Darcy's law in anisothermic porous medium

A linear system of differential equations describing a joint motion of thermoelastic porous body with sufficiently large Lame's constants (absolutely rigid body) and thermofluid occupying porous space is considered. The rigorous justification is fulfilled for homogenization procedures as the dimensionless size of the pores tends to zero, while the porous body is geometrically periodic. As the results, we derive decoupled system consisting of Darcy's system of filtration for thermofluid (first approximation) and anisotropic Lamé's system of equations for thermoelastic solid (second approximation). The proof is based on Nguetseng's two-scale convergence method of homogenization in periodic structures.