Abstract
In the framework of Extended Irreversible Thermodynamics, a model of heat transport due to phonons and electrons is developed. Compatibility with Second Law of Thermodynamics is exploited through a generalized Coleman-Noll procedure. A system of nonlinear partial differential equations, ruling the evolution of the partial heat fluxes, is derived. Propagation of temperature waves through one-dimensional heat conductors is investigated as well.
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Notes
Note that, in the classical Coleman-Noll method [6], only the balance of the energy is substituted into the entropy inequality.
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Acknowledgements
V.A. Cimmelli acknowledges the financial support from the University of Basilicata and the Italian Gruppo Nazionale per la Fisica Matematica.
D. Jou acknowledges the financial support from the Dirección General de Investigación of the Spanish Ministry of Science and Innovation under grant FIS No. 2009-13370-C02-01, the Consolider Project NanoTherm (grant CSD-2010-00044) and the Direcció General de Recerca of the Generalitat of Catalonia under grant No. 2009-SGR-00164.
A. Sellitto acknowledges the financial support from the Italian Gruppo Nazionale per la Fisica Matematica under grant Progetto Giovani 2010.
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Cimmelli, V.A., Jou, D. & Sellitto, A. Heat Transport Equations with Phonons and Electrons. Acta Appl Math 122, 117–126 (2012). https://doi.org/10.1007/s10440-012-9731-1
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DOI: https://doi.org/10.1007/s10440-012-9731-1