Rahul Basu
Sambhram Institute of Technology (SAIT), India
Title: Perturbation analysis of the solidification problem for a sphere in porous media
Biography
Biography: Rahul Basu
Abstract
The moving boundary problem for solidification and melting is of interest to many fields. Carslaw and Jaeger claim only certain solutions known for certain geometries, and it is difficult to find exact solutions for general the case. The moving heat source melting is treated with various transformations together with a decoupling for the heat and mass transfer terms. Some of the earlier works on the interface boundary are by Mullins Sekerka, and Pedroso Domoto. The classic work of Mullins Sekerka dealt with a perturbation analysis of the moving phase interface. Very little published work has appeared on the overall stability of the solid liquid interface in relation to the diffusive field with imposed convective boundary conditions. The classic problem known as the Stefan problem, was formulated over 100 years ago, yet the convective and radiative boundary condition case remains unsolved. In this paper the coupled diffusive heat and mass transfer equations in porous media are solved for convective boundary condition, both by perturbation methods and exact methods. A stability criterion is derived for the moving interface in the convective case, with appropriate linearisations.