On energy and entropy influxes in the Green-Naghdi type III theory of heat conduction. (English) Zbl 1320.74009
Summary: 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.
MSC:
| 74A15 | Thermodynamics in solid mechanics |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
Keywords:
energy influx; entropy influx; Müller-Liu entropy principle; coldness; thermal displacementReferences:
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