<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The paper deals with the meaning of non-equilibrium temperatures in nanosystems with an internal variable, describing defects inside them, and implications on heat transport. In equilibrium all definitions of temperature lead to the same value, but in nonequilibrium steady states they lead to different values, giving information on different degrees of freedom. We discuss the caloric and entropic non-equilibrium temperatures and the relations among them, in defective nanosystems (crystals with dislocations or porous channels, carbon nanotubes in a solid matrix and so on), crossed by an external energy flux. Here, we present a model for nanocrystals with dislocation defects submitted to an external energy flux. The dislocations may have a strong influence on the effective thermal conductivity, and their own dynamics may be coupled in relevant way to the heat flux dynamics. In the linear case the constitutive relations, the rate equations for the internal variable and the heat flux are worked out and a generalized telegraphic heat equation is derived in the anisotropic and isotropic case, describing the thermal disturbances with finite velocity.</p></abstract>

The paper deals with the meaning of non-equilibrium temperatures in nanosystems with an internal variable, describing defects inside them, and implications on heat transport. In equilibrium all definitions of temperature lead to the same value, but in nonequilibrium steady states they lead to different values, giving information on different degrees of freedom. We discuss the caloric and entropic non-equilibrium temperatures and the relations among them, in defective nanosystems (crystals with dislocations or porous channels, carbon nanotubes in a solid matrix and so on), crossed by an external energy flux. Here, we present a model for nanocrystals with dislocation defects submitted to an external energy flux. The dislocations may have a strong influence on the effective thermal conductivity, and their own dynamics may be coupled in relevant way to the heat flux dynamics. In the linear case the constitutive relations, the rate equations for the internal variable and the heat flux are worked out and a generalized telegraphic heat equation is derived in the anisotropic and isotropic case, describing the thermal disturbances with finite velocity.

Non-equilibrium temperatures and heat transport in nanosystems with defects, described by a tensorial internal variable

University of Messina, Department of Mathematical and Computer Sciences, Physical Sciences, Earth Sciences, Messina, Italy

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The paper deals with the meaning of non-equilibrium temperatures in nanosystems with an internal variable, describing defects inside them, and implications on...

Non-equilibrium temperatures and heat transport in nanosystems with defects, described by a tensorial internal variable

Published Online: May 20, 2016

Page range: 81 - 97

Received: Jan 14, 2015

Accepted: Jun 14, 2015

DOI: https://doi.org/10.1515/caim-2016-0007

Keywords
Non-equilibrium Thermodynamics, internal variables, defects of dislocation, nanosystems

© 2016 Liliana Restuccia, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Non-equilibrium temperatures and heat transport in nanosystems with defects, described by a tensorial internal variable

Published Online: May 20, 2016

Page range: 81 - 97

Received: Jan 14, 2015

Accepted: Jun 14, 2015

DOI: https://doi.org/10.1515/caim-2016-0007

KeywordsNon-equilibrium Thermodynamics, internal variables, defects of dislocation, nanosystems

© 2016 Liliana Restuccia, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Non-equilibrium Thermodynamics, internal variables, defects of dislocation, nanosystems