From thermodynamic point of view, you need to consider three conservation laws: mass, momentum and energy. If there is not any flow, then just couple conservation of mass with energy equation. Otherwise, you need to couple them with Brinkman equation to satisfy the boundary conditions. For a specific geometry, it is better to use COMSOL to numerically solve all these equations. There are heaps of tutorials on this topic.
From thermodynamic point of view, you need to consider three conservation laws: mass, momentum and energy. If there is not any flow, then just couple conservation of mass with energy equation. Otherwise, you need to couple them with Brinkman equation to satisfy the boundary conditions. For a specific geometry, it is better to use COMSOL to numerically solve all these equations. There are heaps of tutorials on this topic.
It depends on which software you are using? First i will suggest you to go through Darcy law and then go through the tutorial manual of the software.
if you are writing a code then i will suggest you to add convective terms for the fluid and the conductive term in the the porous media.
heat transfer in porous media is seriously affected by the capillary and adhesive nature of the fluid and solid which results in the evaporation of the flowing liquid hence therefore you must consider phase change as well for the fact that huge amount of latent heat may be involved.
In fluent you can model the heat capacity by using multi-zone approach. A second coincident cell zone is created that represents solid porous material and it stores the internal energy value. There are two approaches: temperature equilibrium and transient heating.