Convection in the Presence of Inertial Effects in an Active Mushy Layer

Abstract

The present work, deals with the analytical investigation of convection in a mushy layer that results due to the morphological instability of the interface during the solidification of a binary or a multicomponent alloy. The dynamical behavior of a mushy layer strongly depends on the complex interactions between the convection and the transfer of heat and solute which can remarkably modify the shape, structure and rate of the crystal growth. Accordingly, the distribution and the dissolution of the dendrites in the layer, induced by the convective process eventually lead to the alteration of the permeability or the solid matrix of the mushy layer under consideration. The specific interest with which the study is carried out is to identify a model and the corresponding parametric values which could suppress the formation of chimney convection and annihilate the formation of freckles which cause imperfections in the resulting solid. The asymptotic limits considered here are a near-eutectic approximations, inertial effects, large far-field temperature and variable permeability. The consideration of large Stefan number incorporates a key balance for the existence of compositional convection. The important results of the present study are, (i) An active mushy layer is more stable than a passive mushy layer (ii) The far-field temperature has a destabilising effect on the marginal stability curves as expected and (iii) The influence of the governing parameters is remarkable on the vertical velocity component, temperature and local solid fraction profiles. Finally it is concluded that, through an analytical approach it is possible to determine the accurate solutions which could control or supress the chimney formation during the solidification process which is a burning problem in the areas like metal casting, sea dynamics etc. It is found that the results of the present study are very much closer to the experimental results.