Skip to main content
Have a personal or library account? Click to login
Theories and heat pulse experiments of non-Fourier heat conduction Cover

Theories and heat pulse experiments of non-Fourier heat conduction

Communications in Applied and Industrial Mathematics
Volume 7 (2016): Issue 2 (June 2016)
By:   
Open Access
|May 2016
References

References

  1. 1. D. D. Joseph and L. Preziosi, Heat waves,, vol. 61, pp. 41–73, 1989.
    Open DOISearch in Google Scholar
  2. 2. D. D. Joseph and L. Preziosi, Addendum to the paper ”heat waves”,, vol. 62, pp. 375–391, 1990.
    Open DOISearch in Google Scholar
  3. 3. D. S. Chandrasekharaiah, Hyperbolic thermoelasticity: A review of recent literature,, vol. 51, no. 12, pp. 705–729, 1998.
    Open DOISearch in Google Scholar
  4. 4. B. Straughan,. New York: Springer, 2011.
    Open DOISearch in Google Scholar
  5. 5. V. A. Cimmelli, Different thermodynamic theories and different heat conduction laws,, vol. 34, no. 4, pp. 299–332, 2009.
    Open DOISearch in Google Scholar
  6. 6. G. Lebon, Heat conduction at micro and nanoscales: A review through the prism of extended irreversible thermodynamics,, vol. 39, no. 1, pp. 35–59, 2014.
    Open DOISearch in Google Scholar
  7. 7. C. Cattaneo, Sulla conduzione del calore,, vol. 3, pp. 83–101, 1948.
    Search in Google Scholar
  8. 8. D. Jou, J. Casas-Vázquez, and G. Lebon,. Springer, 1996.
    Open DOISearch in Google Scholar
  9. 9. I. Müller and T. Ruggeri,, vol. 37. Springer Science & Business Media, 2013.
    Search in Google Scholar
  10. 10. P. Kostädt and M. Liu, On the causality and stability of the relativistic diffusion equation,, vol. 62, p. 023003, 2000.
    Search in Google Scholar
  11. 11. L. Herrera and D. Pavón, Why hyperbolic theories of dissipation cannot be ignored: comments on a paper by Kostädt and Liu,, vol. 64, p. 088503, 2001.
    Search in Google Scholar
  12. 12. P. Kostädt and M. Liu, Alleged acausality of the diffusion equations: reply,, vol. 64, p. 088504, 2001.
    Search in Google Scholar
  13. 13. G. Fichera, Is the Fourier theory of heat propagation paradoxical?,, vol. XLI, pp. 5–28, 1992.
    Open DOISearch in Google Scholar
  14. 14. V. A. Cimmelli, On the causality requirement for diffusive-hyperbolic systems in non-equilibrium thermodynamics,, vol. 29, no. 2, pp. 125–139, 2004.
    Open DOISearch in Google Scholar
  15. 15. P. Ván and T. S. Bíró, Relativistic hydrodynamics - causality and stability,, vol. 704, no. 2039, pp. 201–212, 2008.
    Search in Google Scholar
  16. 16. V. Peshkov, Second sound in Helium II,, vol.8, p. 381, 1944.
    Search in Google Scholar
  17. 17. L. Tisza, Transport phenomena in helium II,, vol. 141, p. 913, 1938.
    Open DOISearch in Google Scholar
  18. 18. L. D. Landau, Two-fluid model of liquid helium II,, vol. 5, no. 1, pp. 71–90, 1941.
    Search in Google Scholar
  19. 19. H. Feshbach and P. M. Morse,. McGraw-Hill Interamericana, 1953.
    Search in Google Scholar
  20. 20. M. P. Vernotte, La véritableéquation de chaleur,, vol. 247, pp. 2103–5, 1958.
    Search in Google Scholar
  21. 21. R. A. Guyer and J. A. Krumhansl, Dispersion relation for a second sound in solids,, vol. 133, p. A1411, 1964.
    Open DOISearch in Google Scholar
  22. 22. R. A. Guyer and J. A. Krumhansl, Solution of the linearized phonon Boltzmann equation,, vol. 148, no. 2, pp. 766–778, 1966.
    Open DOISearch in Google Scholar
  23. 23. R. A. Guyer and J. A. Krumhansl, Thermal conductivity, second sound and phonon hydrodynamic phenomena in nonmetallic crystals,, vol. 148, no. 2, pp. 778–788, 1966.
    Open DOISearch in Google Scholar
  24. 24. C. C. Ackerman and R. A. Guyer, Temperature pulses in dielectric solids,, vol. 50, no. 1, pp. 128–185, 1968.
    Open DOISearch in Google Scholar
  25. 25. C. C. Ackerman and W. C. Overton, Second sound in solid helium-3,, vol. 22, no. 15, p. 764, 1969.
    Open DOISearch in Google Scholar
  26. 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,, vol. 24, no. 3, p. 100, 1970.
    Open DOISearch in Google Scholar
  27. 27. V. Narayanamurti and R. D. Dynes, Observation of second sound in Bismuth,, vol. 26, pp. 1461–1465, 1972.
    Search in Google Scholar
  28. 28. H. E. Jackson and C. T. Walker, Thermal conductivity, second sound and phonon-phonon interactions in NaF,, vol. 3, no. 4, pp. 1428–1439, 1971.
    Search in Google Scholar
  29. 29. W. Kaminski, Hyperbolic heat conduction equations for materials with a nonhomogeneous inner structure,, vol. 112, pp. 555–560, 1990.
    Open DOISearch in Google Scholar
  30. 30. K. Mitra, S. Kumar, A. Vedavarz, and M. K. Moallemi, Experimental evidence of hyperbolic heat conduction in processed meat,, vol. 117, pp. 568–573, 1995.
    Open DOISearch in Google Scholar
  31. 31. H. Herwig and K. Beckert, Fourier versus non-Fourier heat conduction in materials with a nonhomogeneous inner structure,, vol. 122, no. 2, pp. 363–365, 2000.
    Open DOISearch in Google Scholar
  32. 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,, vol. 36, no. 5, pp. 387–392, 2000.
    Open DOISearch in Google Scholar
  33. 33. W. Roetzel, N. Putra, and S. K. Das, Experiment and analysis for non-Fourier conduction in materials with non-homogeneous inner structure,, vol. 42, no. 6, pp. 541–552, 2003.
    Open DOISearch in Google Scholar
  34. 34. E. P. Scott, M. Tilahun, and B. Vick, The question of thermal waves in heterogeneous and biological materials,, vol. 131, p. 074518, 2009.
    Search in Google Scholar
  35. 35. S. K. Das, N. Putra, P. Thiesen, and W. Roetzel, Temperature dependence of thermal conductivity enhancement for nanofluids,, vol. 125, no. 4, pp. 567–574, 2003.
    Open DOISearch in Google Scholar
  36. 36. P. Kim, L. Shi, A. Majumdar, and P. L. McEuen, Thermal transport measurements of individual multiwalled nanotubes,, vol. 87, no. 21, p. 215502, 2001.
    Search in Google Scholar
  37. 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,, vol. 93, no. 2, pp. 793–818, 2003.
    Open DOISearch in Google Scholar
  38. 38. Z. M. Zhang,. New York: McGrawHill, 2007.
    Search in Google Scholar
  39. 39. V. A. Cimmelli, A. Sellitto, and D. Jou, Nonlocal effects and second sound in a nonequilibrium steady state,, vol. 79, p. 014303, 2009.
    Search in Google Scholar
  40. 40. A. Sellitto, V. A. Cimmelli, and D. Jou, Entropy flux and anomalous axial heat transport at the nanoscale,, vol. 87, no. 7, p. 054302, 2013.
    Search in Google Scholar
  41. 41. M. Luzum and P. Romatschke, Conformal relativistic viscous hydrodynamics: Applications to rhic results at,, vol. 78, no. 3, p. 034915, 2008.
    Search in Google Scholar
  42. 42. I. Müller, Toward relativistic thermodynamics,, vol. 34, no. 4, pp. 259–282, 1969.
    Open DOISearch in Google Scholar
  43. 43. W. Israel, Nonstationary irreversible thermodynamics - causal relativistic theory,, vol. 100, no. 1-2, pp. 310–331, 1976.
    Open DOISearch in Google Scholar
  44. 44. W. Israel and J. M. Stewart, Thermodynamics of nonstationary and transient effect in a relativistic gas,, vol. 58, no. 4, pp. 213–215, 1976.
    Open DOISearch in Google Scholar
  45. 45. P. Ván and T. S. Biró, First order and generic stable relativistic dissipative hydrodynamics,, vol. 709, no. 1-2, pp. 106–110, 2012.
    Open DOISearch in Google Scholar
  46. 46. V. A. Cimmelli, D. Jou, T. Ruggeri, and P. Ván, Entropy principle and recent results in non-equilibrium theories,, vol. 16, pp. 1756–1807, 2014.
    Search in Google Scholar
  47. 47. G. Lebon, D. Jou, and J. Casas-Vázquez,. Berlin: Springer, 2008.
    Open DOISearch in Google Scholar
  48. 48. G. Lebon, D. Jou, J. Casas-Vázquez, and W. Muschik, Weakly nonlocal and nonlinear heat transport in rigid solids,, vol. 23, pp. 176–191, 1998.
    Open DOISearch in Google Scholar
  49. 49. W. Dreyer and H. Struchtrup, Heat pulse experiments revisited,, vol. 5, pp. 3–50, 1993.
    Open DOISearch in Google Scholar
  50. 50. C. Eckart, The thermodynamics of irreversible processes, I. The simple fluid,, vol. 58, pp. 267–269, 1940.
    Open DOISearch in Google Scholar
  51. 51. C. Eckart, The thermodynamics of irreversible processes, II. Fluid mixtures,, vol. 58, pp. 269–275, 1940.
    Open DOISearch in Google Scholar
  52. 52. C. Eckart, The thermodynamics of irreversible processes, III. Relativistic theory of the simple fluid,, vol. 58, pp. 919–924, 1940.
    Open DOISearch in Google Scholar
  53. 53. C. Eckart, The thermodynamics of irreversible processes. IV. The theory of elasticity and anelasticity,, vol. 73, no. 4, pp. 373–382, 1948.
    Open DOISearch in Google Scholar
  54. 54. I. Müller, Zur paradoxon der Wärmeleitungstheorie,, vol. 198, pp. 329–344, 1967.
    Open DOISearch in Google Scholar
  55. 55. S. Machlup and L. Onsager, Fluctuations and irreversible processes. II. Systems with kinetic energy,, vol. 91, no. 6, pp. 1512–1515, 1953.
    Search in Google Scholar
  56. 56. I. Gyarmati, The wave approach of thermodynamics and some problems of non-linear theories,, vol. 2, pp. 233–260, 1977.
    Open DOISearch in Google Scholar
  57. 57. J. Verhás,. Budapest: Műszaki Könyvkiadó, 1985.
    Search in Google Scholar
  58. 58. J. Verhás,. Budapest: Akadémiai Kiadó and Kluwer Academic Publisher, 1997.
    Search in Google Scholar
  59. 60. J. Verhás, On the entropy current,, vol. 8, pp. 201–206, 1983.
    Open DOISearch in Google Scholar
  60. 61. V. A. Cimmelli and P. Ván, The effects of nonlocality on the evolution of higher order fluxes in non-equilibrium thermodynamics,, vol. 46, no. 11, pp. 12901–15, 2005.
    Search in Google Scholar
  61. 62. V. Ciancio, V. A. Cimmelli, and P. Ván, On the evolution of higher order fluxes in non-equilibrium thermodynamics,, vol. 45, pp. 126–136, 2007.
    Open DOISearch in Google Scholar
  62. 63. B. Nyíri, On the entropy current,, vol. 16, pp. 179–186, 1991.
    Open DOISearch in Google Scholar
  63. 64. P. Ván, Weakly nonlocal irreversible thermodynamics – the Guyer-Krumhansl and the Cahn-Hilliard equations,, vol. 290, no. 1-2, pp. 88–92, 2001.
    Open DOISearch in Google Scholar
  64. 65. R. Kovács and P. Ván, Generalized heat conduction in heat pulse experiments,, vol. 83, pp. 613–620, 2015.
    Open DOISearch in Google Scholar
  65. 66. S. Forest and M. Amestoy, Hypertemperature in thermoelastic solids,, vol. 336, pp. 347–353, 2008.
    Open DOISearch in Google Scholar
  66. 67. Z.-Y. Guo and Q.-W. Hou, Thermal wave based on the thermomass model,, vol. 132, no. 7, p. 072403, 2010.
    Search in Google Scholar
  67. 68. V. A. Cimmelli, A. Sellitto, and D. Jou, Nonlinear evolution and stability of the heat flow in nanosystems: Beyond linear phonon hydrodynamics,, vol. 82, no. 184302, 2010.
    Search in Google Scholar
  68. 69. P. Ván and T. Fülöp, Universality in heat conduction theory: weakly nonlocal thermodynamics,, vol. 524, no. 8, pp. 470–478, 2012.
    Open DOISearch in Google Scholar
  69. 70. S. J. Rogers, Transport of heat and approach to second sound in some isotopically pure alkali-halide crystals,, vol. 3, no. 4, p. 1440, 1971.
    Open DOISearch in Google Scholar
  70. 71. A. Yanbao Ma., transient ballistic–diffusive heat conduction model for heat pulse propagation in nonmetallic crystals,, vol. 66, pp. 592–602, 2013.
    Open DOISearch in Google Scholar
  71. 72. A. Yanbao Ma., Hybrid phonon gas model for transient ballistic-diffusive heat transport,, vol. 135, no. 4, p. 044501, 2013.
    Search in Google Scholar
  72. 73. L. I. Mandelstam and M. A. Leontovich, On sound dissipation theory in fluids,, vol. 7, no. 3, pp. 438–448, 1937.
    Search in Google Scholar
  73. 74. L. D. Landau and E. M. Lifshitz,. London: Pergamon Press, 1959.
    Search in Google Scholar
  74. 75. D. Y. Tzou, The generalized lagging response in small-scale and high-rate heating,, vol. 38, no. 17, pp. 3231–3240, 1995.
    Search in Google Scholar
  75. 76. T. J. Bright and Z. M. Zhang, Common misperceptions of the hyperbolic heat equation,, vol. 23, no. 3, pp. 601–607, 2009.
    Open DOISearch in Google Scholar
  76. 77. A. E. Green and P. M. Naghdi, A re-examination of the basic postulates of thermomechanics, in, pp. 171–194, 1991.
    Open DOISearch in Google Scholar
  77. 78. S. Bargmann and P. Steinmann, Finite element approaches to non-classical heat conduction in solids,, vol. 9, no. 2, pp. 133–150, 2005.
    Search in Google Scholar
  78. 79. S. Bargmann and P. Steinmann, Classical results for a non-classical theory: remarks on thermodynamic relations in Green–Naghdi thermohyperelasticity,, vol. 19, pp. 59–66, 2007.
    Open DOISearch in Google Scholar
  79. 80. S. Bargmann and P. Steinmann, Modeling and simulation of first and second sound in solids,, vol. 45, pp. 6067–6073, 2008.
    Search in Google Scholar
  80. 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,, vol. 94, no. 6, pp. 487–498, 2014.
    Open DOISearch in Google Scholar
  81. 82. V. A. Cimmelli and W. Kosinski, Nonequilibrium semi-empirical temperature in materials with thermal relaxation,, vol. 43, no. 6, pp. 753–767, 1991.
    Search in Google Scholar
  82. 83. V. A. Cimmelli, W. Kosiński, and K. Saxton, Modified Fourier law – comparison of two approaches,, vol. 44, no. 4, pp. 409–415, 1992.
    Search in Google Scholar
  83. 84. K. Frischmuth and V. A. Cimmelli, Coupling in thermo-mechanical wave propagation in NaF at low temperature,, vol. 50, pp. 703–714, 1998.
    Search in Google Scholar
  84. 85. B. D. Coleman and D. Newman, Implications of a nonlinearity in the theory of second sound in solids,, vol. 37, no. 4, p. 1492, 1988.
    Open DOISearch in Google Scholar
  85. 86. I.-S. Liu and I. Müller, On the thermodynamics and thermostatics of fluids in electromagnetic fields,, vol. 46, no. 2, pp. 149–176, 1972.
    Open DOISearch in Google Scholar
  86. 87. W. Muschik,. Singapore: World Scientific, 1990.
    Open DOISearch in Google Scholar
  87. 88. S. I. Serdyukov, A new version of extended irreversible thermodynamics and dual-phase-lag model in heat transfer,, vol. 281, pp. 16–20, 2001.
    Open DOISearch in Google Scholar
  88. 89. S. I. Serdyukov, On the definitions of entropy and temperature in the extended thermodynamics of irreversible processes,, vol. 8, pp. 93–100, 2007.
    Open DOISearch in Google Scholar
  89. 90. G. Chen, Ballistic-diffusive heat-conduction equations,, vol. 86, no. 11, p. 22974, 2001.
    Search in Google Scholar
  90. 91. G. Chen, Ballistic-diffusive equations for transient heat conduction from nano to macroscales,, vol. 124, no. 2, pp. 320–328, 2002.
    Open DOISearch in Google Scholar
  91. 92. E. Zanchini, Hyperbolic-heat-conduction theories and nondecreasing entropy,, vol. 60, no. 2, p. 991, 1999.
    Open DOISearch in Google Scholar
  92. 93. K. Zhukovsky, Solution of some types of differential equations: Operational calculus and inverse differential operators,, vol. 2014, no. 4548, p. 65, 2014.
    Search in Google Scholar
  93. 94. D. Y. Tzou, Macro- to microscale heat transfer (The lagging behaviour),, vol. 2, 2014.
    Search in Google Scholar
  94. 95. M. Fabrizio and B. Lazzari, Stability and second law of thermodynamics in dual-phase-lag heat conduction,, vol. 74, pp. 484–489, 2014.
    Open DOISearch in Google Scholar
  95. 96. S. A. Rukolaine, Unphysical effects of the dual-phase-lag model of heat conduction,, vol. 78, pp. 58–63, 2014.
    Open DOISearch in Google Scholar
  96. 97. W. Muschik, Why so many ”schools” of thermodynamics?,, vol. 86, p. C1S0801002, 2008.
    Search in Google Scholar
DOI: https://doi.org/10.1515/caim-2016-0011 | Journal eISSN: 2038-0909
Journal RSS Feed
Language: English
Page range: 150 - 166
Submitted on: Jan 17, 2015
Accepted on: Mar 30, 2015
Published on: May 20, 2016
Published by: Italian Society for Applied and Industrial Mathemathics
In partnership with: Paradigm Publishing Services
Keywords:
ballistic propagation,
second sound,
non-equilibrium thermodynamics,
kinetic theory
Related subjects:
Mathematics,
Numerical and computational mathematics,
Applied mathematics

© 2016 Péter Ván, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 7 (2016): Issue 2 (June 2016)
Previous article
Next article