On the modelling of thermal convection in porous media through rate-type equations

The paper investigates current models of flows in porous media from the viewpoint of the mixture theory. The constitutive equations are investigated for compressible, viscous, heat-conducting fluids subject to relaxation phenomena. The thermodynamic analysis is performed via the Clausius-Duhem inequality based directly on the peculiar fields of the mixture. The detailed analysis so developed involves the peculiar heat fluxes and stresses per se while the balance equations for energy and entropy of the whole body would involve also diffusion effects. Following the objectivity principle, the constitutive equations for stresses and heat fluxes are taken to be governed by objective rate equations.