Hydromagnetic Convection in a Mushy Layer with Variable Permeability – An Analytical Study

Abstract

The problem of controlling the formation of freckles which cause imperfection during the solidification of a binary or multicomponent alloy is a challenging one. The present analytical study considers a hydromagnetic model with variable permeability near eutectic –approximation and large far-field temperature and the dynamics of the mushy layer is studied by using a modified perturbation technique. Our results suggest that although the effect of variable permeability is of stabilizing type, by a proper choice of the magnetic and expansion parameters it is possible to have an optimal control over the formation of chimney convection so that the freckles causing imperfection in the resulting solid could be drastically avoided. The profiles of marginal stability curves, vertical velocity, magnetic field, temperature and local solid-fraction are presented, which clearly predict the behavior of the system in an effective way. The results are in excellent agreement with the available results in the limiting cases.