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.