Two Temperature Extension of Phonon Hydrodynamics

References

[1] C. C. Ackerman et al., Second sound in solid helium, Phys. Rev. Lett.16 (1966), no. 18, 789–791.10.1103/PhysRevLett.16.789Search in Google Scholar

[2] T. McNelly et al., Heat pulses in NaF: onset of second sound, Phys. Rev. Lett.24 (1970), no. 3, 100.10.1103/PhysRevLett.24.100Search in Google Scholar

[3] H. E. Jackson, C. T. Walker and T. F. McNelly, Second sound in NaF, Phys. Rev. Lett.25 (1970), no. 1, 26.10.1103/PhysRevLett.25.26Search in Google Scholar

[4] V. Narayanamurti and R. Dynes, Observation of second sound in bismuth, Phys. Rev. Lett.28 (1972), no. 22, 1461.10.1103/PhysRevLett.28.1461Search in Google Scholar

[5] D. W. Pohl and V. Irniger, Observation of second sound in NaF by means of light scattering, Phys. Rev. Lett.36 (1976), no. 9, 480–483.10.1103/PhysRevLett.36.480Search in Google Scholar

[6] S. Huberman et al., Observation of second sound in graphite at temperatures above 100  K, Science364 (2019), no. 6438, 375–379.10.1126/science.aav3548Search in Google Scholar PubMed

[7] D. D. Joseph and L. Preziosi, Heat waves, Rev. Mod. Phys.61 (1989), no. 1, 41–73.10.1103/RevModPhys.61.41Search in Google Scholar

[8] M. Highland et al., Ballistic-phonon heat conduction at the nanoscale as revealed by time-resolved x-ray diffraction and time-domain thermoreflectance, Phys. Rev. B76 (2007), no. 7.10.1103/PhysRevB.76.075337Search in Google Scholar

[9] M. E. Siemens et al., Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams, Nat. Mater.9 (2010), no. 1, 26–30.10.1117/12.871455Search in Google Scholar

[10] A. I. Hochbaum et al., Enhanced thermoelectric performance of rough silicon nanowires, Nature451 (2008), no. 7175, 163.10.1142/9789814317665_0017Search in Google Scholar

[11] Y. C. Hua and B. Y. Cao, Slip boundary conditions in ballistic–diffusive heat transport in nanostructures, Nanoscale Microscale Thermophys. Eng.. 21 (2017), no. 3, 159–176.10.1080/15567265.2017.1344752Search in Google Scholar

[12] Y. C. Hua and B. Y. Cao, Anisotropic heat conduction in two-dimensional periodic silicon nanoporous films, J. Phys. Chem. C121 (2017), no. 9, 5293–5301.10.1021/acs.jpcc.6b11855Search in Google Scholar

[13] N. Mingo and D. Broido, Length dependence of carbon nanotube thermal conductivity and the “problem of long waves”, Nano Lett.5 (2005), no. 7, 1221–1225.10.1021/nl050714dSearch in Google Scholar PubMed

[14] J. Hyun Oh, M. Shin and M. -G. Jang, Phonon thermal conductivity in silicon nanowires: The effects of surface roughness at low temperatures, J. Appl. Phys.111 (2012), no. 4, 044304.10.1063/1.3684973Search in Google Scholar

[15] C. Cattaneo, Sulla conduzione del calore, Atti Semin. Mat. Fis. Univ. Modena3 (1948), 83–101.10.1007/978-3-642-11051-1_5Search in Google Scholar

[16] P. Vernotte, Paradoxes in the continuous theory of the heat equation, C. R. Acad. Sci.246 (1958), no. 3, 154-3.Search in Google Scholar

[17] R. Kovács and P. Ván, Generalized heat conduction in heat pulse experiments, Int. J. Heat Mass Transf.83 (2015), 613–620.10.1016/j.ijheatmasstransfer.2014.12.045Search in Google Scholar

[18] M. Pavelka, V. Klika and M. Grmela, Multiscale Thermo-Dynamics, de Gruyter, Berlin, 2018.10.1515/9783110350951Search in Google Scholar

[19] B. Y. Cao and Z. Y. Guo, Equation of motion of a phonon gas and non-Fourier heat conduction, J. Appl. Phys.102 (2007), no. 5.10.1063/1.2775215Search in Google Scholar

[20] Z. Y. Guo and Q. W. Hou, Thermal wave based on the thermomass model, J. Heat Transf.132 (2010), no. 7, 072403.10.1115/1.4000987Search in Google Scholar

[21] Y. Dong, B. Y. Cao and Z. Y. Guo, Generalized heat conduction laws based on thermomass theory and phonon hydrodynamics, J. Appl. Phys.110 (2011), no. 6.10.1063/1.3634113Search in Google Scholar

[22] Z. Y. Guo, Energy-mass duality of heat and its applications. ES Energy and Environ. (2018).10.30919/esee8c146Search in Google Scholar

[23] 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, Stat. Nonlinear Soft Matter Phys.85 (2012), no. 6 Pt 1, 061107.10.1103/PhysRevE.85.061107Search in Google Scholar

[24] Y. Dong and Z. Y. Guo, Entropy analyses for hyperbolic heat conduction based on the thermomass model, Int. J. Heat Mass Transf.54 (2011), no. 9-10, 1924–1929.10.1016/j.ijheatmasstransfer.2011.01.011Search in Google Scholar

[25] Y. Dong, B. Y. Cao and Z. Y. Guo, Size dependent thermal conductivity of Si nanosystems based on phonon gas dynamics. Physica E, Low-Dimens. Syst. Nanostruct.56 (2014), 256–262.10.1016/j.physe.2013.10.006Search in Google Scholar

[26] Y. Guo and M. Wang, Phonon hydrodynamics and its applications in nanoscale heat transport, Phys. Rep.595 (2015), 1–44.10.1016/j.physrep.2015.07.003Search in Google Scholar

[27] M. Grmela and J. Teichmann, Lagrangian formulation of Maxwell–Cattaneo hydrodynamics, Int. J. Eng. Sci.21 (1983).10.1016/0020-7225(83)90115-5Search in Google Scholar

[28] M. Grmela, L. Hong, D. Jou, G. Lebon and M. Pavelka, Hamiltonian and Godunov structures of the Grad hierarchy, Phys. Rev. E95 (2017), 033121.10.1103/PhysRevE.95.033121Search in Google Scholar PubMed

[29] T. Arima, S. Taniguchi, T. Ruggeri and M. Sugiyama, Contin. Mech. Thermodyn.24 (2011), 271–292.10.1007/s00161-011-0213-xSearch in Google Scholar

[30] T. Ruggeri and M. Sugiyama, Rational Extended Thermodynamics Beyond the Monoatomic Gas, Springer, Heidelberg, 2015.10.1007/978-3-319-13341-6Search in Google Scholar

[31] M. Grmela, GENERIC guide to the multiscale dynamics and thermodynamics, J. Phys. Commun.. 2 (2018), 032001.10.1088/2399-6528/aab642Search in Google Scholar

[32] H. B. Callen, Thermodynamics: An Introduction to the Physical Theories of Equilibrium Thermostatics and Irreversible Thermodynamics, Wiley, 1960.10.1115/1.3644060Search in Google Scholar

[33] D. Jou, J. Casas-Vazquez and G. Lebon, Extended Irreversible Thermodynamics, 4th ed., Springer, 2010.10.1007/978-90-481-3074-0Search in Google Scholar

[34] M. Grmela and G. Lebon, Finite-speed propagation of heat: a nonlocal and nonlinear approach, Physica A248 (1998), 428–441.10.1016/S0378-4371(97)00552-9Search in Google Scholar

[35] M. Grmela, G. Lebon and C. Dubois, Multiscale mechanics and thermodynamic of heat, Phys. Rev. E83 (2011), 061134-1–061134-15.10.1103/PhysRevE.83.061134Search in Google Scholar PubMed

[36] M. Grmela, M. Pavelka, V. Klika, B. Y. Cao and N. Bendian, Entropy and entropy production in multiscale dynamics, J. Non-Equilib. Thermodyn.44 (2019), no. 3, 217–233.10.1515/jnet-2018-0059Search in Google Scholar

[37] R. A. Guyer and J. A. Krumhansl, Solution of the inearized phonon Boltzmann equation, Phys. Rev.148 (1966), no. 2, 766–778.10.1103/PhysRev.148.766Search in Google Scholar

[38] R. A. Guyer and J. A. Krumhansl, Thermal conductivity, second sound, and phonon hydrodynamic phenomena in nonmetallic crystals, Phys. Rev.148 (1966), no. 2, 778–788.10.1103/PhysRev.148.778Search in Google Scholar

[39] V. Klika, M. Pavelka, P. Vágner and M. Grmela, Dynamic maximum entropy reduction, Entropy21 (2019), 715.10.3390/e21070715Search in Google Scholar PubMed PubMed Central

[40] I. Leyva, The relentless pursuit of hypersonic flight, Phys. Today70 (2017), no. 11, 30.10.1063/PT.3.3762Search in Google Scholar

[41] R. Peierls, Zur kinetischen Theorie der Wärmeleitung in Kristallen, Ann. Phys.3 (1929), 1055.10.1002/andp.19293950803Search in Google Scholar

[42] M. Grmela and M. Pavelka, Landau damping in the multiscale Vlasov theory, Kinet. Relat. Models11 (2018), no. 3, 521–545.10.3934/krm.2018023Search in Google Scholar

[43] M. Pavelka, V. Klika and M. Grmela, Thermodynamic explanation of Landau damping by reduction to hydrodynamics, Entropy (2018), 20.10.3390/e20060457Search in Google Scholar PubMed PubMed Central

[44] M. Grmela, V. Klika and M. Pavelka, Gradient and GENERIC time evolution towards reduced dynamics, Phil. Transactions A (2020) (to appear) arXiv:1912.07693v1 [math-ph].10.1098/rsta.2019.0472Search in Google Scholar PubMed PubMed Central

[45] M. Grmela, Extensions of classical hydrodynamics, J. Stat. Phys.132 (2008), 581–602.10.1007/s10955-008-9558-3Search in Google Scholar