Homotopy Perturbation Method for a Stefan Problem with Variable Latent Heat

Abstract

In this paper, homotopy perturbation method is successfully applied to find an approximate solution of one phase Stefan problem with variable latent heat. The results thus obtained are compared graphically with a published analytical solution and are in good agreement.

Keywords

Dates

  • Submission Date2011-06-27
  • Revision Date2012-01-17
  • Acceptance Date2012-01-17

DOI Reference

10.2298/TSCI110627008R

References

  1. Swenson, J. B., Voller, V. R., Paola, C., Parker, G., Marr., J. G., Fluvio-deltaic Sedimentation A generalized Stefan Problem, Euro. J. Appl. Maths., 11(2000), 5 , pp. 433-452
  2. Voller, V. R. , Swenson, J. B. , Paola, C. , An Analytic Solution for a Stefan Problem with Variable Latent Heat, Int. J. Heat Mass Transfer, 47 (2004), 24, pp. 5387-5390
  3. Capart , H., Bellal , M., Young, D.L., Self-similar Evolution of Semi-infinite Alluvial Channels with Moving Boundaries, J. of Sedimentary Research, 77(2007),1, pp.13-22
  4. Voller, V.R., Swenson, J. B., Kim ,W., Paola, C., An Enthalpy Method for Moving Boundary Problems on the Earth's Surface, Int. J. Num. Heat and Fluid Flow, 16 ( 2006), 5, pp. 641-654
  5. Rajeev, Rai, K.N., Das, S., Numerical Solution of a Moving-Boundary Problem with Variable Latent Heat, Int. J. Heat Mass Transfer, 52 (2009),7-8, pp.1913-1917
  6. Crank, J., Free and Moving Boundary Problem, Clarendon Press, Oxford, 1987
  7. Carslaw , H. S., Jaeger, J. C., Conduction of Heat in Solids, Oxford University Press, Oxford, U.K. (1987)
  8. Lin, J. S., Peng, Y. L., Swelling Controlled Release of Drug in Spherical Polymer- Penetrant Systems, Int. J. Heat Mass Transfer, 48 (2005),6, pp.1186-1194
  9. Abdekhodaie, M. J., Cheng, Y.L., Diffusional Release of a Dispersed Solute from a Spherical Polymer Matrix, J. Memb. Sci., 115 (1996), 2, pp.171-178
  10. He, J. H., Some Asymptotic Methods for Strongly Nonlinear Equations, Int. J. Modern Physics B, 20 (2006), 10, pp.1141-1199
  11. He, J. H., Analytical Methods for Thermal Science - an Elementary Introduction, Thermal Science, 15 (2011), Suppl. 1, pp. S1-S3
  12. He, J. H. , Homotopy Perturbation Technique, Comput. Methods Appl. Mech. Engg., 178 (1999), 3-4, pp. 257-262
  13. He, J. H. , A Coupling Method of a Homotopy Technique and a Perturbation Technique for Non-linear Problems, Int. J. Non-linear Mech., 35 (2000),1, pp. 37-43
  14. He, J. H., Homotopy Perturbation Method: A New Nonlinear Analytical Technique, Appl. Math. Comput., 135 (2003),1, pp. 73-79
  15. He, J. H., The Homotopy Perturbation Method for Nonlinear Oscillators with Discontinuities, Appl. Math. Comput., 151 (2004),1, pp. 287-292
  16. He, J. H. , Application of Homotopy Perturbation Method to Nonlinear Wave Equations, Chaos Soliton Fract., 26 (2005), 3, pp. 695-700
  17. He, J. H., Comparison of Homotopy Perturbation Method and Homotopy Analysis Method, Appl. Math. Comput., 156 (2004),2, pp. 527-539
  18. Xicheng Li, Mingyu Xu, Xiaoyun Jiang , Homotopy Perturbation Method to Time- Fractional Diffusion Equation with a Moving Boundary Condition, Applied Mathematics and Computation, 208 (2009), 2, pp. 434 - 439
  19. He, J. H., A Note on the Homotopy Perturbation Method, Thermal Science, 14 (2010), 2, pp. 565-568
  20. Mohyud-Din, S.T., Yildirim, A., Homotopy Perturbation Method for Advection Problems, Nonlinear Science Letters A, 1 (2010), 3, 307-312.
  21. Das, S. , Kumar, R., Gupta, P. K., Analytical Approximate Solution of Space-Time Fractional Diffusion Equation with a Moving Boundary Condition, Zeitschrift für Naturforschung A, 66 a (2011), 1 - 2, pp. 281-288
Volume 18, Issue 2, Pages391 -398