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2016 | OriginalPaper | Chapter

1. Nonequilibrium Thermodynamics and Heat Transport at Nanoscale

Authors : Antonio Sellitto, Vito Antonio Cimmelli, David Jou

Published in: Mesoscopic Theories of Heat Transport in Nanosystems

Publisher: Springer International Publishing

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Abstract

Current frontiers in nanotechnology and materials science [3–5, 9, 10, 12–15, 22, 23, 91] require generalized transport equations beyond the local-equilibrium theory [58, 64, 71, 96]. In particular, heat-transport equations for miniaturized systems whose size is comparable to (or smaller than) the mean-free path of the heat carriers nowadays have become an important topic in science and technology [30– 32, 39, 92]. Analogously, the behavior of systems submitted to high-frequency perturbations which are comparable to the reciprocal of internal relaxation times is studied to optimize the operation of high-frequency devices [55–57, 59, 61, 75, 79]. Equations for heat, mass, charge, and momentum transport have been actively explored in several situations: in miniaturized electronic devices, in nanotubes and nanowires, in theoretical models of energy transport in one-dimensional chains, in rarefied gases, etc. [58, 64]. As a consequence, new thermodynamic formalisms are necessary in this endeavor because thementioned situations clearly exceed the limits of validity of the classical local-equilibrium thermodynamics. This constitutes a formidable challenge for nonequilibrium thermodynamics to better understand its basic concepts, its limits of application, and its frontiers.

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Literature
1.
go back to reference Alvarez, F.X., Jou, D.: Memory and nonlocal effects in heat transports: from diffusive to ballistic regime. Appl. Phys. Lett. 90, 083109 (3 pp.) (2007) Alvarez, F.X., Jou, D.: Memory and nonlocal effects in heat transports: from diffusive to ballistic regime. Appl. Phys. Lett. 90, 083109 (3 pp.) (2007)
2.
go back to reference Alvarez, F.X., Jou, D.: Size and frequency dependence of effective thermal conductivity in nanosystems. J. Appl. Phys. 103, 094321 (8 pp.) (2008) Alvarez, F.X., Jou, D.: Size and frequency dependence of effective thermal conductivity in nanosystems. J. Appl. Phys. 103, 094321 (8 pp.) (2008)
3.
go back to reference Balandin, A.A.: Thermal properties of graphene and nanostructured carbon materials. Nat. Mater. 10, 569–581 (2011)CrossRef Balandin, A.A.: Thermal properties of graphene and nanostructured carbon materials. Nat. Mater. 10, 569–581 (2011)CrossRef
4.
go back to reference Balandin, A., Wang, K.L.: Significant decrease of the lattice thermal conductivity due to phonon confinement in a free-standing semiconductor quantum well. Phys. Rev. B 58, 1544–1549 (1998)CrossRef Balandin, A., Wang, K.L.: Significant decrease of the lattice thermal conductivity due to phonon confinement in a free-standing semiconductor quantum well. Phys. Rev. B 58, 1544–1549 (1998)CrossRef
5.
go back to reference Balandin, A.A., Ghosh, S., Baoand, W., Calizo, I., Teweldebrhan, D., Miao, F., Lau, C.-N.: Superior thermal conductivity of single-layer graphene. Nano Lett. 8, 902–907 (2008)CrossRef Balandin, A.A., Ghosh, S., Baoand, W., Calizo, I., Teweldebrhan, D., Miao, F., Lau, C.-N.: Superior thermal conductivity of single-layer graphene. Nano Lett. 8, 902–907 (2008)CrossRef
6.
go back to reference Banach, Z., Larecki, W.: Nine-moment phonon hydrodynamics based on the modified Grad-type approach: formulation. J. Phys. A: Math. Gen. 37, 9805–9829 (2004)CrossRefMathSciNetMATH Banach, Z., Larecki, W.: Nine-moment phonon hydrodynamics based on the modified Grad-type approach: formulation. J. Phys. A: Math. Gen. 37, 9805–9829 (2004)CrossRefMathSciNetMATH
7.
go back to reference Banach, Z., Larecki, W.: Nine-moment phonon hydrodynamics based on the maximum-entropy closure: one-dimensional flow. J. Phys. A: Math. Gen. 38, 8781–8802 (2005)CrossRefMathSciNetMATH Banach, Z., Larecki, W.: Nine-moment phonon hydrodynamics based on the maximum-entropy closure: one-dimensional flow. J. Phys. A: Math. Gen. 38, 8781–8802 (2005)CrossRefMathSciNetMATH
8.
go back to reference Banach, Z., Larecki, W.: Chapman-Enskog method for a phonon gas with finite heat flux. J. Phys. A: Math. Gen. 41, 375502 (18 pp.) (2008) Banach, Z., Larecki, W.: Chapman-Enskog method for a phonon gas with finite heat flux. J. Phys. A: Math. Gen. 41, 375502 (18 pp.) (2008)
9.
go back to reference Benedetto, G., Boarino, L., Spagnolo, R.: Evaluation of thermal conductivity of porous silicon layers by a photoacoustic method. Appl. Phys. A: Mater. Sci. Process. 64, 155–159 (1997)CrossRef Benedetto, G., Boarino, L., Spagnolo, R.: Evaluation of thermal conductivity of porous silicon layers by a photoacoustic method. Appl. Phys. A: Mater. Sci. Process. 64, 155–159 (1997)CrossRef
10.
go back to reference Benedict, L.X., Louie, S.G., Cohen, M.L.: Heat capacity of carbon nanotubes. Solid State Commun. 100, 177–180 (1996)CrossRef Benedict, L.X., Louie, S.G., Cohen, M.L.: Heat capacity of carbon nanotubes. Solid State Commun. 100, 177–180 (1996)CrossRef
11.
go back to reference Boltzmann, L.: Leçons sur la Théorie des Gaz. Gauthier-Villars, Paris (1902) Boltzmann, L.: Leçons sur la Théorie des Gaz. Gauthier-Villars, Paris (1902)
12.
go back to reference Boukai, A.I., Bunimovich, Y., Tahir-Kheli, J., Yu, J.-K., Goddard-III, W.A., Heath, J.R.: Silicon nanowires as efficient thermoelectric materials. Nature 451, 168–171 (2008)CrossRef Boukai, A.I., Bunimovich, Y., Tahir-Kheli, J., Yu, J.-K., Goddard-III, W.A., Heath, J.R.: Silicon nanowires as efficient thermoelectric materials. Nature 451, 168–171 (2008)CrossRef
13.
go back to reference Cahill, D.C., Ford, W.K., Goodson, K.E., Mahan, G.D., Majumdar, A., Maris, H.J., Merlin, R., Phillpot, S.R.: Nanoscale thermal transport. J. Appl. Phys. 93, 793–818 (2003)CrossRef Cahill, D.C., Ford, W.K., Goodson, K.E., Mahan, G.D., Majumdar, A., Maris, H.J., Merlin, R., Phillpot, S.R.: Nanoscale thermal transport. J. Appl. Phys. 93, 793–818 (2003)CrossRef
14.
go back to reference Cahill, D.G., et al.: Nanoscale thermal transport. II. 2003–2012. Appl. Phys. Rev. 1, 011305 (45 pp.) (2014) Cahill, D.G., et al.: Nanoscale thermal transport. II. 2003–2012. Appl. Phys. Rev. 1, 011305 (45 pp.) (2014)
15.
go back to reference Canham, L.T.: Silicon quantum wire fabrication by electrochemical and chemical dissolution of wafers. Appl. Phys. Lett. 57, 1046–1048 (1990)CrossRef Canham, L.T.: Silicon quantum wire fabrication by electrochemical and chemical dissolution of wafers. Appl. Phys. Lett. 57, 1046–1048 (1990)CrossRef
16.
go back to reference Cao, B.-Y., Guo, Z.-Y.: Equation of motion of a phonon gas and non-Fourier heat conduction. J. Appl. Phys. 102, 053503 (6 pp.) (2007) Cao, B.-Y., Guo, Z.-Y.: Equation of motion of a phonon gas and non-Fourier heat conduction. J. Appl. Phys. 102, 053503 (6 pp.) (2007)
17.
go back to reference Casas-Vázquez, J., Jou, D.: Temperature in nonequilibrium states: a review of open problems and current proposals. Rep. Prog. Phys. 66, 1937–2023 (2003)CrossRef Casas-Vázquez, J., Jou, D.: Temperature in nonequilibrium states: a review of open problems and current proposals. Rep. Prog. Phys. 66, 1937–2023 (2003)CrossRef
18.
19.
go back to reference Cattaneo, C.: Sur une forme de l’équation de la chaleur éliminant le paradoxe d’une propagation instantanée. C. R. Acad. Sc. 247, 431–433 (1958)MathSciNet Cattaneo, C.: Sur une forme de l’équation de la chaleur éliminant le paradoxe d’une propagation instantanée. C. R. Acad. Sc. 247, 431–433 (1958)MathSciNet
20.
go back to reference Chen, G.: Ballistic-diffusion equations for transient heat conduction from nano to macroscales. J. Heat Transf. - T. ASME 124, 320–328 (2001)CrossRef Chen, G.: Ballistic-diffusion equations for transient heat conduction from nano to macroscales. J. Heat Transf. - T. ASME 124, 320–328 (2001)CrossRef
21.
go back to reference Chen, G.: Ballistic-diffusive heat-conduction equations. Phys. Rev. Lett. 86, 2297–2300 (2001)CrossRef Chen, G.: Ballistic-diffusive heat-conduction equations. Phys. Rev. Lett. 86, 2297–2300 (2001)CrossRef
22.
go back to reference Chen, G.: Nanoscale Energy Transport and Conversion - A Parallel Treatment of Electrons, Molecules, Phonons, and Photons. Oxford University Press, Oxford (2005) Chen, G.: Nanoscale Energy Transport and Conversion - A Parallel Treatment of Electrons, Molecules, Phonons, and Photons. Oxford University Press, Oxford (2005)
23.
go back to reference Chung, J.D.,, Kaviany, M.: Effects of phonon pore scattering and pore randomness on effective conductivity of porous silicon. Int. J. Heat Mass Transf. 43, 521–538 (2000)CrossRefMATH Chung, J.D.,, Kaviany, M.: Effects of phonon pore scattering and pore randomness on effective conductivity of porous silicon. Int. J. Heat Mass Transf. 43, 521–538 (2000)CrossRefMATH
24.
go back to reference Cimmelli, V.A.: Mesoscopic approach to inviscid gas dynamics with thermal lag. Ann. Phys. (Berlin) 525, 921–933 (2013) Cimmelli, V.A.: Mesoscopic approach to inviscid gas dynamics with thermal lag. Ann. Phys. (Berlin) 525, 921–933 (2013)
25.
go back to reference Cimmelli, V.A., Frischmuth, K.: Determination of material functions through second sound measurements in a hyperbolic heat conduction theory. Math. Comput. Model. 24, 19–28 (1996)CrossRefMATH Cimmelli, V.A., Frischmuth, K.: Determination of material functions through second sound measurements in a hyperbolic heat conduction theory. Math. Comput. Model. 24, 19–28 (1996)CrossRefMATH
26.
go back to reference Cimmelli, V.A., Frischmuth, K.: Nonlinear effects in thermal wave propagation near zero absolute temperature. Physica B 355, 147–157 (2005)CrossRef Cimmelli, V.A., Frischmuth, K.: Nonlinear effects in thermal wave propagation near zero absolute temperature. Physica B 355, 147–157 (2005)CrossRef
27.
go back to reference Cimmelli, V.A., Frischmuth, K.: Gradient generalization to the extended thermodynamic approach and diffusive-hyperbolic heat conduction. Physica B 400, 257–265 (2007)CrossRef Cimmelli, V.A., Frischmuth, K.: Gradient generalization to the extended thermodynamic approach and diffusive-hyperbolic heat conduction. Physica B 400, 257–265 (2007)CrossRef
28.
go back to reference Cimmelli, V.A., Kosiński, W.: Non-equilibrium semi-empirical temperature in materials with thermal relaxation. Arch. Mech. 47, 753–767 (1991)MATH Cimmelli, V.A., Kosiński, W.: Non-equilibrium semi-empirical temperature in materials with thermal relaxation. Arch. Mech. 47, 753–767 (1991)MATH
29.
go back to reference Cimmelli, V.A., Ván, P.: The effects of nonlocality on the evolution of higher order fluxes in nonequilibrium thermodynamics. J. Math. Phys. 46, 112901 (15 pp.) (2005) Cimmelli, V.A., Ván, P.: The effects of nonlocality on the evolution of higher order fluxes in nonequilibrium thermodynamics. J. Math. Phys. 46, 112901 (15 pp.) (2005)
30.
go back to reference Cimmelli, V.A., Sellitto, A., Jou, D.: Nonlocal effects and second sound in a nonequilibrium steady state. Phys. Rev. B 79, 014303 (13 pp.) (2009) Cimmelli, V.A., Sellitto, A., Jou, D.: Nonlocal effects and second sound in a nonequilibrium steady state. Phys. Rev. B 79, 014303 (13 pp.) (2009)
31.
go back to reference Cimmelli, V.A., Sellitto, A., Jou, D.: Nonequilibrium temperatures, heat waves, and nonlinear heat transport equations. Phys. Rev. B 81, 054301 (9 pp.) (2010) Cimmelli, V.A., Sellitto, A., Jou, D.: Nonequilibrium temperatures, heat waves, and nonlinear heat transport equations. Phys. Rev. B 81, 054301 (9 pp.) (2010)
32.
go back to reference Cimmelli, V.A., Sellitto, A., Jou, D.: Nonlinear evolution and stability of the heat flow in nanosystems: beyond linear phonon hydrodynamics. Phys. Rev. B 82, 184302 (9 pp.) (2010) Cimmelli, V.A., Sellitto, A., Jou, D.: Nonlinear evolution and stability of the heat flow in nanosystems: beyond linear phonon hydrodynamics. Phys. Rev. B 82, 184302 (9 pp.) (2010)
33.
go back to reference Cimmelli, V.A., Jou, D., Ruggeri, T., Ván, P.: Entropy principle and recent results in non-equilibrium theories. Entropy 16, 1756–1807 (2014)CrossRefMathSciNet Cimmelli, V.A., Jou, D., Ruggeri, T., Ván, P.: Entropy principle and recent results in non-equilibrium theories. Entropy 16, 1756–1807 (2014)CrossRefMathSciNet
34.
go back to reference Coleman, B.D., Mizel, V.J.: On the general theory of fading memory. Arch. Ration. Mech. Anal. 29, 18–31 (1968)MathSciNetMATH Coleman, B.D., Mizel, V.J.: On the general theory of fading memory. Arch. Ration. Mech. Anal. 29, 18–31 (1968)MathSciNetMATH
35.
go back to reference Criado-Sancho, J.M., Jou, D., Casas-Vázquez, J.: Nonequilibrium kinetic temperatures in flowing gases. Phys. Lett. A 350, 339–341 (2006)CrossRef Criado-Sancho, J.M., Jou, D., Casas-Vázquez, J.: Nonequilibrium kinetic temperatures in flowing gases. Phys. Lett. A 350, 339–341 (2006)CrossRef
36.
go back to reference de Groot, S.R., Mazur, P.: Nonequilibrium Thermodynamics. North-Holland Publishing Company, Amsterdam (1962) de Groot, S.R., Mazur, P.: Nonequilibrium Thermodynamics. North-Holland Publishing Company, Amsterdam (1962)
37.
go back to reference Dedeurwaerdere, T., Casas-Vázquez, J., Jou, D., Lebon, G.: Foundations and applications of a mesoscopic thermodynamic theory of fast phenomena. Phys. Rev. E 53, 498–506 (1996)CrossRef Dedeurwaerdere, T., Casas-Vázquez, J., Jou, D., Lebon, G.: Foundations and applications of a mesoscopic thermodynamic theory of fast phenomena. Phys. Rev. E 53, 498–506 (1996)CrossRef
38.
go back to reference Demirel, Y., Sandler, I.: Linear-nonequilibrium thermodynamics theory for coupled heat and mass transport. Int. J. Heat Mass Transf. 44, 2439–2451 (2001)CrossRefMATH Demirel, Y., Sandler, I.: Linear-nonequilibrium thermodynamics theory for coupled heat and mass transport. Int. J. Heat Mass Transf. 44, 2439–2451 (2001)CrossRefMATH
39.
go back to reference Dong, Y.: Dynamical Analysis of Non-Fourier Heat Conduction and Its Application in Nanosystems. Springer, Berlin/Heidelberg/New York (2016)CrossRef Dong, Y.: Dynamical Analysis of Non-Fourier Heat Conduction and Its Application in Nanosystems. Springer, Berlin/Heidelberg/New York (2016)CrossRef
40.
go back to reference Dong, Y., Cao, B.-Y., Guo, Z.-Y.: Generalized heat conduction laws based on thermomass theory and phonon hydrodynamics. J. Appl. Phys. 110, 063504 (6 pp.) (2011) Dong, Y., Cao, B.-Y., Guo, Z.-Y.: Generalized heat conduction laws based on thermomass theory and phonon hydrodynamics. J. Appl. Phys. 110, 063504 (6 pp.) (2011)
41.
go back to reference Dong, Y., Cao, B.-Y., Guo, Z.-Y.: General expression for entropy production in transport processes based on the thermomass model. Phys. Rev. E 85, 061107 (8 pp.) (2012) Dong, Y., Cao, B.-Y., Guo, Z.-Y.: General expression for entropy production in transport processes based on the thermomass model. Phys. Rev. E 85, 061107 (8 pp.) (2012)
42.
go back to reference Dong, Y., Cao, B.-Y., Guo, Z.-Y.: Temperature in nonequilibrium states and non-Fourier heat conduction. Phys. Rev. E 87, 032150 (8 pp.) (2013) Dong, Y., Cao, B.-Y., Guo, Z.-Y.: Temperature in nonequilibrium states and non-Fourier heat conduction. Phys. Rev. E 87, 032150 (8 pp.) (2013)
43.
44.
go back to reference Ferrer, M., Jou, D.: Higher-order fluxes and the speed of thermal waves. Int. J. Heat Mass Transf. 34, 3055–3060 (1991)CrossRef Ferrer, M., Jou, D.: Higher-order fluxes and the speed of thermal waves. Int. J. Heat Mass Transf. 34, 3055–3060 (1991)CrossRef
46.
go back to reference Grmela, M., Lebon, G., Dauby, P.C., Bousmina, M.: Ballistic-diffusive heat conduction at nanoscale: GENERIC approach. Phys. Lett. A 339, 237–245 (2005)CrossRefMATH Grmela, M., Lebon, G., Dauby, P.C., Bousmina, M.: Ballistic-diffusive heat conduction at nanoscale: GENERIC approach. Phys. Lett. A 339, 237–245 (2005)CrossRefMATH
47.
go back to reference Guyer, R.A., Krumhansl, J.A.: Solution of the linearized phonon Boltzmann equation. Phys. Rev. 148, 766–778 (1966)CrossRef Guyer, R.A., Krumhansl, J.A.: Solution of the linearized phonon Boltzmann equation. Phys. Rev. 148, 766–778 (1966)CrossRef
48.
go back to reference Guyer, R.A., Krumhansl, J.A.: Thermal conductivity, second sound and phonon hydrodynamic phenomena in nonmetallic crystals. Phys. Rev. 148, 778–788 (1966)CrossRef Guyer, R.A., Krumhansl, J.A.: Thermal conductivity, second sound and phonon hydrodynamic phenomena in nonmetallic crystals. Phys. Rev. 148, 778–788 (1966)CrossRef
49.
go back to reference Gyarmati, I.: On the wave approach of thermodynamics and some problems of non-linear theories. J. Non-Equilib. Thermodyn. 2, 236–260 (1977)CrossRef Gyarmati, I.: On the wave approach of thermodynamics and some problems of non-linear theories. J. Non-Equilib. Thermodyn. 2, 236–260 (1977)CrossRef
50.
go back to reference Győry, E., Márkus, F.: Size dependent thermal conductivity in nano-systems. Thin Solid Films 565, 89–93 (2014)CrossRef Győry, E., Márkus, F.: Size dependent thermal conductivity in nano-systems. Thin Solid Films 565, 89–93 (2014)CrossRef
51.
go back to reference Jackson, H.E., Walker, C.T.: Thermal conductivity, second sound, and phonon-phonon interactions in NaF. Phys. Rev. Lett. 3, 1428–1439 (1971) Jackson, H.E., Walker, C.T.: Thermal conductivity, second sound, and phonon-phonon interactions in NaF. Phys. Rev. Lett. 3, 1428–1439 (1971)
52.
go back to reference Jou, D., Criado-Sancho, M.: Thermodynamic stability and temperature overshooting in dual-phase-lag heat transfer. Phys. Lett. A 48, 172–178 (1998)CrossRef Jou, D., Criado-Sancho, M.: Thermodynamic stability and temperature overshooting in dual-phase-lag heat transfer. Phys. Lett. A 48, 172–178 (1998)CrossRef
53.
go back to reference Jou, D., Restuccia, L.: Mesoscopic transport equations and contemporary thermodynamics: an introduction. Contemp. Phys. 52, 465–474 (2011)CrossRef Jou, D., Restuccia, L.: Mesoscopic transport equations and contemporary thermodynamics: an introduction. Contemp. Phys. 52, 465–474 (2011)CrossRef
54.
go back to reference Jou, D., Casas-Vázquez, J., Lebon, G.: Extended irreversible thermodynamics revisited (1988–1998). Rep. Prog. Phys. 62, 1035–1142 (1999)CrossRef Jou, D., Casas-Vázquez, J., Lebon, G.: Extended irreversible thermodynamics revisited (1988–1998). Rep. Prog. Phys. 62, 1035–1142 (1999)CrossRef
55.
go back to reference Jou, D., Casas-Vázquez, J., Lebon, G., Grmela, M.: A phenomenological scaling approach for heat transport in nano-systems. Appl. Math. Lett. 18, 963–967 (2005)CrossRefMATH Jou, D., Casas-Vázquez, J., Lebon, G., Grmela, M.: A phenomenological scaling approach for heat transport in nano-systems. Appl. Math. Lett. 18, 963–967 (2005)CrossRefMATH
56.
go back to reference Jou, D., Casas-Vázquez, J., Lebon, G.: Extended irreversible thermodynamics of heat transport. A brief introduction. Proc. Est. Acad. Sci. 57, 118–126 (2008)CrossRefMATH Jou, D., Casas-Vázquez, J., Lebon, G.: Extended irreversible thermodynamics of heat transport. A brief introduction. Proc. Est. Acad. Sci. 57, 118–126 (2008)CrossRefMATH
57.
go back to reference Jou, D., Cimmelli, V.A., Sellitto, A.: Nonequilibrium temperatures and second-sound propagation along nanowires and thin layers. Phys. Lett. A 373, 4386–4392 (2009)CrossRefMATH Jou, D., Cimmelli, V.A., Sellitto, A.: Nonequilibrium temperatures and second-sound propagation along nanowires and thin layers. Phys. Lett. A 373, 4386–4392 (2009)CrossRefMATH
58.
go back to reference Jou, D., Casas-Vázquez, J., Lebon, G.: Extended Irreversible Thermodynamics, 4th revised edn. Springer, Berlin (2010)CrossRefMATH Jou, D., Casas-Vázquez, J., Lebon, G.: Extended Irreversible Thermodynamics, 4th revised edn. Springer, Berlin (2010)CrossRefMATH
59.
go back to reference Jou, D., Criado-Sancho, M., Casas-Vázquez, J.: Heat fluctuations and phonon hydrodynamics in nanowires. J. Appl. Phys. 107, 084302 (4 pp.) (2010) Jou, D., Criado-Sancho, M., Casas-Vázquez, J.: Heat fluctuations and phonon hydrodynamics in nanowires. J. Appl. Phys. 107, 084302 (4 pp.) (2010)
60.
go back to reference Jou, D., Cimmelli, V.A., Sellitto, A.: Dynamical temperature and renormalized flux variable in extended thermodynamics of rigid heat conductors. J. Non-Equilib. Thermodyn. 36, 373–392 (2011)CrossRefMATH Jou, D., Cimmelli, V.A., Sellitto, A.: Dynamical temperature and renormalized flux variable in extended thermodynamics of rigid heat conductors. J. Non-Equilib. Thermodyn. 36, 373–392 (2011)CrossRefMATH
61.
go back to reference Jou, D., Sellitto, A., Alvarez, F.X.: Heat waves and phonon-wall collisions in nanowires. Proc. R. Soc. A 467, 2520–2533 (2011)CrossRefMathSciNet Jou, D., Sellitto, A., Alvarez, F.X.: Heat waves and phonon-wall collisions in nanowires. Proc. R. Soc. A 467, 2520–2533 (2011)CrossRefMathSciNet
62.
go back to reference Kovács, R., Ván, P.: Generalized heat conduction in heat pulse experiments. Int. J. Heat Mass Transf. 83, 613–620 (2015)CrossRef Kovács, R., Ván, P.: Generalized heat conduction in heat pulse experiments. Int. J. Heat Mass Transf. 83, 613–620 (2015)CrossRef
63.
go back to reference Lebon, G., Ruggieri, M., Valenti, A.: Extended thermodynamics revisited: Renormalized flux variables and second sound in rigid solids. J. Phys.: Condens. Matter 20, 025223 (11 pp.) (2008) Lebon, G., Ruggieri, M., Valenti, A.: Extended thermodynamics revisited: Renormalized flux variables and second sound in rigid solids. J. Phys.: Condens. Matter 20, 025223 (11 pp.) (2008)
64.
go back to reference Lebon, G., Jou, D., Casas-Vázquez, J.: Understanding Nonequilibrium Thermodynamics. Springer, Berlin (2008)CrossRefMATH Lebon, G., Jou, D., Casas-Vázquez, J.: Understanding Nonequilibrium Thermodynamics. Springer, Berlin (2008)CrossRefMATH
65.
go back to reference Lebon, G., Machrafi, H., Grmela, M., Dubois, C.: An extended thermodynamic model of transient heat conduction at sub-continuum scales. Proc. R. Soc. A 467, 3241–3256 (2011)CrossRefMathSciNetMATH Lebon, G., Machrafi, H., Grmela, M., Dubois, C.: An extended thermodynamic model of transient heat conduction at sub-continuum scales. Proc. R. Soc. A 467, 3241–3256 (2011)CrossRefMathSciNetMATH
66.
go back to reference Lee, S., Broido, D., Esfarjani, K., Chen, G.: Hydrodynamic phonon transport in suspended graphene. Nat. Commun. 6, 6290 (9 pp.) (2015) Lee, S., Broido, D., Esfarjani, K., Chen, G.: Hydrodynamic phonon transport in suspended graphene. Nat. Commun. 6, 6290 (9 pp.) (2015)
67.
go back to reference Lundstrom, M.: Fundamentals of Carrier Transport. Cambridge University Press, Cambridge (2000)CrossRef Lundstrom, M.: Fundamentals of Carrier Transport. Cambridge University Press, Cambridge (2000)CrossRef
68.
go back to reference Luzzi, R., Vasconcellos, A.R., Casas-Vázquez, J., Jou, D.: Characterization and measurement of a nonequilibrium temperature-like variable in irreversible thermodynamics. Physica A 234, 699–714 (1997)CrossRef Luzzi, R., Vasconcellos, A.R., Casas-Vázquez, J., Jou, D.: Characterization and measurement of a nonequilibrium temperature-like variable in irreversible thermodynamics. Physica A 234, 699–714 (1997)CrossRef
69.
go back to reference Machrafi, H., Lebon, G.: Size and porosity effects on thermal conductivity of nanoporous material with an extension to nanoporous particles embedded in ahost matrix. Phys. Lett. A 379, 968–973 (2015)CrossRef Machrafi, H., Lebon, G.: Size and porosity effects on thermal conductivity of nanoporous material with an extension to nanoporous particles embedded in ahost matrix. Phys. Lett. A 379, 968–973 (2015)CrossRef
70.
go back to reference Márkus, F., Gambár, K.: Heat propagation dynamics in thin silicon layers. Int. J. Heat Mass Transf. 56, 495–500 (2013)CrossRef Márkus, F., Gambár, K.: Heat propagation dynamics in thin silicon layers. Int. J. Heat Mass Transf. 56, 495–500 (2013)CrossRef
71.
go back to reference Minnich, A.J.: Advances in the measurement and computation of thermal phonon transport properties. J. Phys.: Condens. Matter 27, 053202 (21 pp.) (2015) Minnich, A.J.: Advances in the measurement and computation of thermal phonon transport properties. J. Phys.: Condens. Matter 27, 053202 (21 pp.) (2015)
72.
go back to reference Müller, I., Ruggeri, T.: Rational Extended Thermodynamics, 2nd edn. Springer, New York (1998)CrossRefMATH Müller, I., Ruggeri, T.: Rational Extended Thermodynamics, 2nd edn. Springer, New York (1998)CrossRefMATH
73.
go back to reference Narayanamurti, V., Dynes, R.D.: Observation of second sound in bismuth. Phys. Rev. Lett. 28, 1461–1465 (1972)CrossRef Narayanamurti, V., Dynes, R.D.: Observation of second sound in bismuth. Phys. Rev. Lett. 28, 1461–1465 (1972)CrossRef
74.
go back to reference Öttinger, H.C.: Beyond Equilibrium Thermodynamics. Wiley, New York (2005)CrossRef Öttinger, H.C.: Beyond Equilibrium Thermodynamics. Wiley, New York (2005)CrossRef
75.
go back to reference Pattamatta, A., Madnia, C.K.: Modeling heat transfer in Bi2Te3-Sb2Te3 nanostructures. Int. J. Heat Mass Transf. 52, 860–869 (2009)CrossRefMATH Pattamatta, A., Madnia, C.K.: Modeling heat transfer in Bi2Te3-Sb2Te3 nanostructures. Int. J. Heat Mass Transf. 52, 860–869 (2009)CrossRefMATH
76.
go back to reference Ruggeri, T., Sugiyama, M.: Rational Extended Thermodynamics Beyond the Monatomic Gas. Springer International Publishing, Switzerland (2015)CrossRefMATH Ruggeri, T., Sugiyama, M.: Rational Extended Thermodynamics Beyond the Monatomic Gas. Springer International Publishing, Switzerland (2015)CrossRefMATH
77.
go back to reference Sellitto, A., Cimmelli, V.A.: A continuum approach to thermomass theory. J. Heat Transf. - T. ASME 134, 112402 (6 pp.) (2012) Sellitto, A., Cimmelli, V.A.: A continuum approach to thermomass theory. J. Heat Transf. - T. ASME 134, 112402 (6 pp.) (2012)
78.
go back to reference Sellitto, A., Cimmelli, V.A.: Flux limiters in radial heat transport in silicon nanolayers. J. Heat Transf. - T. ASME 136, 071301 (6 pp.) (2014) Sellitto, A., Cimmelli, V.A.: Flux limiters in radial heat transport in silicon nanolayers. J. Heat Transf. - T. ASME 136, 071301 (6 pp.) (2014)
79.
go back to reference Sellitto, A., Alvarez, F.X., Jou, D.: Phonon-wall interactions and frequency-dependent thermal conductivity in nanowires. J. Appl. Phys. 109, 064317 (8 pp.) (2011) Sellitto, A., Alvarez, F.X., Jou, D.: Phonon-wall interactions and frequency-dependent thermal conductivity in nanowires. J. Appl. Phys. 109, 064317 (8 pp.) (2011)
80.
go back to reference Serdyukov, S.I.: A new version of extended irreversible thermodynamics and dual-phase-lag model in heat transfer. Phys. Lett. A 281, 16–20 (2001)CrossRefMATH Serdyukov, S.I.: A new version of extended irreversible thermodynamics and dual-phase-lag model in heat transfer. Phys. Lett. A 281, 16–20 (2001)CrossRefMATH
81.
go back to reference Serdyukov, S.I.: Higher order heat and mass transfer equations and their justification in extended irreversible thermodynamics. Theor. Found. Chem. Eng. 47, 89–103 (2013)CrossRef Serdyukov, S.I.: Higher order heat and mass transfer equations and their justification in extended irreversible thermodynamics. Theor. Found. Chem. Eng. 47, 89–103 (2013)CrossRef
82.
go back to reference Serdyukov, S.I., Voskresenskii, N.M., Bel’nov, V.K., Karpov, I.I.: Extended irreversible thermodynamics and generalization of the dual-phase-lag model in heat transfer. J. Non-Equilib. Thermodyn. 28, 207–219 (2003)CrossRef Serdyukov, S.I., Voskresenskii, N.M., Bel’nov, V.K., Karpov, I.I.: Extended irreversible thermodynamics and generalization of the dual-phase-lag model in heat transfer. J. Non-Equilib. Thermodyn. 28, 207–219 (2003)CrossRef
83.
go back to reference Sieniutycz, S.: Conservation Laws in Variational Thermo-Hydrodynamics. Kluwer Academic Publishers, Dordrecht (1994)CrossRefMATH Sieniutycz, S.: Conservation Laws in Variational Thermo-Hydrodynamics. Kluwer Academic Publishers, Dordrecht (1994)CrossRefMATH
84.
go back to reference Smith, G.F.: On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Int. J. Eng. Sci. 9, 899–916 (1971)CrossRefMATHMathSciNet Smith, G.F.: On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Int. J. Eng. Sci. 9, 899–916 (1971)CrossRefMATHMathSciNet
86.
go back to reference Struchtrup, H.: Macroscopic Transport Equations for Rarefied Gas Flows: Approximation Methods in Kinetic Theory - Interaction of Mechanics and Mathematics. Springer, New York (2005)MATH Struchtrup, H.: Macroscopic Transport Equations for Rarefied Gas Flows: Approximation Methods in Kinetic Theory - Interaction of Mechanics and Mathematics. Springer, New York (2005)MATH
87.
go back to reference Tzou, D.Y.: Nonlocal behavior in phonon transport. Int. J. Heat Mass Transf. 54, 475–481 (2011)CrossRefMATH Tzou, D.Y.: Nonlocal behavior in phonon transport. Int. J. Heat Mass Transf. 54, 475–481 (2011)CrossRefMATH
88.
go back to reference Tzou, D.Y.: Macro- to Microscale Heat Transfer: The Lagging Behaviour, 2nd edn. Wiley, Chichester (2014) Tzou, D.Y.: Macro- to Microscale Heat Transfer: The Lagging Behaviour, 2nd edn. Wiley, Chichester (2014)
89.
go back to reference Tzou, D.Y., Guo, Z.-Y.: Nonlocal behavior in thermal lagging. Int. J. Therm. Sci. 49, 1133–1137 (2010)CrossRef Tzou, D.Y., Guo, Z.-Y.: Nonlocal behavior in thermal lagging. Int. J. Therm. Sci. 49, 1133–1137 (2010)CrossRef
90.
go back to reference Vasconcellos, A.R., Luzzi, R., Jou, D., Casas-Vázquez, J.: Thermal waves in an extended hydrodynamic approach. Physica A 212, 369–381 (1994)CrossRef Vasconcellos, A.R., Luzzi, R., Jou, D., Casas-Vázquez, J.: Thermal waves in an extended hydrodynamic approach. Physica A 212, 369–381 (1994)CrossRef
91.
go back to reference Vázquez, F., del Río, J.A.: Thermodynamic characterization of the diffusive transport to wave propagation transition in heat conducting thin films. J. Appl. Phys. 112, 123707 (8 pp.) (2012) Vázquez, F., del Río, J.A.: Thermodynamic characterization of the diffusive transport to wave propagation transition in heat conducting thin films. J. Appl. Phys. 112, 123707 (8 pp.) (2012)
92.
go back to reference Vázquez, F., Márkus, F., Gambár, K.: Quantized heat transport in small systems: A phenomenological approach. Phys. Rev. E 79, 031113 (7 pp.) (2009) Vázquez, F., Márkus, F., Gambár, K.: Quantized heat transport in small systems: A phenomenological approach. Phys. Rev. E 79, 031113 (7 pp.) (2009)
93.
go back to reference Verhás, J.: On the entropy current. J. Non-Equilib. Thermodyn. 8, 201–206 (1983)CrossRef Verhás, J.: On the entropy current. J. Non-Equilib. Thermodyn. 8, 201–206 (1983)CrossRef
94.
go back to reference Vernotte, P.: Les paradoxes de la théorie continue de l’équation de la chaleur. C. R. Acad. Sc. 246, 3154–3155 (1958)MathSciNet Vernotte, P.: Les paradoxes de la théorie continue de l’équation de la chaleur. C. R. Acad. Sc. 246, 3154–3155 (1958)MathSciNet
95.
go back to reference Xu, M.T., Wang, L.Q.: Dual-phase lagging heat conduction based on Boltzmann transport equation. Int. J. Heat Mass Transf. 48, 5616–5624 (2005)CrossRefMATH Xu, M.T., Wang, L.Q.: Dual-phase lagging heat conduction based on Boltzmann transport equation. Int. J. Heat Mass Transf. 48, 5616–5624 (2005)CrossRefMATH
96.
go back to reference Yang, N., Xu, X., Zhang, G., Li, B.: Thermal transport in nanostructures. AIP Adv. 2, 041410 (24 pp.) (2012) Yang, N., Xu, X., Zhang, G., Li, B.: Thermal transport in nanostructures. AIP Adv. 2, 041410 (24 pp.) (2012)
97.
go back to reference Zhang, Z.M.: Nano/Microscale Heat Transfer. McGraw-Hill, New York (2007) Zhang, Z.M.: Nano/Microscale Heat Transfer. McGraw-Hill, New York (2007)
Metadata
Title
Nonequilibrium Thermodynamics and Heat Transport at Nanoscale
Authors
Antonio Sellitto
Vito Antonio Cimmelli
David Jou
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-27206-1_1

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