A THEORY OF HEAT AND MASS TRANSFER IN VISCOELASTIC SOLIDS WITH MICROSTRUCTURES

In the present work, the linear theory of micropolar thermo-viscoelasticity with mass diffusion is established. The constitutive relations are obtained for a mixture of diffusive masses in the bulk medium, and then the uniqueness theorem is proved using the Laplace transform and the positive definiteness assumptions on the initial case of the thermoelastic modulus. The reciprocity relation is established avoiding Laplace transform. Some consequences on the reciprocity relation are discussed. The variational theorem is proved. The integral representation is obtained for the model equations; hence, the Maysel's, Somigliana's and Green's formulae are derived. Finally, the mixed boundary value problem is considered and reduced to a system of four Fredholm-Volterra integral equations.