Biot's equations for multiphase media with temperature gradient on the basis of generalized variational principle

The system of generalized Biot's equations, describing waves propagation in a multi-phase or multi- component medium in the presence of heat exchange between phases, is derived on the basis of generalized variational principle [Maximov G.A. DD2006, p. 173-177]. It is shown that in the presence of N phases 2N propagating eigen-modes can exist in this medium. At high frequencies N modes are of the mechanical (acoustical) type and N modes are of the diffusive (thermal) type of propagation. At low frequencies there is the single acoustical (wave) mode and the rest 2N-1 modes possess the diffusion (thermal) type of behavior. For a two-component medium without temperature exchange the developed approach is reduced to the well known Biot's model. The account of the temperature field yields the generalized Biot's model for two components medium.