International Journal of Thermophysics

, Volume 31, Issue 4–5, pp 900–925 | Cite as

Effective Thermal Properties of Multilayered Systems with Interface Thermal Resistance in a Hyperbolic Heat Transfer Model

  • J. Ordóñez-Miranda
  • J. J. Alvarado-Gil


One-dimensional thermal wave transport in multilayered systems with an interface thermal resistance is studied under the framework of the Cattaneo–Vernotte hyperbolic heat conduction model, considering modulated heat excitation under Dirichlet and Neumann boundary conditions. For a single semi-infinite layer, analytical formulas useful in the measurement of its thermal relaxation time as well as additional thermal properties are presented. For a composite-layered system, in the thermally thin regime, with the Dirichlet boundary condition, the well known effective thermal resistance formula is obtained, while for the Neumann problem, only the heat capacity identity is found. In contrast, in the thermally thick case, an analytical expression for both Dirichlet and Neumann conditions is obtained for the effective thermal diffusivity of the whole system in terms of the thermal properties of the individual layers and their interface thermal resistance. The limits of applicability of this equation, in the thermally thick regime, are shown to provide useful and simple results in the characterization of layered systems and that they can be reduced to the results obtained using the Fourier approach. The role of the thermal relaxation time, the interface thermal resistance, and the implications of these results in the possibility of enhancement in heat transport are discussed.


Effective thermal properties Hyperbolic heat conduction Layered system Thermal properties determination Thermal resistance 


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  1. 1.
    Torquato S.: Random Heterogeneous Materials. Springer-Verlag, New York (2001)Google Scholar
  2. 2.
    Carslaw H.S., Jaeger J.C.: Conduction of Heat in Solids. Oxford University Press, London (1959)Google Scholar
  3. 3.
    Leung W.P., Tam A.C.: J. Appl. Phys. 56, 153 (1984)CrossRefADSGoogle Scholar
  4. 4.
    Choi S.U.S., Zhang Z.G., Yu W., Lockwood F.E., Grulke E.A.: Appl. Phys. Lett. 79, 2252 (2001)CrossRefADSGoogle Scholar
  5. 5.
    Eastman J.A., Choi S.U.S., Li S., Yu W., Thompson L.J.: Appl. Phys. Lett. 78, 718 (2001)CrossRefADSGoogle Scholar
  6. 6.
    Kaminski W.: ASME J. Heat Transf. 112, 555 (1990)CrossRefGoogle Scholar
  7. 7.
    Joseph D.D., Preziosi L.: Rev. Mod. Phys. 61, 41 (1989)MATHCrossRefMathSciNetADSGoogle Scholar
  8. 8.
    Tzou D.Y.: Macro- to Microscale Heat Transfer: The Lagging Behavior. Taylor and Francis, New York (1997)Google Scholar
  9. 9.
    Sahoo R.K.: Cryogenics 34, 203 (1994)CrossRefGoogle Scholar
  10. 10.
    Vedavarz A., Kumar S., Moallemi M.K.: ASME J. Heat Transf. 116, 221 (1994)CrossRefGoogle Scholar
  11. 11.
    Cattaneo C.: Atti. Semin. Mat. Fis. Univ. Modena 3, 83 (1948)MathSciNetGoogle Scholar
  12. 12.
    Vernotte P.: C.R. Hebdomadaires des Seances de l’Academie des Sciences 246, 3154 (1958)MathSciNetGoogle Scholar
  13. 13.
    Ozisik M.N., Tzou D.Y.: ASME J. Heat Transf. 116, 526 (1994)CrossRefGoogle Scholar
  14. 14.
    Tzou D.Y.: J. Thermophys. Heat Transf. 9, 686 (1995)CrossRefGoogle Scholar
  15. 15.
    Tzou D.Y.: ASME J. Heat Transf. 117, 8 (1995)CrossRefGoogle Scholar
  16. 16.
    Ho J.-R., Kuo C.-P., Jiaung W.-S.: Int. J. Heat Mass Transf. 46, 55 (2003)MATHCrossRefGoogle Scholar
  17. 17.
    Galovic S., Kotoski D.: J. Appl. Phys. 93, 3063 (2003)CrossRefADSGoogle Scholar
  18. 18.
    Wang L., Zhou X., Wei X.: Heat Conduction: Mathematical Models and Analytical Solutions. Springer-Verlag, Berlin, Heidelberg (2008)Google Scholar
  19. 19.
    Roetzel W., Putra N., Das S.K.: Int. J. Therm. Sci. 42, 541 (2003)CrossRefGoogle Scholar
  20. 20.
    Mitra K., Kumar S., Vedavarz A., Moallemi M.K.: ASME J. Heat Transf. 117, 568 (1995)CrossRefGoogle Scholar
  21. 21.
    Cheng L., Xu M.T., Wang L.Q.: Int. J. Heat Mass Transf. 51, 6018 (2008)MATHCrossRefGoogle Scholar
  22. 22.
    Vadasz J.J., Govender S., Vadasz P.: Int. J. Heat Mass Transf. 48, 2673 (2005)CrossRefGoogle Scholar
  23. 23.
    Al-Nimr M.A., Naji M., Abdallah R.I.: Int. J. Thermophys. 25, 949 (2004)CrossRefGoogle Scholar
  24. 24.
    Dramicanin M.D., Ristovski Z.D., Djokovic V., Galovic S.: Appl. Phys. Lett. 73, 321 (1998)CrossRefADSGoogle Scholar
  25. 25.
    Khadrawi A.F., Al-Nimr M.A., Hammad M.: Int. J. Thermophys. 23, 581 (2002)CrossRefGoogle Scholar
  26. 26.
    Lucio J.L., Alvarado-Gil J.J., Zelaya-Angel O., Vargas H.: Phys. Status Solidi A 150, 695 (1995)CrossRefADSGoogle Scholar
  27. 27.
    Mansanares A.M., Vargas H., Galembeck F., Buijs J., Bicanic D.: J. Appl. Phys. 70, 7046 (1991)CrossRefADSGoogle Scholar
  28. 28.
    Marin E., Pichardo J.L., Cruz-Orea A., Diaz P., Torres-Delgado G., Delgadillo I., Alvarado-Gil J.J., Mendoza-Alvarez J.G., Vargas H.: J. Phys. D: Appl. Phys. 29, 981 (1996)CrossRefADSGoogle Scholar
  29. 29.
    Lor W.B., Chu H.S.: Int. J. Heat Mass Transf. 43, 653 (2000)MATHCrossRefGoogle Scholar
  30. 30.
    J. Ordóñez-Miranda, J.J. Alvarado-Gil, ASME J. Heat Transf. (2010). doi: 10.1115/1.4000748
  31. 31.
    Ramadan K.: Int. J. Therm. Sci. 48, 14 (2009)CrossRefGoogle Scholar
  32. 32.
    Ramadan K., Al-Nimr M.A.: ASME J. Heat Transf. 130, 074501 (2008)CrossRefGoogle Scholar
  33. 33.
    Ramadan K., Al-Nimr M.A.: Heat Transf. Eng. 30, 677 (2009)CrossRefADSGoogle Scholar
  34. 34.
    Ramadan K., Al-Nimr M.A.: Int. J. Therm. Sci. 48, 1718 (2009)CrossRefGoogle Scholar
  35. 35.
    Tominaga T., Ito K.: Jpn. J. Appl. Phys. 27, 2392 (1988)CrossRefADSGoogle Scholar
  36. 36.
    Mansanares A.M., Bento A.C., Vargas H., Leite N.F., Miranda L.C.M.: Phys. Rev. B 42, 4477 (1990)CrossRefADSGoogle Scholar
  37. 37.
    Salazar A., Sánchez-Lavega A., Terrón J.M.: J. Appl. Phys. 84, 3031 (1998)CrossRefADSGoogle Scholar
  38. 38.
    Ordonez-Miranda J., Alvarado-Gil J.J.: Int. J. Therm. Sci. 48, 2053 (2009)CrossRefGoogle Scholar
  39. 39.
    Almond D.P., Patel P.M.: Photothermal Science and Techniques. Chapman and Hall, London (1996)Google Scholar
  40. 40.
    Mcdonald F.A., Westel G.C.: J. Appl. Phys. 49, 2313 (1978)CrossRefADSGoogle Scholar
  41. 41.
    Pichardo J.L., Alvarado-Gil J.J.: J. Appl. Phys. 89, 4070 (2001)CrossRefADSGoogle Scholar
  42. 42.
    Li B.-C., Zhang S.-Y.: J. Phys. D: Appl. Phys. 30, 1447 (1997)CrossRefADSGoogle Scholar
  43. 43.
    Salazar A.: Eur. J. Phys. 24, 351 (2003)MATHCrossRefADSGoogle Scholar
  44. 44.
    Rosencwaig A., Gersho A.: J. Appl. Phys. 47, 64 (1976)CrossRefADSGoogle Scholar
  45. 45.
    Tzou D.Y.: ASME J. Heat Transf. 111, 232 (1989)CrossRefGoogle Scholar
  46. 46.
    Tzou D.Y.: Int. J. Eng. Sci. 29, 1167 (1991)MATHCrossRefGoogle Scholar
  47. 47.
    Tzou D.Y.: ASME J. Appl. Mech. 59, 862 (1992)MATHCrossRefGoogle Scholar
  48. 48.
    Tzou D.Y.: J. Thermophys. Heat Transf. 16, 30 (2002)CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Applied Physics DepartmentCentro de Investigación y de Estudios Avanzados del I.P.N-Unidad MéridaMéridaMéxico

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