New Oscillatory Instability in a Mushy Layer in a Modulated Environment during the Solidification of Binary Alloys

Abstract

In this paper, the effect of gravity modulation on a new oscillatory instability in a mushy layer is discussed. During the solidification of binary mixture from a cold boundary quite often, the planar solidification front becomes unstable due to the constitutional under cooling, resulting in a mushy layer that separates completely the liquid phase from the completely solid phase. Here, the mushy layer is a reactive porous medium, whose internal structure is composed of fine—scale crystals through which the residual melt can flow. Some of the important results of the present investigation are:(i) There exists a limit for the Stefan number, which incorporates a key balance necessary for the existence of oscillatory instability under gravity modulation. (ii) The model incorporates a complex interaction of heat transfer, modulatory convection and solidification. (iii) The steady and oscillatory modes strongly depend on seven dimensionless parameters. (iv) The oscillatory instability is driven solely from the interior of the mushy layer and exists for all wave numbers. (v) A thorough discussion of the results reveals the different transition boundaries associated with the feasible combination of the parameters. (vi) The system becomes more unstable to both real and oscillatory instabilities as the Stefan number increases for a fixed of value of the modulation parameter. (vii) Modulated convection in a mushy layer could be enhanced or suppressed by a suitable choice of the governing parameters. Finally it is observed that, the results are of practical interest.