On energy and entropy infuxes in the Green-Naghdi Type III theory of heat conduction

Abstract

The energy-influx/entropy-influx relation in the Green-Naghdi Type III theory of heat conduction is examined within a thermodynamical framework à la Müller-Liu, where that relation is not specified a priori irrespectively of the constitutive class under attention. It is shown that the classical assumption, i.e. that the entropy influx and the energy influx are proportional via the absolute temperature, holds true if heat conduction is, in a sense that is made precise, isotropic. In addition, it is proved that influx proportionality cannot be postulated in general, because a counterexample can be given in the case of transversely isotropic conduction. © 2013 The Author(s) Published by the Royal Society.