HOMOTOPY PERTURBATION METHOD FOR A STEFAN PROBLEM WITH VARIABLE LATENT HEAT by RAJEEV

The mathematical model of the movement of the shoreline in a sedimentary ocean basin (A Shoreline Problem) is a Stefan problem with variable latent heat. Swenson et al. [1] utilized an analogy with one-phase melting problem and developed a mathematical model for movement of shoreline in a sedimentary basin in response to changes in sediment line flux, tectonic subsidence of Earth's crust and sea level change. Voller et al. [2] presented an analytical similarity solution for a Stefan problem with variable latent heat which is a limit case of the shoreline model. Later, Capart et al. [3] presented mathematical solutions for several sedimentary problems featuring semi-infinite alluvial channels evolving under diffusional sediment transport. Voller et al. [4] discussed a novel moving boundary problem related to shoreline movement in a sedimentary basin, which was solved by enthalpy method. They have shown how shoreline problem can be solved by using the same numerical tools which were already used for solving classical Stefan's melting problem. In 2009, Rajeev et al. [5] presented a numerical method for a moving boundary problem with variable latent heat and the comparisons were made with the results of Voller et al. [2]. The Stefan problem is a special non-linear problem which is difficult to get the exact solution [6, 7]. Many approximate methods have been used to solve the Stefan problem e. g., the perturbation method [8], combination of variable method [9]. He [10] also presented a survey of some recent developments in asymptotic techniques, which are valid not only for weakly non-linear equations, but also for strongly ones. Recently, He [11] presented some effective analytical methods to solve the problems arising in thermal science. Rajeev: Homotopy Perturbation Method for a Stefan Problem with Variable ... THERMAL SCIENCE: Year 2014, Vol. 18, No. 2, pp. 391-398 391