Nonlinear compositional convection in mushy layers

摘要: This paper presents some extensions of two main problems nonlinear compositional convection in horizontal mushy layers during the solidification binary alloys that were recently investigated by author (Riahi2002, 2004). Under a near-eutectic approximation and limit large far-field temperature, we determine number twoand three-dimensional weakly solutions, stability these solutions with respect to arbitrary disturbances is then investigated. First, problem oscillatory modes convection, which was absence permeability parameter K1 (Riahi2002), extended include effects K1, over range values other parameters, for both motion. It found, particular, results reported Riahi (2002) are recovered if zero or sufficiently small. In such case two-dimensional form simple-travelling rolls mostly only stable preferred solutions. However, as more realistic cases, not small, replaced simple travelling waves rectangles, squares hexagons. Next, revisit mixed steady (Riahi2004), where appeared be sensitive approximated value 3.14 π used numerical calculation. Here find updated results, based on accurate 3.141592654 π, plus additional new results. standing hexagonal solution relatively wide whose properties now much better agreement available experimental (Tait et al.1992).