What are the equations used for studying heat transfer in a porous media? I am working with COMSOL Mukltiphysics. i have considered a compressible fluid flow within the porous media which is a closed system. I wish to couple heat transfer to it. Apart from Fourier's law what are other equations relevant to study heat transfer? One more question is that can we use heat transfer equations for incompressible flow if the fluid flow is compressible in nature?
Unless I'm mistaken, I think the equations of the generalized models are the best way to simulate Darcy regime, Forchheimer, Brinckmann, Forshheimer-Brinkmann ... regimes depending on Darcy scale...
for the compressibility, if the flow is compressible and you know the Mach number
For packed beds I know Kunii et al. and Cybulski et al have good empirical relations for heat transfer at low Reynolds number (upto Re=100 I think) and Achenbach correlation is for higher Reynolds number. In all these correlations the Nusselt number is some function of particle Reynolds number. The fact that your flow is compressible should not invalidate use of empirical relations for the Nusselt number. If there is appreciable change in fluid density across your model you can just locally calculate the Nusselt number and heat transfer coefficient as a function of Reynolds number which depends on density of the fluid.
The governing equations is still the same good old [heat] transport equation (or ADR or ADE). But, for 3 phase medium: Solid, Liquid and Gas. There are some closures for counting for interaction/transfer of heat between the three phases.
You can find that governing equation in "soil physics" books, or" porous media" books, or "continuum mechanic" books which is written for chemical engineering. Search for the keyword "Continuum mixture theory"
See:
Principles of Heat Transfer in Porous Media, By Maasoud Kaviany
Handbook of porous media By Kambiz Vafai
I. Muller, A thermodynamic theory of mixtures of fluids, Arch. Rat. Mech. Anal., 28, 1-39, 1968.
Hope it helps,
Kaveh
Unless I'm mistaken, I think the equations of the generalized models are the best way to simulate Darcy regime, Forchheimer, Brinckmann, Forshheimer-Brinkmann ... regimes depending on Darcy scale...
for the compressibility, if the flow is compressible and you know the Mach number
hello
please see this model
https://www.comsol.fr/model/free-convection-in-a-porous-medium-278
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