headerpos: 12198
 
 
 

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
Publisher
Journal Information
» Editorial Board
» Editorial Policy
» Archival Policy
» Article Publication Charges
» Copyright and Licensing Policy
Guidelines for Authors
» For Authors
» Instructions to Authors
» LaTex style files
Guidelines for Reviewers
» For Reviewers
» Review Form
Open Access
List of Issues
» 2019
» 2018
» 2017
» 2016
» 2015
» 2014
» 2013
» 2012
» 2011
» 2010
» 2009
» 2008
Vol. 57, Issue 4
Vol. 57, Issue 3
Vol. 57, Issue 2
Vol. 57, Issue 1
» Back Issues Phys. Math.
» Back Issues Chemistry
» Back issues (full texts)
  in Google. Phys. Math.
» Back issues (full texts)
  in Google. Chemistry
» Back issues (full texts)
  in Google Engineering
» Back issues (full texts)
  in Google Ecology
» Back issues in ETERA Füüsika, Matemaatika jt
Subscription Information
» Prices
Internet Links
Support & Contact
Publisher
» Staff
» Other journals

Extended irreversible thermodynamics of heat transport. A brief introduction; pp. 118–126

(Full article in PDF format) doi: 10.3176/proc.2008.3.01


Authors

David Jou, José Casas-Vázquez, Georgy Lebon

Abstract

Current frontiers of technology require generalized transport equations incorporating memory, non-local effects, and non-linear effects. Extended Irreversible Thermodynamics provides such transport equations in a form compatible with the second law of thermodynamics, and that, for low frequency and short mean-free paths, reduce to the classical transport equations. Here we present the basic concepts of extended irreversible thermodynamics, namely, the fluxes as independent variables, and their evolution equations as generalized transport equations obeying the second law of thermodynamics. We show that these equations cover a rich phenomenology in heat transport, including thermal waves, phonon hydrodynamics, ballistic transport, and saturation in the fluxes for high values of the thermodynamic forces.

Keywords

non-equilibrium thermodynamics, ballistic heat transport, extended irreversible thermodynamics, thermal waves.

References

Alvarez , F. X. and Jou , D. 2007. Memory and the non-local effects in heat transport from diffusive and ballistic regimes. Appl. Phys. Lett. , 90 , 083109 (3 pages).

Anile , A. M. , Allegretto , W. and Ringhofer , C. 2003. Mathematical Problems in Semi-conductor Physics. Lecture Notes in Mathematics , Vol. 1823. Springer , Berlin.

Casas-Vázquez , J. and Jou , D. 2003. Temperature in non-equilibrium states: a review of open problems and current proposals. Rep. Prog. Phys. , 66 , 1937–2023.
doi:10.1088/0034-4885/66/11/R03

Cimmelli , V. A. and Kosinski , W. 1991. Non-equilibrium semi-empirical temperature in materials with thermal relaxation. Arch. Mech. , 43 , 753–767.

Cimmelli , V. A. and Van , P. 2005. The effect of non-locality on the evolution of higher order fluxes in non-equilibrium thermodynamics. J. Math. Phys. , 46 , 112901 (15 pages).

Coleman , B. D. , Fabrizio , M. and Owen , D. R. 1982. The thermodynamics of second sound incrystals. Arch. Rat. Mech. Anal. , 31 , 135–158.

Dreyer , W. and Struchtrup , H. 1993. Heat pulse experiments revisited. Continuum Mech. Thermodyn. , 5 , 3–50.
doi:10.1007/BF01135371

Eu , B. C. 1992. Kinetic Theory and Irreversible Thermo­dynamics. Wiley , New York.

Eu , B. C. 1998. Nonequilibrium Statistical Mechanics: Ensemble Method. Kluwer , Dordrecht.

Guyer , R. A. and Krumhansl , J. A. 1966. Solution of the linearized Boltzmann phonon equation. Phys. Rev. , 148 , 766–778.
doi:10.1103/PhysRev.148.766

Herlach , D. , Galenko , P. and Holland-Moritz , D. 2007. Meta­stable Solids from Undercooled Melts. Pergamon Materials Series , Elsevier , Amsterdam.
doi:10.1016/S1470-1804(07)80023-X

Joseph , D. D. and Preziosi , L. 1989. Heat waves. Rev. Mod. Phys. , 61 , 41–74.
doi:10.1103/RevModPhys.61.41

Joseph , D. D. and Preziosi , L. 1990. Heat waves. Addenda , 62 , 375–392.

Jou , D. , Casas-Vázquez , J. and Lebon , G. 1988. Extended irreversible thermodynamics. Rep. Prog. Phys. , 51 , 1105–1179.
doi:10.1088/0034-4885/51/8/002

Jou , D. , Casas-Vázquez , J. and Lebon , G. 1999. Extended irreversible thermodynamics revisited (1988–1998). Rep. Prog. Phys. , 62 , 1035–1142.
doi:10.1088/0034-4885/62/7/201

Jou , D. , Casas-Vázquez , J. and Lebon , G. 2001a. Extended Irreversible Thermodynamics , 3rd ed. Springer , Berlin.

Jou , D. , Casas-Vázquez , J. and Criado-Sancho , M. 2001b. Thermodynamics of Fluids under Flow. Springer , Berlin.

Jou , D. , Casas-Vázquez , J. , Lebon , G. and Grmela , M. 2005. A phenomenological scaling approach for heat trans­port in nano-systems. Appl. Math. Lett. , 18 , 963–967.
doi:10.1016/j.aml.2004.06.026

Lebon , G. , Jou , D. and Casas-Vázquez , J. 2008. Understanding Non-equilibrium Thermodynamics. Foundations , Applications , Frontiers. Springer.

Levermore , C. D. 1996. Moment closure hierarchy for kinetic theories. J. Stat. Phys. , 83 , 1021–1065.
doi:10.1007/BF02179552

Luzzi , R. , Vasconcellos , A. R. and Ramos , J. G. 2001. Statistical Foundations of Irreversible Thermo­dynamics. Teubner , Leipzig.

Luzzi , R. , Vasconcellos , A. R. and Ramos , J. G. 2002. Pre­dictive Statistical Mechanics: A Non-equilibrium Ensemble Formalism. Kluwer , Dordrecht.

Maugin , G. A. 1999. The Thermo-mechanics of Nonlinear Irreversible Behaviours. World Scientific , Singapore.

Maugin , G. A. and Muschik , W. 1994a. Thermodynamics with internal variables. Part I. General concepts. J. Non-Equilib. Thermodyn. , 19 , 217–250.

Maugin , G. A. and Muschik , W. 1994b. Thermodynamics with internal variables. Part II. Applications. J. Non-Equilib. Thermodyn. , 19 , 250–289.

Mongiovi , M. S. and Jou , D. 2007. Thermodynamical derivation of a hydrodynamical model of inhomogeneous superfluid turbulence. Phys. Rev. B , 75 , 024507.
doi:10.1103/PhysRevB.75.024507

Morro , A. and Ruggeri , T. 1987. Second sound and internal energy in solids. Int. J. Non-Linear Mech. , 22 , 27–36.
doi:10.1016/0020-7462(87)90046-1

Müller , I. and Ruggeri , T. 1997. Rational Extended Thermo­dynamics. Springer , NewYork.

Nicolis , G. and Prigogine , I. 1989. Exploring Complexity. Free­man , New York.

Öttinger , H. C. 2005. Beyond Equilibrium Thermodynamics. Wiley Interscience , New York.

Tzou , D. Y. 1997. Macro-to-Microscale Heat Transfer. The Lagging Behaviour. Taylor and Francis , New York.

Verhas , J. 1983. On the entropy current. J. Non-Equilib. Thermodyn. , 8 , 201–206.

Verhas , J. 1997. Thermodynamics and Rheology. Kluwer , Dordrecht.

Wang , C. C. 1964. The principle of fading memory. Arch. Rat. Mech. Anal. , 18 , 343–366.
doi:10.1007/BF00281325

Zakari , M. 1997. A continued fraction expansion for flux limiters. Physica A , 240 , 676–684.
doi:10.1016/S0378-4371(97)00017-4

 
Back

Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December