How can I solve a system of partial differential equations?

Hi,

in the equation 10 is lambda s zero and that is the reason why it is a first order PDE system.

The two partial differential equations describe the heating and cooling in a packed bed storage.

How can I solve the following first-order PDE' system in time and 1 d space with MATLAB?

Can i use the pdepe MATLAB Command?

Thank you for your help

Answer 1

[Torsten]

Use a first-order difference quotient to discretize dT_f/dz in space and use ODE15S to solve the resulting system of ordinary differential equations. Look up "Method-of-Lines" for more details.

pdepe is suited to solve 2nd order PDEs - first-order PDEs will usually make difficulties.

[Philipp Vogel]

Hello Torsten

thank you for your answer.

In my example i have a cylinder filled with solid fuel for example stones. The fluid in this case air flows through the cylinder and cools down. While the solid warms up. The air temperature ( Tf) and the solid temperature (Ts) are in kelvin.

I have discretize the partial differential system and the boundary conditions are:

Tf(0,t) = 525;

Tf(z,t) = 325;

Ts(0,t) = 293;

dTfdt(i) = (-eta*((Tf(i+1)-Tf(i-1))/(2*dz))/v-h_vol(Tf(i)-Ts(i))/ (v*rho_f*c_f);

dTsdt(i) = (-h_vol*(Ts(i)-Tf(i)))/((1-eta)*rho_s*rho_f)

How do i have to implement the discretizing equations in the ODE15S command?

[Ao Yang]

Hello Philipp

I've been trying to solve this PDE system recently as well, also about the packed bed thermal storage problem, and my equations are similar to yours, but I'm finding it very difficult to slove if i discretize dT/dx of fluid in space. I want to ask, have u already found a solution? Thanks/!