column (m)

% Initialization

T = 298.15 * ones(N, 1); % Initial temperature (K)

T(N) = 393.15; % Boundary condition at the top of the column (K)

% Finite difference method

numSteps = round(tFinal / dt);

for step = 1:numSteps

% Temperature profile update

for i = 2:(N-1)

T(i) = T(i) + dt * ((lambda_L / dz^2) * (T(i+1) - 2 * T(i) + T(i-1)) + ...

(rho_p * C_g / dz) * (T(i) - T(i-1)) + ...

(C_g * rho_p / dt) * (T(i) - 298.15) + ...

((1 - epsilon) / epsilon) * h_f * a_s * (T(i) - T(N)) + ...

(4 * h_w / (epsilon * d_int)) * (T(i) - T(1)));

end

% Boundary conditions update

T(1) = T(2); % Temperature at the bottom of the column (adiabatic)

T(N) = 273.14; % Boundary condition at the top of the column (K)

end

% Plotting

z = linspace(0, L, N);

figure;

plot(z, T);

xlabel('Column Height (m)');

ylabel('Temperature (K)');

title('Temperature Distribution in the Adsorption Column');

[Ofentse Maila]

i am still not getting the curve that simulate the tempearture distributed along the column height, please recommend to me what modification i i should do in order to obtain the curve

[Torsten]

What is the mathematical model for the temperature ? Could you supply the PDE with initial and boundary conditions ? Your discretized form from above looks quite strange.

Answer 1

[Torsten]

If you don't want to save the temperatures for all time steps, you need at least two arrays T_old and T_new such that your advancing in time would somehow look like

T_new(i) = T_old(i) + dt*...

instead of

T(i) = T(i) + dt * ...

The latter will make problems because you mix old and new temperatures in the expressions following the dt * .