Cargando…
On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations
Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entr...
Autores principales: | , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2019
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514686/ https://www.ncbi.nlm.nih.gov/pubmed/33266919 http://dx.doi.org/10.3390/e21020204 |
_version_ | 1783586645365227520 |
---|---|
author | Li, Shu-Nan Cao, Bing-Yang |
author_facet | Li, Shu-Nan Cao, Bing-Yang |
author_sort | Li, Shu-Nan |
collection | PubMed |
description | Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entropy production rate. Using the relaxation time approximation and power series expansion, macroscopic approximations are derived for these entropic concepts. For the standard BTE, our results can recover the entropic frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT) as if there exists a well-defined effective thermal conductivity. For the fractional BTEs corresponding to the generalized Cattaneo equation (GCE) class, the entropy flux and entropy production rate will deviate from the forms in CIT and EIT. In these cases, the entropy flux and entropy production rate will contain fractional-order operators, which reflect memory effects. |
format | Online Article Text |
id | pubmed-7514686 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75146862020-11-09 On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations Li, Shu-Nan Cao, Bing-Yang Entropy (Basel) Article Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entropy production rate. Using the relaxation time approximation and power series expansion, macroscopic approximations are derived for these entropic concepts. For the standard BTE, our results can recover the entropic frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT) as if there exists a well-defined effective thermal conductivity. For the fractional BTEs corresponding to the generalized Cattaneo equation (GCE) class, the entropy flux and entropy production rate will deviate from the forms in CIT and EIT. In these cases, the entropy flux and entropy production rate will contain fractional-order operators, which reflect memory effects. MDPI 2019-02-21 /pmc/articles/PMC7514686/ /pubmed/33266919 http://dx.doi.org/10.3390/e21020204 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Li, Shu-Nan Cao, Bing-Yang On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations |
title | On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations |
title_full | On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations |
title_fullStr | On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations |
title_full_unstemmed | On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations |
title_short | On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations |
title_sort | on entropic framework based on standard and fractional phonon boltzmann transport equations |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514686/ https://www.ncbi.nlm.nih.gov/pubmed/33266919 http://dx.doi.org/10.3390/e21020204 |
work_keys_str_mv | AT lishunan onentropicframeworkbasedonstandardandfractionalphononboltzmanntransportequations AT caobingyang onentropicframeworkbasedonstandardandfractionalphononboltzmanntransportequations |