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

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.