Derivation of the equations of nonisothermal acoustics in elastic porous media

We consider the problem of the joint motion of a thermoelastic solid skeleton and a viscous thermofluid in pores, when the physical process lasts for a few dozens of seconds. These problems arise in describing the propagation of acoustic waves. We rigorously derive the homogenized equations (i.e., the equations not containing fast oscillatory coefficients) which are different types of nonclassical acoustic equations depending on relations between the physical parameters and the homogenized heat equation. The proofs are based on Nguetseng’s two-scale convergence method.