On Energy and Entropy Influxes in the Green-Naghdi Type III Theory of Heat Conduction

TL;DR

This paper investigates the relationship between energy and entropy influxes in the Green-Naghdi Type III heat conduction theory, revealing conditions under which classical assumptions hold or fail, especially in anisotropic materials.

Contribution

It clarifies the conditions for the classical energy-entropy influx relation within the Green-Naghdi Type III framework, highlighting differences between isotropic and transversely isotropic conduction.

Findings

Classical proportionality holds in isotropic conduction.

Proportionality does not hold in transversely isotropic conduction.

The relation depends on the material's anisotropy.

Abstract

The energy-influx/entropy-influx relation in the Green-Naghdi Type III theory of heat conduction is examined within a thermodynamical framework \`a la Mueller-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 proven that the standard assumption does not hold in case of transversely isotropic conduction.