On a thermodynamic model of fluid-saturated porous-medium

In order to describe isotropic pore structure of a solid skeleton saturated with a fluid, two internal state variables are introduced: a volume porosity $f_v$ and a structural parameter $\kappa$. The internal friction in the skeleton material is incorporated by a tensor-valued internal state variable $\boldsymbol{\alpha}$. Thermal properties are described by a single entropy density function $\eta$ and two thermal state variables $\beta^s$ and $\beta^f$. In the energy balance law, both heat fluxes appear and an added mass effect is incorporated to manifest the influence of the pore structure of the skeleton on the fluid motion. Consequences of the second law of thermodynamics are formulated in the form of four potential relations for stresses and heat flux vectors together with a representation of interaction forces.