Two Temperature Extension of Phonon Hydrodynamics

Phonon hydrodynamics uses the fields of the total energy and the heat flux as state variables. We extend it by promoting the microscopic internal energy field into the status of an extra independent state variable. The governing equations of both the phonon and the extended (two temperature) phonon...

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Bibliographic Details
Published inJournal of non-equilibrium thermodynamics Vol. 45; no. 3; pp. 291 - 304
Main Authors Cao, Bing-Yang, Grmela, Miroslav, Guo, Zeng-Yuan, Hua, Yu-Chao, Nie, Ben-Dian
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 26.07.2020
Walter de Gruyter GmbH
Subjects
Computational fluid dynamics
Fluid flow
Fluid mechanics
GENERIC
Heat flux
heat transport
Hydrodynamics
Internal energy
Mathematical analysis
Phonons
State variable
thermodynamics
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Summary:Phonon hydrodynamics uses the fields of the total energy and the heat flux as state variables. We extend it by promoting the microscopic internal energy field into the status of an extra independent state variable. The governing equations of both the phonon and the extended (two temperature) phonon hydrodynamics are formulated as particular realizations of the abstract GENERIC equation. Such unified formulation makes both theories manifestly compatible with mechanics and thermodynamics. Also differences and similarities (in the physical content, in the mathematical structure, and in qualitative properties of solutions) between the two heat transfer theories, as well as their mutual compatibility, become manifestly displayed.
ISSN:0340-0204
1437-4358
DOI:10.1515/jnet-2020-0029