A nonlinear model of thermoelectricity with two temperatures: Application to quasicrystalline nanowires
type: Item
instance of: scholarly article
title: A nonlinear model of thermoelectricity with two temperatures: Application to quasicrystalline nanowires
zbMATH Open document ID: 1346.80003
DOI: 10.1063/1.4947060
author: A. Sellitto
author: V. A. Cimmelli
author: Patrizia Rogolino
published in: Journal of Mathematical Physics
publication date: 2016-05-09T00:00:00Z
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 80A17
Mathematics Subject Classification ID: 74D10
Mathematics Subject Classification ID: 74F20
Mathematics Subject Classification ID: 52C23
Mathematics Subject Classification ID: 82D15
Mathematics Subject Classification ID: 82D35
Mathematics Subject Classification ID: 82D37
Mathematics Subject Classification ID: 82C05
Mathematics Subject Classification ID: 82D77
zbMATH DE Number: 6578054
zbMATH Keywords: nonlinear thermodynamic model
zbMATH Keywords: quasi-crystals
zbMATH Keywords: phonons
zbMATH Keywords: electrons
zbMATH Keywords: transport
zbMATH Keywords: thermoelectricity
zbMATH Keywords: second law of thermodynamics
zbMATH Keywords: thermomass theory
zbMATH Keywords: efficiency of the thermoelectric generator
zbMATH Keywords: entropy production
zbMATH Keywords: total heat flux
zbMATH Keywords: constitutive equations
zbMATH Keywords: thermodynamic compatibility
zbMATH Keywords: multi-temperature theory of fluid mixtures
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1063/1.4947060
OpenAlex ID: W2342607131
cites work: Understanding Non-equilibrium Thermodynamics
cites work: Q4597625
cites work: Thermoelectrics. Basic principles and new materials developments
cites work: Q3643422
cites work: Mesoscopic theories of heat transport in nanosystems
cites work: Generalized temperature and non-classical heat conduction in rigid bodies
cites work: Heat transport equations with phonons and electrons
cites work: Heat conduction in multi-temperature mixtures of fluids: the role of the average temperature
cites work: Q5793240
cites work: Entropy principle and recent results in non-equilibrium theories
cites work: The thermodynamics of elastic materials with heat conduction and viscosity
cites work: A new perspective on the form of the first and second laws in rational thermodynamics: Korteweg fluids as an example
cites work: Exploitation of the entropy principle: Proof of Liu theorem if the gradients of the governing equations are considered as constraints
cites work: Entropy analyses for hyperbolic heat conduction based on the thermomass model
cites work: Nonlocal behavior in phonon transport
cites work: An amendment to the second law
cites work: Entropy principle, non-regular processes, and generalized exploitation procedures
cites work: On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors
cites work: Different thermodynamic theories and different heat conduction laws
cites work: A thermodynamical approach to Eddington factors
review text: The joint transport of heat and electric current is called a thermoelectric effect. The aim of the paper is to describe the nonlinear thermoelectric coupling in quasi-crystals, materials that are located at the borderline between metals and semiconductors. Guided by the relevance of nonlinear effects at the nanometric length scales, it is assumed that the thermoelectric transport is due to the combined flows of phonons and electrons, whose thermodynamic properties are somewhat different. The analysis pertains to materials with no production of the electric charge per unit volume (that excludes doped semiconductors or systems where positive ions naturally appear). One allows the near equilibrium and equilibrium temperatures of phonon and electron components to the heat flux to be different. Thermodynamic compatibility of the obtained transport equations, that are additionally coupled to constitutive equations for the heat flux, is investigated to yield the non-negative entropy production in the process. Here, appropriate macroscopic transport equations come from the so-called thermo-mass theory. The efficiency of the thermoelectric coupling in quasicrystalline nanowires is estimated. The authors note that accounting for two different temperature scales seems clear from the theoretical viewpoint, but currently there is no experimental evidence confirming the existence of different phonon and electron temperature labels. As such, the paper can be regarded as the first effort towards a mathematical model to describe thermoelectric effects at nanoscale, capable of providing hints toward a detailed experimental scrutiny.
reviewed by: Piotr Garbaczewski
description: scientific article; zbMATH DE number 6578054