Effects of centrifugal and coriolis forces on a hydromagnetic chimney convection in a mushy layer

Abstract

Nonlinear buoyancy driven convection in the melt and in cylindrical chimneys in a mushy layer during alloy solidification and subjected to an externally imposed strong magnetic field is investigated under a high-gravity environment, where the rotation axis is inclined at an angle γ to the high-gravity vector. The convection in the chimneys produces freckles in the final form of the solidified material, which are imperfections that reduce the quality of the solidified material. Asymptotic and scaling analyses, in the limit of sufficiently large solutal Rayleigh number, are applied to a nonaxisymmetric nonlinear convection in a finite Prandtl number melt and in the chimneys. Ranges in the parameter space are found where chimney convection can be intensified or weakened with either increasing Coriolis parameter T or centrifugal acceleration parameter A. Chimney convection generally decreases with increasing magnetic parameter Q (Chandrasekhar number). Within certain parameter ranges, chimney convection can have a much lower amplitude and lower rate of change with respect to A or Q if T is large and if γ<180°, as compared to the corresponding amplitude and the rate of change in the case for γ>180° keeping all the other parameter values the same as in the γ<180° case.