Non-Local Vectorial Internal Variables and Generalized Guyer-Krumhansl Evolution Equations for the Heat Flux
In this paper, we ask ourselves how non-local effects affect the description of thermodynamic systems with internal variables. Usually, one assumes that the internal variables are local, but that their evolution equations are non-local, i.e., for instance, that their evolution equations contain non-...
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MDPI AG
2023-08-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/9/1259 |
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| author | Liliana Restuccia David Jou |
| author_facet | Liliana Restuccia David Jou |
| author_sort | Liliana Restuccia |
| collection | DOAJ |
| description | In this paper, we ask ourselves how non-local effects affect the description of thermodynamic systems with internal variables. Usually, one assumes that the internal variables are local, but that their evolution equations are non-local, i.e., for instance, that their evolution equations contain non-local differential terms (gradients, Laplacians) or integral terms with memory kernels. In contrast to this typical situation, which has led to substantial progress in several fields, we ask ourselves whether in some cases it would be convenient to start from non-local internal variables with non-local evolution equations. We examine this point by considering three main lengths: the observation scale <i>R</i> defining the elementary volumes used in the description of the system, the mean free path <i>l</i> of the microscopic elements of the fluid (particles, phonons, photons, and molecules), and the overall characteristic size <i>L</i> of the global system. We illustrate these ideas by considering three-dimensional rigid heat conductors within the regime of phonon hydrodynamics in the presence of thermal vortices. In particular, we obtain a generalization of the Guyer–Krumhansl equation, which may be of interest for heat transport in nanosystems or in systems with small-scale inhomogeneities. |
| first_indexed | 2024-03-10T22:47:13Z |
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| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T22:47:13Z |
| publishDate | 2023-08-01 |
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| spelling | doaj.art-4f60dca64b464337aaff2c330c3630a22023-11-19T10:35:07ZengMDPI AGEntropy1099-43002023-08-01259125910.3390/e25091259Non-Local Vectorial Internal Variables and Generalized Guyer-Krumhansl Evolution Equations for the Heat FluxLiliana Restuccia0David Jou1Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale F. Stagno d’Alcontres, Salita Sperone 31, 98166 Messina, ItalyGrup de Fisíca Estadística, Universitat Autònoma de Barcelona, 08193 Bellaterra, SpainIn this paper, we ask ourselves how non-local effects affect the description of thermodynamic systems with internal variables. Usually, one assumes that the internal variables are local, but that their evolution equations are non-local, i.e., for instance, that their evolution equations contain non-local differential terms (gradients, Laplacians) or integral terms with memory kernels. In contrast to this typical situation, which has led to substantial progress in several fields, we ask ourselves whether in some cases it would be convenient to start from non-local internal variables with non-local evolution equations. We examine this point by considering three main lengths: the observation scale <i>R</i> defining the elementary volumes used in the description of the system, the mean free path <i>l</i> of the microscopic elements of the fluid (particles, phonons, photons, and molecules), and the overall characteristic size <i>L</i> of the global system. We illustrate these ideas by considering three-dimensional rigid heat conductors within the regime of phonon hydrodynamics in the presence of thermal vortices. In particular, we obtain a generalization of the Guyer–Krumhansl equation, which may be of interest for heat transport in nanosystems or in systems with small-scale inhomogeneities.https://www.mdpi.com/1099-4300/25/9/1259continuum thermodynamicsheat transportclassical irreversible thermodynamicsinternal variablesphonon hydrodynamics |
| spellingShingle | Liliana Restuccia David Jou Non-Local Vectorial Internal Variables and Generalized Guyer-Krumhansl Evolution Equations for the Heat Flux Entropy continuum thermodynamics heat transport classical irreversible thermodynamics internal variables phonon hydrodynamics |
| title | Non-Local Vectorial Internal Variables and Generalized Guyer-Krumhansl Evolution Equations for the Heat Flux |
| title_full | Non-Local Vectorial Internal Variables and Generalized Guyer-Krumhansl Evolution Equations for the Heat Flux |
| title_fullStr | Non-Local Vectorial Internal Variables and Generalized Guyer-Krumhansl Evolution Equations for the Heat Flux |
| title_full_unstemmed | Non-Local Vectorial Internal Variables and Generalized Guyer-Krumhansl Evolution Equations for the Heat Flux |
| title_short | Non-Local Vectorial Internal Variables and Generalized Guyer-Krumhansl Evolution Equations for the Heat Flux |
| title_sort | non local vectorial internal variables and generalized guyer krumhansl evolution equations for the heat flux |
| topic | continuum thermodynamics heat transport classical irreversible thermodynamics internal variables phonon hydrodynamics |
| url | https://www.mdpi.com/1099-4300/25/9/1259 |
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