Magnetohydrodynamic stationary and oscillatory convective stability in a mushy layer during binary alloy solidification

Abstract

• Mushy layer growth during solidification of a bottom cooled binary alloy. • Magnetohydrodynamic stationary and oscillatory convective stability in the mushy layer • Results are presented for various values of mush Hartmann numbers in the range, 0 ≤ Ha m ≤ 50. • The critical Rayleigh number for stationary convection shows a linear relationship with increasing Ha m . • Increasing magnetic strength shows reduction in wavenumber and in the number of rolls in the mushy layer. For the case of solidification of a bottom cooled binary alloy, the magnetohydrodynamic stationary and oscillatory convective stability in the mushy layer is investigated analytically using normal mode linear stability analysis. In the limit of large Stefan number ( S t ), a near–eutectic approximation with large far field temperature is considered in the present research. To ascertain the instability in the mushy layer, the strength of the superimposed magnetic field is so chosen that it corresponds to a given mush Hartmann number ( Ha m ) of the problem. The results are presented for various values of mush Hartmann numbers in the range, 0 ≤ Ha m ≤ 50. The critical Rayleigh number for stationary convection shows a linear relationship with increasing Ha m . The magnetohydrodynamic effect imparts a stabilizing influence during stationary convection. In comparison to that of the stationary convective mode, the oscillatory mode appears to be critically susceptible at higher values of β (β = S t /℘ 2 ϒ 2 , ℘ is the compositional ratio, ϒ = 1 + S t /℘), and vice versa for lower β values. Analogous to the behavior for stationary convection, the magnetic field also offers a stabilizing effect in oscillatory convection and thus influences global stability of the mushy layer. Increasing magnetic strength shows reduction in the wavenumber and in the number of rolls formed in the mushy layer.