## Packed bed storage modeling probelm

Hello, I have to make a numerical model of a packed bed storage full of spheres where I have to predict both fluid temperature and solid temperature across the bed length. Its a transient 1D coupled heat transfer problem where I know only the fluid inlet temperature. I am a newbie at matlab and I tried to develop code with the help of chatgpt for charging phase but it doesn’t work. I also have to derive code for storage and discharging phase. Can you kindly help me with it?

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 = 1; % Time step size in seconds

Nt = 720; % 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

% 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;Hello, I have to make a numerical model of a packed bed storage full of spheres where I have to predict both fluid temperature and solid temperature across the bed length. Its a transient 1D coupled heat transfer problem where I know only the fluid inlet temperature. I am a newbie at matlab and I tried to develop code with the help of chatgpt for charging phase but it doesn’t work. I also have to derive code for storage and discharging phase. Can you kindly help me with it?

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 = 1; % Time step size in seconds

Nt = 720; % 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

% 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; Hello, I have to make a numerical model of a packed bed storage full of spheres where I have to predict both fluid temperature and solid temperature across the bed length. Its a transient 1D coupled heat transfer problem where I know only the fluid inlet temperature. I am a newbie at matlab and I tried to develop code with the help of chatgpt for charging phase but it doesn’t work. I also have to derive code for storage and discharging phase. Can you kindly help me with it?

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 = 1; % Time step size in seconds

Nt = 720; % 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

% 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; model, urgent MATLAB Answers — New Questions