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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| Published in | Journal of non-equilibrium thermodynamics Vol. 45; no. 3; pp. 291 - 304 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin
De Gruyter
26.07.2020
Walter de Gruyter GmbH |
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| Abstract | 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. |
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| AbstractList | Abstract
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. 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. |
| Author | Cao, Bing-Yang Hua, Yu-Chao Nie, Ben-Dian Guo, Zeng-Yuan Grmela, Miroslav |
| Author_xml | – sequence: 1 givenname: Bing-Yang surname: Cao fullname: Cao, Bing-Yang email: caoby@tsinghua.edu.cn organization: Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of 4 Engineering Mechanics, 12442 Tsinghua University, Beijing 100084, China – sequence: 2 givenname: Miroslav surname: Grmela fullname: Grmela, Miroslav email: miroslav.grmela@polymtl.ca organization: École Polytechnique de Montréal, C.P.079 suc. Centre-ville, Montréal H3C 3A7, Québec, Canada – sequence: 3 givenname: Zeng-Yuan surname: Guo fullname: Guo, Zeng-Yuan email: demgzy@tsinghua.edu.cn organization: Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of 4 Engineering Mechanics, 12442 Tsinghua University, Beijing 100084, China – sequence: 4 givenname: Yu-Chao surname: Hua fullname: Hua, Yu-Chao email: huayuchao19@163.com organization: Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of 4 Engineering Mechanics, 12442 Tsinghua University, Beijing 100084, China – sequence: 5 givenname: Ben-Dian surname: Nie fullname: Nie, Ben-Dian email: nbd15@mails.tsinghua.edu.cn organization: Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of 4 Engineering Mechanics, 12442 Tsinghua University, Beijing 100084, China |
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| Snippet | 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... Abstract Phonon hydrodynamics uses the fields of the total energy and the heat flux as state variables. We extend it by promoting the microscopic internal... |
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| SubjectTerms | Computational fluid dynamics Fluid flow Fluid mechanics GENERIC Heat flux heat transport Hydrodynamics Internal energy Mathematical analysis Phonons State variable thermodynamics |
| Title | Two Temperature Extension of Phonon Hydrodynamics |
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