Skip to main content
Log in

Heat pulse experiments revisited

  • Review Article
  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract

This is a review of heat propagation — theory and experiment — in dielectric solids at low temperatures where the phenomenon of second sound occurs. The review does not merely present a list of the various explanations of the observed phenomena. Rather it views them as special cases of a unified theory which is formulated within the framework of extended thermodynamics of phonos. Field equations are derived by averaging over the phonon-Boltzmann equation and initial and boundary value problems are solved. Thus it became possible to achieve a full explanation of the observations of the heat-pulse experiments in which ballistic phonons, second sound and ordinary heat conduction compete.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. Peierls: “Zur kinetischen Theorie der Wärmeleitung in Kristallen”, Ann. Phys. 3 (1929) 1055

    Google Scholar 

  2. C. Cattaneo: “Sulla Conduzione del Calore”, Atti del Seminario Matematico e Fisico della Univ. di Modena 3 (1948) 83

    Google Scholar 

  3. J. C. Ward & J. Wilks: “The Velocity of Second Sound in Liquid Helium near to Absolute Zero”, Phil. Mag. 42 (1951) 314

    Google Scholar 

  4. J. C. Ward & J. Wilks: “Second Sound and the Thermo-Mechanical Effect at very Low Temperatures”, Phil. Mag. 43 (1952) 48

    Google Scholar 

  5. R. J. von Gutfeld & A. H. Nethercot, Jr.: “Heat Pulses in Quartz and Sapphire at Low Temperatures”, Phys. Rev. Lett. 12 (1964) 641

    Google Scholar 

  6. R. A. Guyer & J. A. Krumhansl: “Dispersion Relation for Second Sound in Solids”, Phys. Rev. 133 (1964) A 1411

    Google Scholar 

  7. R. A. Guyer & J. A. Krumhansl: “Solution of the Linearized Phonon Boltzmann Equation”, Phys. Rev. 148 (1964) 766

    Google Scholar 

  8. R. A. Guyer & J. A. Krumhansl: “Thermal Conductivity, Second Sound and Phonon Hydrodynamic Phenomena in Non-metallic Crystals”, Phys. Rev. 148 (1966) 778

    Google Scholar 

  9. C. C. Ackermann; B. Bertman; H. A., Fairbanks & R. A. Guyer: “Second Sound in Solid Helium”, Phys. Rev. Lett. 16 (1966) 789

    Google Scholar 

  10. T. F. McNelly; S. J. Rogers; D. J. Channin; R. J. Rollefson; W. M. Goubau; G. E. Schmidt; J. A. Krumhansl & R. O. Pohl: “Heat Pulses in NaF: Onset of Second Sound”, Phys. Rev. Lett. 24 (1970) 100

    Google Scholar 

  11. H. E. Jackson; Ch. T. Walker & T. F. McNelly: “Second Sound in NaF”, Phys. Rev. Lett. 25, (1970) 26

    Google Scholar 

  12. V. Narayanamurti & D. C. Dynes: “Observation of Second Sound in Bismuth”, Phys. Rev. Lett. 28 (1972) 1461

    Google Scholar 

  13. I. Müller, “Thermodynamics”, Pitman Boston 1985

    Google Scholar 

  14. I-Shih Liu & I. Müller: “Extended Thermodynamics of Classical and Degenerate Gases”, Arch. Rational Mech. Anal. 83 (1983)

  15. J. Callaway: “Model for Lattice Thermal Conductivity at Low Temperatures”, Phys. Rev. 113 (1959) 1046

    Google Scholar 

  16. W. Dreyer: “Maximisation of the Entropy in Non-Equilibrium”, J. Phys. A: Math. Gen. 20 (1987) 6505

    Google Scholar 

  17. T. Ruggeri & A. Strumia: “Main field and convex covariant, density for quasi-linear hyperbolic systems”, Ann. Inst. Henri Poincaré, XXXIV (1981) 65 G. Boillat: “Sur l'existence et la recherche d'équation de conservation supplémenttaires pour les systèmes hyperboliques”, C.R. Acad. Sc. Paris 278 A (1974) 909

    Google Scholar 

  18. A. Einstein: “Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme”, Ann. d. Phys. 22 (1907) 180

    Google Scholar 

  19. P. Debye: “Zur Theorie der spezifischen Wärmen”, Ann. Phys. 39 (4) (1912) 789

    Google Scholar 

  20. R. Peierls: “Quantum Theory of Solids”, Oxford University Press 1955

  21. J. F. Lee; F. W. Sears & D. L. Turcotte: “Statistical Thermodynamics”, Addison-Wesley Reading 1973

    Google Scholar 

  22. Reissland: “Physics of Phonons”, John Wiley & Sons London 1973

    Google Scholar 

  23. W. Larecki & S. Piekarski: “Phonon gas hydrodynamics based on the maximum entropy principle and the extended field theory of a rigid conductor of heat”, Arch. Mech. 43 (2–3) (1992) 163

    Google Scholar 

  24. G. Leibfried: “Gittertheorie der mechanischen und thermischen Eigenschaften der Kristalle”, Handbuch d. Physik, ed. S. Flügge, Vol. 7 Springer Berlin 1955

    Google Scholar 

  25. S. Simon: “On the use of models for phonon collision operators”, J. Phys. C.: Solid St. Phys. 4 (1971) 2785

    Google Scholar 

  26. C. Herring: “Role of Low-Energy Phonons in Thermal Conduction”, Phys. Rev. 95 (1954) 954

    Google Scholar 

  27. H. G. B. Casimir: “Note on the conduction of heat in crystals”, Physica V. 495 1939

  28. P. D. Thacher: “Effect of Boundaries and Isotopes on the Thermal Conductivity of LiF”, Phys. Rev. 156 (1967) 975

    Google Scholar 

  29. P. Carruthers: “Theory of Thermal Conductivity of Solids at Low Temperatures”, Rev. Mod. Phys. 33 (1961) 92

    Google Scholar 

  30. H. E. Jackson & C. T. Walker: “Thermal Conductivity, Second Sound, and Phonon-Phonon Interactions in NaF”, Phys. Rev. B, 3 (1971) 1428

    Google Scholar 

  31. C. C. Ackermann & R. A. Guyer: “Temperature Pulses in Dielectric Solids,” Ann. Phys. (N.Y.) 50 (1968) 128

    Google Scholar 

  32. L. Tisza: “Transport Phenomena in He II”, Nature, 141 (1938)

  33. L. D. Landau: “The Theory of Superfluidity of Helium II”, J. Phys. (U.S.S.R.) 5 (1941)

  34. J. A. Sussmann & A. Thellung: “Thermal Conductivity of Perfect Dielectric Crystals in the Absence of Umklapp Processes”, Proc. Phys. Soc. 81 (1963) 1122.

    Google Scholar 

  35. S. J. Rogers: “Transport of Heat and Approach to Second Sound in Some Isotropically Pure Alkali-Halide-Crystals”, Phys. Rev. B 3 (1971), 1440

    Google Scholar 

  36. H. Beck & R. Beck: “Heat Pulse Propagation in Dielectric Solids” Phys. Rev. B. 8 (1973) 1669

    Google Scholar 

  37. B. D. Coleman & D. C. Newman: “Implications of non-linearity in the theory of second sounds in solids”, Phys. Rev. B 37 (1988) 1492

    Google Scholar 

  38. T. Ruggeri; A. Muracchini & L. Seccia: “Shock Waves and Second Sound in a Rigid Heat Conductor: A Critical Temperature for NaF and Bi”, Phys. Rev. Lett. 64 (1990) 2640

    Google Scholar 

  39. W. Dreyer & S. Seelecke: “Entropy and Causality as Criteria for the Existence of Shock Waves in Low Temperature Heat Conduction,”, Continuum Mech. Thermodyn. 4 (1992) 23

    Google Scholar 

  40. W. Larecki: “Symmetric conservative form of low temperature phonon gas hydrodynamics—II. Equations of heat transport and thermal waves in the case of linear isotropic approximation of phonon frequency spectrum”, Nuovo Cimento 140 (1992) 141

    Google Scholar 

  41. A. M. Anile, S. Pennisi & M. Sammertino: “A Thermodynamical Approach to Eddington Factors”,J. Math. Phys. 32 (1991) 544

    Google Scholar 

  42. G. M. Kremer & I. Müller: “Radiation Thermodynamics”, J. Math. Phys. 33 (1992) 2265

    Google Scholar 

  43. B. D. Coleman, M. Fabrizio & D. R. Owen: “Thermodynamics and Constituve Relations for Second Sound in Crystals” in: “New Perspectives in Thermodynamics”, ed. J. Serres Springer Berlin 1986

    Google Scholar 

  44. O. Weis: “Thermal Phonon Radiation”, Z. f. angew. Physik 26 (1969) 327

    Google Scholar 

  45. B. Taylor; H. J. Maris; C. Elbaum: “Phonon Focusing in Solids”, Phys. Rev. Lett. 23 (1969) 416

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dreyer, W., Struchtrup, H. Heat pulse experiments revisited. Continuum Mech. Thermodyn 5, 3–50 (1993). https://doi.org/10.1007/BF01135371

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01135371

Keywords

Navigation