How can I solve a system of partial differential equations?

조회 수: 2 (최근 30일)
Philipp Vogel
Philipp Vogel 2019년 7월 28일
댓글: Ao Yang 2020년 11월 6일
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?
PDE_System.PNG
Thank you for your help

답변 (1개)

Torsten
Torsten 2019년 7월 29일
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.
  댓글 수: 2
Philipp Vogel
Philipp Vogel 2019년 7월 30일
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.
Schüttgutspeicher.PNG
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
Ao Yang 2020년 11월 6일
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/!

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