Phonon- and electron-temperature waves in a Maxwell-Cattaneo heat-conduction theory

References

• J. Fourier, The Analytical Theory of Heat. Cambridge: Cambridge University Press, 1878.
   Google Scholar
• W. Muschik, “Empirical foundation and axiomatic treatment of non-equilibrium temperature,” Arch. Rational Mech. Anal., vol. 66, no. 4, pp. 379–401, 1977. DOI: 10.1007/BF00248902.
   Web of Science ®Google Scholar
• J. Casas-Vázquez and D. Jou, “Temperature in nonequilibrium states: a review of open problems and current proposals,” Rep. Prog. Phys., vol. 66, no. 11, pp. 1937–2023, 2003. DOI: 10.1088/0034-4885/66/11/R03.
   Web of Science ®Google Scholar
• A. Puglisi, A. Sarracino and A. Vulpiani, “Temperature in and out of equilibrium: a review of concepts, tools and attempts,” Phys. Rep., vol. 709–710, pp. 1–60, 2017. DOI: 10.1016/j.physrep.2017.09.001.
   Web of Science ®Google Scholar
• S. Lepri, R. Livi and A. Politi, “Heat conduction in Chains of nonlinear oscillators,” Phys. Rev. Lett., vol. 78, no. 10, pp. 1896–1899, 1997. DOI: 10.1103/PhysRevLett.78.1896.
   Web of Science ®Google Scholar
• F. M. Jiang, D. Y. Liu and J. H. Zhou, “Non-Fourier heat conduction phenomena in porous material heated by microsecond laser pulse,” Microscale Thermophys. Eng., vol. 6, no. 4, pp. 331–346, 2003. DOI: 10.1080/10893950290098386.
   Web of Science ®Google Scholar
• C. Chang, D. Okawa, H. Garcia, A. Majumdar and A. Zettl, “Breakdown of fourier’s law in nanotube thermal conductors,” Phys. Rev. Lett., vol. 101, pp. 075903, 2008. DOI: 10.1103/PhysRevLett.101.075903.
   PubMed Web of Science ®Google Scholar
• T. T. Lam, “Thermal propagation in solids due to surface laser pulsation and oscillation,” Int. J. Therm. Sci., vol. 49, no. 9, pp. 1639–1648, 2010. DOI: 10.1016/j.ijthermalsci.2010.03.010.
   Web of Science ®Google Scholar
• H.-T. Qi, H. Xu and X.-W. Guo, “The Cattaneo-type time fractional heat conduction equation for laser heating,” Comput. Math. Appl., vol. 66, no. 5, pp. 824–831, 2013. DOI: 10.1016/j.camwa.2012.11.021.
   Web of Science ®Google Scholar
• R. Kovács and P. Ván, “Generalized heat conduction in heat pulse experiments,” Int. J. Heat Mass Transfer, vol. 83, pp. 613–620, 2015. DOI: 10.1016/j.ijheatmasstransfer.2014.12.045.
   Web of Science ®Google Scholar
• G. Fichera, “Is the Fourier theory of heat propagation paradoxical?,” Rend. Circ. Mat. Palermo, vol. 41, no. 1, pp. 5–28, 1992. DOI: 10.1007/BF02844459.
   Google Scholar
• B. Hu, B. Li and H. Zhao, “Heat conduction in one-dimensional nonintegrable systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics, vol. 61, no. 4 Pt A, pp. 3828–3831, 2000. DOI: 10.1103/physreve.61.3828.
   PubMed Web of Science ®Google Scholar
• V. C. Liu, “On the instantaneous propagation paradox of heat conduction,” J. Non-Equilib. Thermodyn., vol. 4, pp. 143–148, 1979.
   Web of Science ®Google Scholar
• D. D. Joseph and L. Preziosi, “Heat waves,” Rev. Mod. Phys., vol. 61, no. 1, pp. 41–73, 1989. DOI: 10.1103/RevModPhys.61.41.
   Web of Science ®Google Scholar
• C. Cattaneo, “Sulla conduzione del calore,” Atti Sem. Mat. Fis. Univ. Modena, vol. 3, pp. 83–101, 1948.
   Google Scholar
• D. Jou, J. Casas-Vázquez and G. Lebon, Extended Irreversible Thermodynamics. Berlin: Springer, fourth revised ed., 2010,
   Google Scholar
• Y. Taitel, “On the parabolic, hyperbolic and discrete formulation of the heat conduction equation,” Int. J. Heat Mass Transfer, vol. 15, no. 2, pp. 369–371, 1972. DOI: 10.1016/0017-9310(72)90085-3.
   Web of Science ®Google Scholar
• A. Barletta and E. Zanchini, “Unsteady heat conduction by internal-energy waves in solids,” Phys. Rev. B, vol. 55, no. 21, pp. 14208–14213, 1997. DOI: 10.1103/PhysRevB.55.14208.
   Web of Science ®Google Scholar
• E. Zanchini, “Hyperbolic heat-conduction theories and nondecreasing entropy,” Phys. Rev. B, vol. 60, no. 2, pp. 991–997, 1999. DOI: 10.1103/PhysRevB.60.991.
   Web of Science ®Google Scholar
• K. R. Sharma, Damped Wave Transport and Relaxation. Amsterdam, Netherlands: Elsevier, 2005.
   Google Scholar
• R. A. Guyer and J. A. Krumhansl, “Solution of the linearized phonon Boltzmann equation,” Phys. Rev., vol. 148, no. 2, pp. 766–778, 1966. DOI: 10.1103/PhysRev.148.766.
   Web of Science ®Google Scholar
• D. Y. Tzou, “A unified field approach for heat conduction from micro-to-macro-scales,” J. Heat Trans. - T. ASME, vol. 117, no. 1, pp. 8–16, 1995. DOI: 10.1115/1.2822329.
   Web of Science ®Google Scholar
• Y. Dong, B.-Y. Cao and Z.-Y. Guo, “General expression for entropy production in transport processes based on the thermomass model,” Phys. Rev. E, vol. 85, no. 6, pp. 061107, 2012. DOI: 10.1103/PhysRevE.85.061107.
   Web of Science ®Google Scholar
• Y. Dong, B.-Y. Cao and Z.-Y. Guo, “Temperature in nonequilibrium states and non-Fourier heat conduction,” Phys. Rev. E, vol. 87, no. 3, pp. 032150, 2013. DOI: 10.1103/PhysRevE.87.032150.
   Web of Science ®Google Scholar
• D. Y. Tzou, “Longitudinal and transverse phonon transport in dielectric crystals,” J. Heat Trans. - T. ASME, vol. 136, pp. 042401, 2014. DOI: 10.1115/1.4026005.
   Web of Science ®Google Scholar
• D. Jou, A. Sellitto and V. A. Cimmelli, “Phonon temperature and electron temperature in thermoelectric coupling,” J. Non-Equilib. Thermodyn., vol. 38, pp. 335–361, 2013. DOI: 10.1515/jnetdy-2013-0020.
   Web of Science ®Google Scholar
• A. Sellitto, V. A. Cimmelli and D. Jou, “Influence of electron and phonon temperature on the efficiency of thermoelectric conversion,” Int. J. Heat Mass Trans., vol. 80, pp. 344–352, 2015. DOI: 10.1016/j.ijheatmasstransfer.2014.09.032.
   Web of Science ®Google Scholar
• S. Berciaud, M. Y. Han, K. F. Mak, L. E. Brus, P. Kim and T. F. Heinz, “Electron and optical phonon temperatures in electrically biased graphene,” Phys. Rev. Lett., vol. 104, no. 22, pp. 227401, 2010. DOI: 10.1103/PhysRevLett.104.227401.
   PubMed Web of Science ®Google Scholar
• M. Schreier, et al., “Magnon, phonon, and electron temperature profiles and the spin Seebeck effect in magnetic insulator/normal metal hybrid structures,” Phys. Rev. B, vol. 88, no. 9, pp. 094410, 2013. DOI: 10.1103/PhysRevB.88.094410.
   Web of Science ®Google Scholar
• L. X. Benedict, S. G. Louie and M. L. Cohen, “Heat capacity of carbon nanotubes,” Solid State Commun., vol. 100, no. 3, pp. 177–180, 1996. DOI: 10.1016/0038-1098(96)00386-9.
   Web of Science ®Google Scholar
• Z. Lin, L. V. Zhigilei and V. Celli, “Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium,” Phys. Rev. B, vol. 77, no. 7, pp. 075133, 2008. DOI: 10.1103/PhysRevB.77.075133.
   Web of Science ®Google Scholar
• P. E. Hopkins, P. M. Norris, L. M. Phinney, S. A. Policastro and R. G. Kelly, “Thermal conductivity in nanoporous gold films during electron-phonon nonequilibrium,” J. Nanomater., vol. 2008, pp. 1–7, 2008. DOI: 10.1155/2008/418050.
   Web of Science ®Google Scholar
• W. Muschik and H. Ehrentraut, “An amendment to the second law,” J. Non-Equilib. Thermodyn., vol. 21, pp. 175–192, 1996.
   Web of Science ®Google Scholar
• V. A. Cimmelli, D. Jou, T. Ruggeri and P. Ván, “Entropy principle and recent results in non-equilibrium theories,” Entropy, vol. 16, no. 3, pp. 1756–1807, 2014. DOI: 10.3390/e16031756.
   Web of Science ®Google Scholar
• A. Sellitto, V. Tibullo and Y. Dong, “Nonlinear heat-transport equation beyond fourier law: application to heat-wave propagation in isotropic thin layers,” Continuum Mech. Thermodyn, vol. 29, no. 2, pp. 411–428, 2017. DOI: 10.1007/s00161-016-0538-6.
   Web of Science ®Google Scholar
• G. Lebon, D. Jou, J. Casas-Vázquez and W. Muschik, “Weakly nonlocal and nonlinear heat transport in rigid solids,” J. Non-Equilib. Thermodyn., vol. 23, pp. 176–191, 1998.
   Web of Science ®Google Scholar
• P. Ván, “Weakly nonlocal irreversible thermodynamics,” Ann. Phys., vol. 12, no. 3, pp. 146–173, 2003. DOI: 10.1002/andp.200310002.
   Web of Science ®Google Scholar
• B. D. Coleman and W. Noll, “The thermodynamics of elastic materials with heat conduction and viscosity,” Arch. Rational Mech. Anal., vol. 13, no. 1, pp. 167–178, 1963. DOI: 10.1007/BF01262690.
   Web of Science ®Google Scholar
• V. A. Cimmelli, A. Sellitto and V. Triani, “A new perspective on the form of the first and second laws in rational thermodynamics: Korteweg fluids as an example,” J. Non-Equilib. Thermodyn., vol. 35, pp. 251–265, 2010. DOI: 10.1515/jnetdy.2010.015.
   Web of Science ®Google Scholar
• V. A. Cimmelli, A. Sellitto and V. Triani, “A new thermodynamic framework for second-grade Korteweg-type viscous fluids,” J. Math. Phys, vol. 50, no. 5, pp. 053101, 2009. DOI: 10.1063/1.3129490.
   Web of Science ®Google Scholar
• V. A. Cimmelli, A. Sellitto and V. Triani, “A generalized Coleman-Noll procedure for the exploitation of the entropy principle,” Proc. R. Soc. A, vol. 466, no. 2115, pp. 911–925, 2010. DOI: 10.1098/rspa.2009.0383.
   Google Scholar
• I.-S. Liu, “Method of Lagrange multipliers for exploitation of entropy principle,” Arch. Rational Mech. Anal., vol. 46, no. 2, pp. 131–138, 1972. DOI: 10.1007/BF00250688.
   Web of Science ®Google Scholar
• W. Muschik, C. Papenfuss and H. Ehrentraut, “A sketch of continuum thermodynamics,” J. Non-Newtonian Fluid Mech., vol. 96, no. 1–2, pp. 255–290, 2001. DOI: 10.1016/S0377-0257(00)00141-5.
   Web of Science ®Google Scholar
• B. Straughan, Heat Waves. Berlin: Springer, 2011.
   Google Scholar
• M. I. Kaganov, I. M. Lifshitz and M. V. Tanatarov, “Relaxation between electrons and crystalline lattices,” Sov. Phys. JETP, vol. 4, pp. 173, 1957.
   Google Scholar
• A. Majumdar and P. Reddy, “Role of electron-phonon coupling in thermal conductance of metal-nonmetal interfaces,” Appl. Phys. Lett., vol. 84, no. 23, pp. 4768–4770, 2004. DOI: 10.1063/1.1758301.
   Web of Science ®Google Scholar
• C. B. Satterthwaite and R. W. Ure, Jr., “Electrical and thermal properties of Bi2Te3,” Phys. Rev., vol. 108, no. 5, pp. 1164–1170, 1957. DOI: 10.1103/PhysRev.108.1164.
   Web of Science ®Google Scholar
• A. Mavrokefalos, A. L. Moore, M. T. Pettes, L. Shi, W. Wang and X. Li, “Thermoelectric and structural characterizations of individual electrodeposited bismuth telluride nanowires,” J. Appl. Phys., vol. 105, no. 10, pp. 104318, 2009. DOI: 10.1063/1.3133145.
   Web of Science ®Google Scholar
• B. Qiu, L. Sun and X. Ruan, “Lattice thermal conductivity reduction in Bi2Te3 quantum wires with smooth and rough surfaces: A molecular dynamics study,” Phys. Rev. B, vol. 83, no. 3, pp. 035312, 2011. DOI: 10.1103/PhysRevB.83.035312.
   Web of Science ®Google Scholar