Analytical and computational studies of magneto-convection in solidifying mushy layer.

摘要

Natural convection in solidifying binary media is of great interest due to its applications in material processing and crystal growth industries. Convective flows between the layers of melt during alloy solidification is known to produce mechanical imperfections such as freckle's. Hence it is important to investigate the criterion for freckling and discover the means of suppressing it.;A mushy layer, which has both solid and fluid components and is formed between underlying solid and overlying liquid, is known to produce chimneys, which are narrow, vertical vents, devoid of solid. We consider the problem of magneto-convection in a horizontal mushy layer during the solidification of binary alloys. Both cases of permeable and impermeable mush-liquid interface were investigated. We carry out the numerical investigation for particular range of parameter values which cover those of available experimental studies. Cases of constant and variable permeability coupled with mush-liquid interface boundary conditions were included in the present study. The governing coupled non-linear partial differential equations are non-dimensionalized and solved to get steady basic state solution. Using multiple shooting technique we determine the steady state solutions in a range of critical Rayleigh number. We analyse the effect of, Chandrasekhar number Q, far-field temperature, permeability of the medium, mush-liquid interface condition, on the problem. The results of the analysis and computation indicate that increasing Q has the stabilizing effect on the solidification, because the critical Rayleigh number increases with increasing the strength of magnetic field. But permeable mush-liquid interface condition destabilizes the convection by reducing the critical Rayleigh number. It was also found that for moderate or small values of Robert's number, the critical Rayleigh number is mostly insensitive. The most important finding of the present investigation is that the convection in a mushy layer decreases upon increasing the strength of externally imposed magnetic field and increasing far-field temperature. These theoretical results have been observed in related experiments of damped magneto-convection by Vives and Perry (1987).