Transport in Porous Media

, Volume 82, Issue 2, pp 385–399 | Cite as

On Perturbation and Marginal Stability Analysis of Magneto-Convection in Active Mushy Layer

  • Dambaru BhattaEmail author
  • Mallikarjunaiah S. Muddamallappa
  • Daniel N. Riahi


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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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Dambaru Bhatta
    • 1
    Email author
  • Mallikarjunaiah S. Muddamallappa
    • 1
  • Daniel N. Riahi
    • 1
  1. 1.Department of MathematicsThe University of Texas-Pan AmericanEdinburgUSA

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