This present study considers the problem of steady magneto-convection in a horizontal mushy layer with variable permeability and an impermeable mush–liquid interface during directional solidification of binary alloys. We model the flow by introducing a uniform magnetic field in the mushy layer which is considered as a porous medium where Darcy’s law holds and the permeability is a function of the local solid volume fraction. Basic-state solutions are obtained analytically using the no-flow condition. With the help of multiple shooting techniques, we obtain numerical solutions to the linear perturbation system for non-magnetic and magnetic cases. Numerical results are presented showing the effects of the magnetic field and the permeability of the layer. These results demonstrate that the application of an external magnetic field has stabilizing effects on the convection and can reduce the tendency for chimney formation in the mushy layer. In addition, variable permeability, which corresponds to an active mushy layer, indicates more stable and realizable flow system as compared to the case of constant permeability.
Variable permeability Porous media Mushy layer Magneto-convection
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Fowler A.C.: The formation of freckles in binary alloys. IMA J. Appl. Math. 35, 159–174 (1985)CrossRefGoogle Scholar
Hills R., Loper D., Roberts P.: A thermodynamically consistent model of a mushy zone. Q. J. Mech. Appl. Math. 36, 505–539 (1983)CrossRefGoogle Scholar
Muddamallappa M.S., Bhatta D., Riahi D.N.: Numerical investigation on marginal stability and convection with and without magnetic field in a mushy layer, Trans. Porous Media (2008, in press). doi:10.1007/s11242-008-9319-4
Okhuysen, B.S.: Analytical and computational studies of convection in solidifying binary media. Ph.D. thesis, Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, USA (2005)Google Scholar
Okhuysen B.S., Riahi D.N.: Nonlinear buoyant convection in mushy layers during alloy solidification of alloys. J. Porous Media 11, 291–303 (2008a)CrossRefGoogle Scholar
Okhuysen B.S., Riahi D.N.: Flow instabilities of liquid and mushy regions during alloy solidification and under high gravity environment induced by rotation. Int. J. Eng. Sci. 46, 189–201 (2008b)CrossRefGoogle Scholar
Riahi D.N.: Effects of a vertical magnetic field on chimney convection in a mushy layer. J. Cryst. Growth 216, 501–511 (2000)CrossRefGoogle Scholar
Riahi D.N.: Effects of centrifugal and coriolis forces on a hydromagnetic chimney convection in a mushy layer. J. Cryst. Growth 226, 393–405 (2001)CrossRefGoogle Scholar
Tait S., Jaupart C.: Compositional convection in a reactive crystalline mush and melt differentiation. J. Geophys. Res. 97, 6735–6756 (1992)CrossRefGoogle Scholar
Vives C., Perry C.: Effects of magnetically damped convection during the controlled solidification of metals and alloys. Int. J. Heat Mass Transf. 30(3), 479–496 (1987)CrossRefGoogle Scholar