On the Generalized Heat Conduction Laws in the Reversible Thermodynamics of a Continuous Medium

A general covariance variational model of reversible thermodynamics is developed in which the kinematic and force variables are the components of unified tensor objects in the space−time continuum, and the resolving equations of the dynamic thermoelasticity and heat-conduction of an ideal (defect-free) media are described by the 4D-vector equation. It is shown that the formulations of relations of the generalized Duhamel−Neumann representation and the Maxwell−Cattaneo law follow directly from the constitutive relations of the space−time-continuum model without additional hypotheses and assumptions. It is proved that the Maxwell−Cattaneo and Fourier generalized heat-conduction laws are unambiguously characterized by well-known thermomechanical parameters determined under isothermal and adiabatic conditions for reversible coupled deformation processes and heat-conduction despite the fact that one usually relates both the Fourier law and the relaxation time in the Maxwell−Cattaneo law with the dissipative processes.