One-Phase Stefan-Like Problems with Latent Heat Depending on the Position and Velocity of the Free Boundary and with Neumann or Robin Boundary Conditions at the Fixed Face

A one-phase Stefan-type problem for a semi-infinite material which has as its main feature a variable latent heat that depends on the power of the position and the velocity of the moving boundary is studied. Exact solutions of similarity type are obtained for the cases when Neumann or Robin boundary conditions are imposed at the fixed face. Required relationships between data are presented in order that these problems become equivalent to the problem where a Dirichlet condition at the fixed face is considered. Moreover, in the case where a Robin condition is prescribed, the limit behaviour is studied when the heat transfer coefficient at the fixed face goes to infinity.

On the Adomian decomposition method for solving the Stefan problem

Purpose – The purpose of this paper is concerned with a reliable treatment of the classical Stephan problem. The Adomian decomposition method (ADM) is used to carry out the analysis, Moreover, the authors extend the work to examine the Stefan problem with variable latent heat. The study confirms the accuracy and efficiency of the employed method. Design/methodology/approach – The new technique, as presented in this paper in extending the applicability of the ADM, has been shown to be very efficient for solving the Stefan problem. Findings – The Stefan problem with variable latent heat was examined as well. The ADM was effectively used for analytic treatment of the Stefan problem with and without variable latent heat. Originality/value – The paper presents a new solution algorithm for the Stefan problem.

Homotopy perturbation method for a Stefan problem with variable latent heat

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.

On the Solutions of a Stefan Problem with Variable Latent Heat

This paper is concerned with a reliable treatment of the Stephan problem with variable latent heat. The power series solutions have been presented. The method is examined for computational efficiency and accuracy. Also, an analytical solution based on a similarity variable is presented in the case when the Dirichlet boundary condition at the water-ice interface depends on time.