A note on Onsager’s relations

Abstract

Abstract. A nonlinear viscoelastic material with the heat flux obeying a generalization of Cattaneo's law is considered. It is shown that for slow processes with small gradients of temperature the exact constitutive equations can be approximated by those of a linear viscous material with Fourier heat conduction. As a consequence of the thermodynamic restrictions on the original constitutive equations, the approximate constitutive equations are shown to satisfy the principle of local equilibrium for energy and entropy, and the kinetic coefficients giving the viscous stress and heat flux vector satisfy Onsager's relations.

Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity

“…[4]), shows that for slow motions x«, ot -• 0, the integral law (3.1) can be approximated by a differential-type law involving the kinetic coefficients. I refer to [14] for the proof of the retardation theorem within the context of the single-integral laws.…”

“…In the existence theory a crucial role is played by a certain symmetry of the coefficients of viscosity and my goal is to show that this symmetry follows from the thermodynamic properties of the original "integral" model. The method of proof is similar to the one employed in Silhavy [14] where it was shown that the Onsager symmetry relations can be derived for Navier-Stokes viscous materials with Fourier's heat conduction.…”