THERMAL SCIENCE

International Scientific Journal

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
PAPER SUBMITTED: 2011-06-27
PAPER REVISED: 2012-01-17
PAPER ACCEPTED: 2012-01-17
DOI REFERENCE: https://doi.org/10.2298/TSCI110627008R
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2014, VOLUME 18, ISSUE No. 2, PAGES [391 - 398]
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, 10.1017/s0956792500004198
[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, 10.1016/j.ijheatmasstransfer.2004.07.007
[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, 10.2110/jsr.2007.009
[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, 10.1108/09615530610669157
[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, 10.1016/j.ijheatmasstransfer.2008.08.036
[6] Crank, J., Free and Moving Boundary Problem, Clarendon Press, Oxford, 1987, 10.2307/2008018
[7] Carslaw , H. S., Jaeger, J. C., Conduction of Heat in Solids, Oxford University Press, Oxford, U.K. (1987), 10.1038/scientificamerican1262-92
[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, 10.1016/j.ijheatmasstransfer.2004.08.031
[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, 10.1016/0376-7388(96)00018-x
[10] He, J. H., Some Asymptotic Methods for Strongly Nonlinear Equations, Int. J. Modern Physics B, 20 (2006), 10, pp.1141-1199, 10.1142/s0217979206033796
[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, 10.1016/s0045-7825(99)00018-3
[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, 10.1016/s0020-7462(98)00085-7
[14] He, J. H., Homotopy Perturbation Method: A New Nonlinear Analytical Technique, Appl. Math. Comput., 135 (2003),1, pp. 73-79, 10.1016/s0096-3003(01)00312-5
[15] He, J. H., The Homotopy Perturbation Method for Nonlinear Oscillators with Discontinuities, Appl. Math. Comput., 151 (2004),1, pp. 287-292, 10.1016/s0096-3003(03)00341-2
[16] He, J. H. , Application of Homotopy Perturbation Method to Nonlinear Wave Equations, Chaos Soliton Fract., 26 (2005), 3, pp. 695-700, 10.1016/j.chaos.2005.03.006
[17] He, J. H., Comparison of Homotopy Perturbation Method and Homotopy Analysis Method, Appl. Math. Comput., 156 (2004),2, pp. 527-539, 10.1016/j.amc.2003.08.008
[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, 10.1016/j.amc.2008.12.023
[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, 10.5560/zna.2011.66a0281

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence