rhoS = 2750; % Solid density [kg/m^3]
cpS = 850; % Solid specific heat capacity [J/(kg*K)]
ks = 1.28; % Effective thermal conductivity of solid [W/(m*K)]
epsilon = 0.36; % Void fraction
has = 47223.11473; % Heat transfer coefficient between solid and fluid [W/(m^2*K)]
Uw = 4.5118; % External heat transfer coefficient [W/(m^2*K)]
Tinfinity = 21 + 273.15; % Ambient temperature [K]
TinF = 83 + 273.15; % Inlet fluid temperature [K]
TinS = 21 + 273.15; % Initial solid temperature [K]
L = .14605; % Height of the packed bed [m]
u = 5.94; % Specific HTF mass flow rate [kg/(m^2*s)]
D = 0.1016; % Diameter of the bed [m]
dp = 0.01407; % Particle diameter [m]
rhoF = 1.08; % Fluid density [kg/m^3]
cpF = 1008; % Fluid specific heat [J/(kg*K)]
% Set up computational domain
Nx = 50; % Number of spatial steps
dx = L / Nx; % Spatial step size
dt = 0.0001; % Time step size in seconds
Nt = 7200000; % Number of time steps
% Initialize temperature profiles
TS = ones(Nx, 1) * TinS; % Initial solid temperature profile
TF = ones(Nx, 1) * TinF; % Initial fluid temperature profile
TF(1) = Tinfinity;
% Simulation loop
for n = 1:Nt
TS_new = TS;
TF_new = TF;
for i = 2:Nx-1
% Fluid temperature equation
TF_new(i) = TF(i) + dt * (-u * (TF(i) - TF(i-1)) / dx + (has/(rhoF * cpF * epsilon)) * (TS(i) - TF(i)));
% Solid temperature equation
d2TSdx2 = (TS(i+1) - 2*TS(i) + TS(i-1)) / dx^2;
TS_new(i) = TS(i) + dt * ((ks/(rhoS * cpS * (1 - epsilon))) * d2TSdx2 ...
+ (has/(rhoS * cpS * (1 - epsilon))) * (TF(i) - TS(i)) ...
+ (Uw * D * pi / (rhoS * cpS * (1 - epsilon))) * (Tinfinity - TS(i)));
end
% Fluid temperature equation (last point)
TF_new(Nx) = TF(Nx) + dt * (-u * (TF(Nx) - TF(Nx-1)) / dx + (has/(rhoF * cpF * epsilon)) * (TS(Nx) - TF(Nx)));
% Update temperatures
TS = TS_new;
TF = TF_new;
% Apply boundary conditions
TF(1) = TinF; % Constant inlet temperature for fluid
TS(1) = TS(2); % Adiabatic boundary for solid at inlet
TS(Nx) = TS(Nx-1); %Adiabatic boundary for solid at outlet
end
% Plotting the results
x = linspace(0, L, Nx);
plot(x, TS-273.15, 'r', x, TF-273.15, 'b');
xlabel('Bed Length (m)');
ylabel('Temperature (°C)');
legend('Solid Temperature', 'Fluid Temperature');
title('Temperature Distribution Along the Bed Length');
grid on;
