Theories and heat pulse experiments of non-Fourier heat conduction

1. D. D. Joseph and L. Preziosi, Heat waves, Reviews of Modern Physics, vol. 61, pp. 41–73, 1989.10.1103/RevModPhys.61.41Search in Google Scholar

2. D. D. Joseph and L. Preziosi, Addendum to the paper ”heat waves”, Reviews of Modern Physics, vol. 62, pp. 375–391, 1990.10.1103/RevModPhys.62.375Search in Google Scholar

3. D. S. Chandrasekharaiah, Hyperbolic thermoelasticity: A review of recent literature, Applied Mechanics Reviews, vol. 51, no. 12, pp. 705–729, 1998.10.1115/1.3098984Search in Google Scholar

4. B. Straughan, Heat waves. New York: Springer, 2011.10.1007/978-1-4614-0493-4Search in Google Scholar

5. V. A. Cimmelli, Different thermodynamic theories and different heat conduction laws, Journal of Non-Equilibrium Thermodynamics, vol. 34, no. 4, pp. 299–332, 2009.10.1515/JNETDY.2009.016Search in Google Scholar

6. G. Lebon, Heat conduction at micro and nanoscales: A review through the prism of extended irreversible thermodynamics, Journal of Non-Equilibrium Thermodynamics, vol. 39, no. 1, pp. 35–59, 2014.10.1515/jnetdy-2013-0029Search in Google Scholar

7. C. Cattaneo, Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena, vol. 3, pp. 83–101, 1948.Search in Google Scholar

8. D. Jou, J. Casas-Vázquez, and G. Lebon, Extended irreversible thermodynamics. Springer, 1996.10.1007/978-3-642-97671-1Search in Google Scholar

9. I. Müller and T. Ruggeri, Rational extended thermodynamics, vol. 37. Springer Science & Business Media, 2013.Search in Google Scholar

10. P. Kostädt and M. Liu, On the causality and stability of the relativistic diffusion equation, Physical Reviews D, vol. 62, p. 023003, 2000.Search in Google Scholar

11. L. Herrera and D. Pavón, Why hyperbolic theories of dissipation cannot be ignored: comments on a paper by Kostädt and Liu, Physical Reviews D, vol. 64, p. 088503, 2001.Search in Google Scholar

12. P. Kostädt and M. Liu, Alleged acausality of the diffusion equations: reply, Physical Reviews D, vol. 64, p. 088504, 2001.Search in Google Scholar

13. G. Fichera, Is the Fourier theory of heat propagation paradoxical?, Rediconti del Circolo Matematico di Palermo, vol. XLI, pp. 5–28, 1992.10.1007/BF02844459Search in Google Scholar

14. V. A. Cimmelli, On the causality requirement for diffusive-hyperbolic systems in non-equilibrium thermodynamics, Journal of Non-Equilibrium Thermodynamics, vol. 29, no. 2, pp. 125–139, 2004.10.1515/JNETDY.2004.008Search in Google Scholar

15. P. Ván and T. S. Bíró, Relativistic hydrodynamics - causality and stability, The European Physical Journal - Special Topics, vol. 704, no. 2039, pp. 201–212, 2008.Search in Google Scholar

16. V. Peshkov, Second sound in Helium II, J. Phys. (Moscow), vol.8, p. 381, 1944.Search in Google Scholar

17. L. Tisza, Transport phenomena in helium II, Nature, vol. 141, p. 913, 1938.10.1038/141913a0Search in Google Scholar

18. L. D. Landau, Two-fluid model of liquid helium II, Journal of Physics, vol. 5, no. 1, pp. 71–90, 1941.Search in Google Scholar

19. H. Feshbach and P. M. Morse, Methods of theoretical physics. McGraw-Hill Interamericana, 1953.Search in Google Scholar

20. M. P. Vernotte, La véritableéquation de chaleur, Comptes rendus hebdomadaires des séances de l’Académie des sciences, vol. 247, pp. 2103–5, 1958.Search in Google Scholar

21. R. A. Guyer and J. A. Krumhansl, Dispersion relation for a second sound in solids, Physical Review, vol. 133, p. A1411, 1964.10.1103/PhysRev.133.A1411Search in Google Scholar

22. R. A. Guyer and J. A. Krumhansl, Solution of the linearized phonon Boltzmann equation, Physical Review, vol. 148, no. 2, pp. 766–778, 1966.10.1103/PhysRev.148.766Search in Google Scholar

23. R. A. Guyer and J. A. Krumhansl, Thermal conductivity, second sound and phonon hydrodynamic phenomena in nonmetallic crystals, Physical Review, vol. 148, no. 2, pp. 778–788, 1966.10.1103/PhysRev.148.778Search in Google Scholar

24. C. C. Ackerman and R. A. Guyer, Temperature pulses in dielectric solids, Annals of Physics, vol. 50, no. 1, pp. 128–185, 1968.10.1016/0003-4916(68)90320-5Search in Google Scholar

25. C. C. Ackerman and W. C. Overton, Second sound in solid helium-3, Physical Review Letters, vol. 22, no. 15, p. 764, 1969.10.1103/PhysRevLett.22.764Search in Google Scholar

26. T. F. McNelly, S. J. Rogers, D. J. Channin, R. J. Rollefson, W. M. Goubau, G. E. Schmidt, J. A. Krumhansl, and R. O. Pohl, Heat pulses in NaF: onset of second sound, Physical Review Letters, vol. 24, no. 3, p. 100, 1970.10.1103/PhysRevLett.24.100Search in Google Scholar

27. V. Narayanamurti and R. D. Dynes, Observation of second sound in Bismuth, Physical Review Letters, vol. 26, pp. 1461–1465, 1972.Search in Google Scholar

28. H. E. Jackson and C. T. Walker, Thermal conductivity, second sound and phonon-phonon interactions in NaF, Physical Review B, vol. 3, no. 4, pp. 1428–1439, 1971.Search in Google Scholar

29. W. Kaminski, Hyperbolic heat conduction equations for materials with a nonhomogeneous inner structure, Journal of Heat Transfer, vol. 112, pp. 555–560, 1990.10.1115/1.2910422Search in Google Scholar

30. K. Mitra, S. Kumar, A. Vedavarz, and M. K. Moallemi, Experimental evidence of hyperbolic heat conduction in processed meat, Journal of Heat Transfer, vol. 117, pp. 568–573, 1995.10.1115/1.2822615Search in Google Scholar

31. H. Herwig and K. Beckert, Fourier versus non-Fourier heat conduction in materials with a nonhomogeneous inner structure, Journal of Heat Transfer, vol. 122, no. 2, pp. 363–365, 2000.10.1115/1.521471Search in Google Scholar

32. H. Herwig and K. Beckert, Experimental evidence about the controversy concerning Fourier or non-Fourier heat conduction in materials with a nonhomogeneous inner structure, Heat and Mass Transfer, vol. 36, no. 5, pp. 387–392, 2000.10.1007/s002310000081Search in Google Scholar

33. W. Roetzel, N. Putra, and S. K. Das, Experiment and analysis for non-Fourier conduction in materials with non-homogeneous inner structure, International Journal of Thermal Sciences, vol. 42, no. 6, pp. 541–552, 2003.10.1016/S1290-0729(03)00020-6Search in Google Scholar

34. E. P. Scott, M. Tilahun, and B. Vick, The question of thermal waves in heterogeneous and biological materials, Journal of Biomechanical Engineering, vol. 131, p. 074518, 2009.Search in Google Scholar

35. S. K. Das, N. Putra, P. Thiesen, and W. Roetzel, Temperature dependence of thermal conductivity enhancement for nanofluids, Journal of Heat Transfer, vol. 125, no. 4, pp. 567–574, 2003.10.1115/1.1571080Search in Google Scholar

36. P. Kim, L. Shi, A. Majumdar, and P. L. McEuen, Thermal transport measurements of individual multiwalled nanotubes, Physical Review Letters, vol. 87, no. 21, p. 215502, 2001.Search in Google Scholar

37. D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, Nanoscale thermal transport, Journal of Applied Physics, vol. 93, no. 2, pp. 793–818, 2003.10.1063/1.1524305Search in Google Scholar

38. Z. M. Zhang, Nano/microscale heat transfer. New York: McGrawHill, 2007.Search in Google Scholar

39. V. A. Cimmelli, A. Sellitto, and D. Jou, Nonlocal effects and second sound in a nonequilibrium steady state, Physical Review B, vol. 79, p. 014303, 2009.Search in Google Scholar

40. A. Sellitto, V. A. Cimmelli, and D. Jou, Entropy flux and anomalous axial heat transport at the nanoscale, Physical Review B, vol. 87, no. 7, p. 054302, 2013.Search in Google Scholar

41. M. Luzum and P. Romatschke, Conformal relativistic viscous hydrodynamics: Applications to rhic results at sNN=200 GeV$\sqrt {s_{NN}} = 200\;{\rm{GeV}}$ , Physical Review C, vol. 78, no. 3, p. 034915, 2008.Search in Google Scholar

42. I. Müller, Toward relativistic thermodynamics, Archive for Rational Mechanics and Analysis, vol. 34, no. 4, pp. 259–282, 1969.10.1007/BF00248569Search in Google Scholar

43. W. Israel, Nonstationary irreversible thermodynamics - causal relativistic theory, Annals of Physics, vol. 100, no. 1-2, pp. 310–331, 1976.10.1016/0003-4916(76)90064-6Search in Google Scholar

44. W. Israel and J. M. Stewart, Thermodynamics of nonstationary and transient effect in a relativistic gas, Physics Letters A, vol. 58, no. 4, pp. 213–215, 1976.10.1016/0375-9601(76)90075-XSearch in Google Scholar

45. P. Ván and T. S. Biró, First order and generic stable relativistic dissipative hydrodynamics, Physics Letters B, vol. 709, no. 1-2, pp. 106–110, 2012.10.1016/j.physletb.2012.02.006Search in Google Scholar

46. V. A. Cimmelli, D. Jou, T. Ruggeri, and P. Ván, Entropy principle and recent results in non-equilibrium theories, Entropy, vol. 16, pp. 1756–1807, 2014.Search in Google Scholar

47. G. Lebon, D. Jou, and J. Casas-Vázquez, Understanding non-equilibrium thermodynamics. Berlin: Springer, 2008.10.1007/978-3-540-74252-4Search in Google Scholar

48. G. Lebon, D. Jou, J. Casas-Vázquez, and W. Muschik, Weakly nonlocal and nonlinear heat transport in rigid solids, Journal of Non-Equilibrium Thermodynamics, vol. 23, pp. 176–191, 1998.10.1515/jnet.1998.23.2.176Search in Google Scholar

49. W. Dreyer and H. Struchtrup, Heat pulse experiments revisited, Continuum Mechanics and Thermodynamics, vol. 5, pp. 3–50, 1993.10.1007/BF01135371Search in Google Scholar

50. C. Eckart, The thermodynamics of irreversible processes, I. The simple fluid, Physical Review, vol. 58, pp. 267–269, 1940.10.1103/PhysRev.58.267Search in Google Scholar

51. C. Eckart, The thermodynamics of irreversible processes, II. Fluid mixtures, Physical Review, vol. 58, pp. 269–275, 1940.10.1103/PhysRev.58.269Search in Google Scholar

52. C. Eckart, The thermodynamics of irreversible processes, III. Relativistic theory of the simple fluid, Physical Review, vol. 58, pp. 919–924, 1940.10.1103/PhysRev.58.919Search in Google Scholar

53. C. Eckart, The thermodynamics of irreversible processes. IV. The theory of elasticity and anelasticity, Physical Review, vol. 73, no. 4, pp. 373–382, 1948.10.1103/PhysRev.73.373Search in Google Scholar

54. I. Müller, Zur paradoxon der Wärmeleitungstheorie, Zeitschrift für Physik, vol. 198, pp. 329–344, 1967.10.1007/BF01326412Search in Google Scholar

55. S. Machlup and L. Onsager, Fluctuations and irreversible processes. II. Systems with kinetic energy, Physical Review, vol. 91, no. 6, pp. 1512–1515, 1953.Search in Google Scholar

56. I. Gyarmati, The wave approach of thermodynamics and some problems of non-linear theories, Journal of Non-Equilibrium Thermodynamics, vol. 2, pp. 233–260, 1977.10.1515/jnet.1977.2.4.233Search in Google Scholar

57. J. Verhás, Termodinamikaés reológia. Budapest: Műszaki Könyvkiadó, 1985.Search in Google Scholar

58. J. Verhás, Thermodynamics and Rheology. Budapest: Akadémiai Kiadó and Kluwer Academic Publisher, 1997.Search in Google Scholar

60. J. Verhás, On the entropy current, Journal of Non-Equilibrium Thermodynamics, vol. 8, pp. 201–206, 1983.10.1515/jnet.1983.8.3.201Search in Google Scholar

61. V. A. Cimmelli and P. Ván, The effects of nonlocality on the evolution of higher order fluxes in non-equilibrium thermodynamics, Journal of Mathematical Physics, vol. 46, no. 11, pp. 12901–15, 2005.Search in Google Scholar

62. V. Ciancio, V. A. Cimmelli, and P. Ván, On the evolution of higher order fluxes in non-equilibrium thermodynamics, Mathematical and Computer Modelling, vol. 45, pp. 126–136, 2007.10.1016/j.mcm.2006.04.009Search in Google Scholar

63. B. Nyíri, On the entropy current, Journal of Non-Equilibrium Thermodynamics, vol. 16, pp. 179–186, 1991.10.1515/jnet.1991.16.2.179Search in Google Scholar

64. P. Ván, Weakly nonlocal irreversible thermodynamics – the Guyer-Krumhansl and the Cahn-Hilliard equations, Physics Letters A, vol. 290, no. 1-2, pp. 88–92, 2001.10.1016/S0375-9601(01)00657-0Search in Google Scholar

65. R. Kovács and P. Ván, Generalized heat conduction in heat pulse experiments, International Journal of Heat and Mass Transfer, vol. 83, pp. 613–620, 2015.10.1016/j.ijheatmasstransfer.2014.12.045Search in Google Scholar

66. S. Forest and M. Amestoy, Hypertemperature in thermoelastic solids, Comptes Rendus Mecanique, vol. 336, pp. 347–353, 2008.10.1016/j.crme.2008.01.007Search in Google Scholar

67. Z.-Y. Guo and Q.-W. Hou, Thermal wave based on the thermomass model, Journal of Heat Transfer, vol. 132, no. 7, p. 072403, 2010.Search in Google Scholar

68. V. A. Cimmelli, A. Sellitto, and D. Jou, Nonlinear evolution and stability of the heat flow in nanosystems: Beyond linear phonon hydrodynamics, Physical Review B, vol. 82, no. 184302, 2010.Search in Google Scholar

69. P. Ván and T. Fülöp, Universality in heat conduction theory: weakly nonlocal thermodynamics, Annalen der Physik, vol. 524, no. 8, pp. 470–478, 2012.10.1002/andp.201200042Search in Google Scholar

70. S. J. Rogers, Transport of heat and approach to second sound in some isotopically pure alkali-halide crystals, Physical Review B, vol. 3, no. 4, p. 1440, 1971.10.1103/PhysRevB.3.1440Search in Google Scholar

71. A. Yanbao Ma., transient ballistic–diffusive heat conduction model for heat pulse propagation in nonmetallic crystals, International Journal of Heat and Mass Transfer, vol. 66, pp. 592–602, 2013.10.1016/j.ijheatmasstransfer.2013.06.069Search in Google Scholar

72. A. Yanbao Ma., Hybrid phonon gas model for transient ballistic-diffusive heat transport, Journal of Heat Transfer, vol. 135, no. 4, p. 044501, 2013.Search in Google Scholar

73. L. I. Mandelstam and M. A. Leontovich, On sound dissipation theory in fluids, JETP, vol. 7, no. 3, pp. 438–448, 1937.Search in Google Scholar

74. L. D. Landau and E. M. Lifshitz, Fluid mechanics. London: Pergamon Press, 1959.Search in Google Scholar

75. D. Y. Tzou, The generalized lagging response in small-scale and high-rate heating, J. Heat Mass Transfer, vol. 38, no. 17, pp. 3231–3240, 1995.Search in Google Scholar

76. T. J. Bright and Z. M. Zhang, Common misperceptions of the hyperbolic heat equation, Journal of Thermophysics and Heat Transfer, vol. 23, no. 3, pp. 601–607, 2009.10.2514/1.39301Search in Google Scholar

77. A. E. Green and P. M. Naghdi, A re-examination of the basic postulates of thermomechanics, in Proceedings of the Royal Society: Mathematical and Physical Sciences, pp. 171–194, 1991.10.1098/rspa.1991.0012Search in Google Scholar

78. S. Bargmann and P. Steinmann, Finite element approaches to non-classical heat conduction in solids, Computer Modeling in Engineering Sciences, vol. 9, no. 2, pp. 133–150, 2005.Search in Google Scholar

79. S. Bargmann and P. Steinmann, Classical results for a non-classical theory: remarks on thermodynamic relations in Green–Naghdi thermohyperelasticity, Continuum Mechanics and Thermodynamics, vol. 19, pp. 59–66, 2007.10.1007/s00161-007-0045-xSearch in Google Scholar

80. S. Bargmann and P. Steinmann, Modeling and simulation of first and second sound in solids, International Journal of Solids and Structures, vol. 45, pp. 6067–6073, 2008.Search in Google Scholar

81. S. Bargmann and A. Favata, Continuum mechanical modeling of laser-pulsed heating in polycrystals: A multi-physics problem of coupling diffusion, mechanics, and thermal waves, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, vol. 94, no. 6, pp. 487–498, 2014.10.1002/zamm.201300116Search in Google Scholar

82. V. A. Cimmelli and W. Kosinski, Nonequilibrium semi-empirical temperature in materials with thermal relaxation, Archives of Mechanics, vol. 43, no. 6, pp. 753–767, 1991.Search in Google Scholar

83. V. A. Cimmelli, W. Kosiński, and K. Saxton, Modified Fourier law – comparison of two approaches, Archive of Mechanics, vol. 44, no. 4, pp. 409–415, 1992.Search in Google Scholar

84. K. Frischmuth and V. A. Cimmelli, Coupling in thermo-mechanical wave propagation in NaF at low temperature, Archives of Mechanics, vol. 50, pp. 703–714, 1998.Search in Google Scholar

85. B. D. Coleman and D. Newman, Implications of a nonlinearity in the theory of second sound in solids, Physical Review B, vol. 37, no. 4, p. 1492, 1988.10.1103/PhysRevB.37.14929944666Search in Google Scholar

86. I.-S. Liu and I. Müller, On the thermodynamics and thermostatics of fluids in electromagnetic fields, Archive for Rational Mechanics and Analysis, vol. 46, no. 2, pp. 149–176, 1972.10.1007/BF00250689Search in Google Scholar

87. W. Muschik, Aspects of Non-Equilibrium Thermodynamics. Singapore: World Scientific, 1990.10.1142/0991Search in Google Scholar

88. S. I. Serdyukov, A new version of extended irreversible thermodynamics and dual-phase-lag model in heat transfer, Physics Letters A, vol. 281, pp. 16–20, 2001.10.1016/S0375-9601(01)00074-3Search in Google Scholar

89. S. I. Serdyukov, On the definitions of entropy and temperature in the extended thermodynamics of irreversible processes, C. R. Physique, vol. 8, pp. 93–100, 2007.10.1016/j.crhy.2006.12.010Search in Google Scholar

90. G. Chen, Ballistic-diffusive heat-conduction equations, Physical Review Letters, vol. 86, no. 11, p. 22974, 2001.Search in Google Scholar

91. G. Chen, Ballistic-diffusive equations for transient heat conduction from nano to macroscales, ASME Journal of Heat Transfer, vol. 124, no. 2, pp. 320–328, 2002.10.1115/1.1447938Search in Google Scholar

92. E. Zanchini, Hyperbolic-heat-conduction theories and nondecreasing entropy, Physical Review B, vol. 60, no. 2, p. 991, 1999.10.1103/PhysRevB.60.991Search in Google Scholar

93. K. Zhukovsky, Solution of some types of differential equations: Operational calculus and inverse differential operators, The Scientific World Journal, vol. 2014, no. 4548, p. 65, 2014.Search in Google Scholar

94. D. Y. Tzou, Macro- to microscale heat transfer (The lagging behaviour), Taylor and Francis, vol. 2, 2014.Search in Google Scholar

95. M. Fabrizio and B. Lazzari, Stability and second law of thermodynamics in dual-phase-lag heat conduction, International Journal of Heat and Mass Transfer, vol. 74, pp. 484–489, 2014.10.1016/j.ijheatmasstransfer.2014.02.027Search in Google Scholar

96. S. A. Rukolaine, Unphysical effects of the dual-phase-lag model of heat conduction, International Journal of Heat and Mass Transfer, vol. 78, pp. 58–63, 2014.10.1016/j.ijheatmasstransfer.2014.06.066Search in Google Scholar

97. W. Muschik, Why so many ”schools” of thermodynamics?, Atti dell’Accademia Peloritana dei Pericolanti, Classe di Scienze Fisiche, Matematiche e Naturali, Suppl. I, vol. 86, p. C1S0801002, 2008.Search in Google Scholar