Skip to main content
SpringerLink
Log in

Hyperbolic Heat Conduction in a Functionally Graded Hollow Sphere

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

Abstract

Non-Fourier hyperbolic heat conduction in a heterogeneous sphere is investigated in this article. Except for the thermal relaxation time, which is assumed to be constant, all other material properties vary continuously within the sphere in the radial direction following a power law. Boundary conditions of the sphere are assumed to be spherically symmetric, leading to a one-dimensional heat conduction problem. The problem is solved analytically in the Laplace domain, and the final results in the time domain are obtained using numerical inversion of the Laplace transform. The transient responses of temperature and heat flux are investigated for different non-homogeneity parameters and normalized thermal relaxation constants. The current results for the specific case of a homogeneous sphere are validated by results available in the literature.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Koizumi M.: Compos. Part B-Eng. 28, 1 (1997)

    Article  Google Scholar 

  2. Koizumi M., Niino M.: MRS Bull. 20, 19 (1995)

    Google Scholar 

  3. Maurer M.J., Thompson H.A.: J. Heat Transfer 95, 284 (1973)

    Google Scholar 

  4. Vernotte P.: Comptes Rendus 246, 3145 (1958)

    MathSciNet  Google Scholar 

  5. Cattaneo C.: Mat. Fis. Univ. Modena 3, 83 (1948)

    MathSciNet  Google Scholar 

  6. Tzou D.Y.: J. Heat Transfer 117, 8 (1995)

    Article  Google Scholar 

  7. Chen G.: Phys. Rev. Lett. 286, 2297 (2001)

    Article  ADS  Google Scholar 

  8. Joshi A.A., Majumdar A.: J. Appl. Phys. 74, 31 (1993)

    Article  ADS  Google Scholar 

  9. Mahan G.D., Claro F.: Phys. Rev. B 38, 1963 (1998)

    Article  ADS  Google Scholar 

  10. Callaway J.: Phys. Rev. 113, 1046 (1959)

    Article  MATH  ADS  Google Scholar 

  11. Fang X.Q., Hub C.: Thermochim. Acta 453, 128 (2007)

    Article  Google Scholar 

  12. Glass D.E., Ozisik M.N., Vick B.: Int. J. Heat Mass Transfer 30, 1623 (1987)

    Article  MATH  Google Scholar 

  13. Zanchini E., Pulvirenti B.: Heat Mass Transfer 33, 319 (1998)

    Article  ADS  Google Scholar 

  14. Ozisik M.N., Vick B.: Int. J. Heat Mass Transfer 27, 1845 (1984)

    Article  Google Scholar 

  15. Al-Nimr M.A., Naji M.: Int. J. Thermophys. 21, 281 (2000)

    Article  Google Scholar 

  16. Tang D.W., Araki N.: Heat Mass Transfer 31, 359 (1996)

    Article  ADS  Google Scholar 

  17. Tang D.W., Araki N.: Int. J. Heat Mass Transfer 39, 1585 (1996)

    Article  MATH  Google Scholar 

  18. Tang D.W., Araki N.: Mater. Sci. Eng. A 292, 173 (2000)

    Article  Google Scholar 

  19. Jiang F.M., Sousa A.C.M.: J. Thermophys. Heat Transfer 19, 595 (2005)

    Article  Google Scholar 

  20. Tsai C.S., Hung C.: Int. J. Heat Mass Transfer 46, 5137 (2003)

    Article  MATH  Google Scholar 

  21. Marciak-Kozlowska J., Mucha Z., Kozlowski M.: Int. J. Thermophys. 16, 1489 (1995)

    Article  Google Scholar 

  22. Noda N.: J. Therm. Stresses 22, 477 (1999)

    Article  MathSciNet  Google Scholar 

  23. Eslami M.R., Babaei M.H., Poultangari R.: Int. J. Pres. Ves. Pip. 82, 522 (2005)

    Article  Google Scholar 

  24. Hosseini S.M., Akhlaghi M., Shakeri M.: Heat Mass Transfer 43, 669 (2006)

    Article  ADS  Google Scholar 

  25. P.J. Antaki, Key features of analytical solutions for hyperbolic heat conduction. in 30th Thermophysical Conference, San Diego, California (1995)

  26. Jiang F.: Heat Mass Transfer 42, 1083 (2006)

    Article  ADS  Google Scholar 

  27. Nowinski J.N.: Theory of Thermoelasticity with Applications. Sijthoff & Noordhoff Int. Pubs. B.V., Alphen aan den Rijn, Netherlands (1978)

    MATH  Google Scholar 

  28. Durbin F.: Comput. J. 17, 371 (1974)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, Canada, E3B 5A3

    M. H. Babaei & Z. T. Chen

Authors
  1. M. H. Babaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Z. T. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Z. T. Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Babaei, M.H., Chen, Z.T. Hyperbolic Heat Conduction in a Functionally Graded Hollow Sphere. Int J Thermophys 29, 1457–1469 (2008). https://doi.org/10.1007/s10765-008-0502-1

Download citation

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10765-008-0502-1

Keywords

Search

Navigation