A continuum theory, for a heat-conducting, porous elastic solid saturated by a mixture of heat-conducting, viscous compressible fluids, is developed using the continuum theory of mixtures. Gradients of the fluid densities and the second deformation gradient of the solid constituent are included among the independent constitutive variables as proposed by Mu¨ller [17]. The Clausius-Duhem entropy inequality and the principle of material indifference are used to obtain rational constitutive relations for the medium. Linear constitutive equations are presented, and a theory equivalent to a generalization of the Biot equations is obtained.

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