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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 174604, 20 pages
doi:10.1155/2012/174604
Research Article

Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact Resistances

Hamid El Qarnia,1 Fayssal El Adnani,1 and El Khadir Lakhal2

1Department of Physics, Faculty of Sciences Semlalia, Cadi Ayyad University, Fluid Mechanics and Energetics Laboratory, Affiliate to CNRST, URAC 27, P.O. Box 2390, Marrakesh, Morocco
2Department of Physics, Faculty of Sciences Semlalia, Cadi Ayyad University, Automatic, Environmental and Transfer Process Laboratory, Affiliate to CNRST, URAC 28, P.O. Box 2390, Marrakesh, Morocco

Received 2 February 2012; Accepted 19 July 2012

Academic Editor: Oluwole D. Makinde

Copyright © 2012 Hamid El Qarnia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Clarendon Press, Oxford, UK, 1959. View at Zentralblatt MATH
  2. C. Charach, Y. Zarmi, and A. Zemel, “New perturbation method for planar phase-change processes with time-dependent boundary conditions,” Journal of Applied Physics, vol. 62, no. 11, pp. 4375–4381, 1987. View at Publisher · View at Google Scholar · View at Scopus
  3. N. Y. Li and J. R. Barber, “Sinusoidal perturbation solutions for planar solidification,” International Journal of Heat and Mass Transfer, vol. 32, no. 5, pp. 935–941, 1989. View at Publisher · View at Google Scholar · View at Scopus
  4. A. Aziz and J. Y. Benzies, “Application of perturbation techniques to heat-transfer problems with variable thermal properties,” International Journal of Heat and Mass Transfer, vol. 19, no. 3, pp. 271–276, 1976. View at Publisher · View at Google Scholar · View at Scopus
  5. J. Caldwell and Y. Y. Kwan, “On the perturbation method for the Stefan problem with time-dependent boundary conditions,” International Journal of Heat and Mass Transfer, vol. 46, no. 8, pp. 1497–1501, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. F. Yigit, “Sinusoidal perturbation solution for solidification of pure materials on a planar mold of finite thickness,” International Journal of Thermal Sciences, vol. 47, no. 1, pp. 25–34, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. C. C. Hwang, S. Lin, and L. F. Shen, “Effects of wall conduction and interface thermal resistance on the phase-change problem,” International Journal of Heat and Mass Transfer, vol. 37, no. 13, pp. 1849–1855, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. C. K. Stephan and B. Holzknecht, “Die Asymptotischen Losungen Fur Vorgange Des Erstarrens,” International Journal of Heat and Mass Transfer, vol. 19, no. 6, pp. 597–602, 1976. View at Publisher · View at Google Scholar
  9. S. Kharche and J. A. Howarth, “The inward solidification of a liquid cylinder with periodic axial perturbation of the boundary temperature or heat flux,” International Communications in Heat and Mass Transfer, vol. 27, no. 7, pp. 903–912, 2000. View at Publisher · View at Google Scholar · View at Scopus
  10. F. S. Kharche and J. A. Howarth, “The inward solidification of a liquid cylinder with periodic axial perturbation of the boundary geometry, and constant boundary temperature or heat flux,” International Communications in Heat and Mass Transfer, vol. 27, no. 7, pp. 913–923, 2000. View at Publisher · View at Google Scholar · View at Scopus
  11. R. I. Pedroso and G. A. Domoto, “Exact solution by perturbation method for planar solidification of a saturated liquid with convection at the wall,” International Journal of Heat and Mass Transfer, vol. 16, no. 9, pp. 1816–1819, 1973. View at Publisher · View at Google Scholar · View at Scopus
  12. R. I. Pedroso and G. A. Domoto, “Inward spherical solidification-solution by the method of strained coordinates,” International Journal of Heat and Mass Transfer, vol. 16, no. 5, pp. 1037–1043, 1973. View at Publisher · View at Google Scholar · View at Scopus
  13. H. Ching-Lun and S. Yen-Ping, “Perturbation solutions of planar diffusion-controlled moving-boundary problems,” International Journal of Heat and Mass Transfer, vol. 18, no. 5, pp. 689–695, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. M. M. Yan and P. N. S. Huang, “Perturbation solutions to phase change problem subject to convection and radiation,” Journal of Heat Transfer, vol. 101, no. 1, pp. 96–100, 1979. View at Publisher · View at Google Scholar · View at Scopus
  15. A. Aziz and V. J. Lunardini, “Perturbation techniques in phase change heat transfer,” Applied Mechanics Reviews, vol. 46, pp. 29–67, 1993. View at Publisher · View at Google Scholar
  16. A. Aziz and T. Y. Na, Perturbation Methods in Heat Transfer, Series in Computational Methods in Mechanics and Thermal Sciences, Hemisphere, NewYork, NY, USA, 1st edition, 1984. View at Zentralblatt MATH
  17. A. Farhad Najafi and P. Ahmadi, “Perturbation techniques in freezingheat transfer with constant and sinusoidal surface temperature,” in Proeedings of the 19th International Symposium on Transport Phenomena (ISTP19'08), University of Iceland, Reykjavík, Iceland, August 2008.
  18. A. D. Solomon, “Mathematical modeling of phase change processes for latent heat thermal energy storage,” Report no. ORNL/CSD-39, Union Carbide Corporation, 1979.