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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Koizumi M.: Compos. Part B-Eng. 28, 1 (1997)
Koizumi M., Niino M.: MRS Bull. 20, 19 (1995)
Maurer M.J., Thompson H.A.: J. Heat Transfer 95, 284 (1973)
Vernotte P.: Comptes Rendus 246, 3145 (1958)
Cattaneo C.: Mat. Fis. Univ. Modena 3, 83 (1948)
Tzou D.Y.: J. Heat Transfer 117, 8 (1995)
Chen G.: Phys. Rev. Lett. 286, 2297 (2001)
Joshi A.A., Majumdar A.: J. Appl. Phys. 74, 31 (1993)
Mahan G.D., Claro F.: Phys. Rev. B 38, 1963 (1998)
Callaway J.: Phys. Rev. 113, 1046 (1959)
Fang X.Q., Hub C.: Thermochim. Acta 453, 128 (2007)
Glass D.E., Ozisik M.N., Vick B.: Int. J. Heat Mass Transfer 30, 1623 (1987)
Zanchini E., Pulvirenti B.: Heat Mass Transfer 33, 319 (1998)
Ozisik M.N., Vick B.: Int. J. Heat Mass Transfer 27, 1845 (1984)
Al-Nimr M.A., Naji M.: Int. J. Thermophys. 21, 281 (2000)
Tang D.W., Araki N.: Heat Mass Transfer 31, 359 (1996)
Tang D.W., Araki N.: Int. J. Heat Mass Transfer 39, 1585 (1996)
Tang D.W., Araki N.: Mater. Sci. Eng. A 292, 173 (2000)
Jiang F.M., Sousa A.C.M.: J. Thermophys. Heat Transfer 19, 595 (2005)
Tsai C.S., Hung C.: Int. J. Heat Mass Transfer 46, 5137 (2003)
Marciak-Kozlowska J., Mucha Z., Kozlowski M.: Int. J. Thermophys. 16, 1489 (1995)
Noda N.: J. Therm. Stresses 22, 477 (1999)
Eslami M.R., Babaei M.H., Poultangari R.: Int. J. Pres. Ves. Pip. 82, 522 (2005)
Hosseini S.M., Akhlaghi M., Shakeri M.: Heat Mass Transfer 43, 669 (2006)
P.J. Antaki, Key features of analytical solutions for hyperbolic heat conduction. in 30th Thermophysical Conference, San Diego, California (1995)
Jiang F.: Heat Mass Transfer 42, 1083 (2006)
Nowinski J.N.: Theory of Thermoelasticity with Applications. Sijthoff & Noordhoff Int. Pubs. B.V., Alphen aan den Rijn, Netherlands (1978)
Durbin F.: Comput. J. 17, 371 (1974)
Author information
Authors and Affiliations
Corresponding author
Rights 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
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10765-008-0502-1