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The energy-influx/entropy-influx relation in the Green-Naghdi Type III theoryof heat conduction is examined within a thermodynamical framework \`a laMueller-Liu, where that relation is not specified a priori irrespectively ofthe constitutive class under attention. It is shown that the classicalassumption, i.e., that the entropy influx and the energy influx areproportional via the absolute temperature, holds true if heat conduction is, ina sense that is made precise, isotropic. In addition, it is proven that thestandard assumption does not hold in case of transversely isotropic conduction.

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