Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ADJOINT SYSTEM FOR A MAGNETO-CONVECTIVE FLOW IN AN ACTIVE MUSHY LAYER

  • Bhatta, Dambaru (Department of Mathematics, The University of Texas-Pan American) ;
  • Riahi, Daniel N. (Department of Mathematics, The University of Texas-Pan American)
  • Received : 2010.10.26
  • Accepted : 2011.01.21
  • Published : 2011.09.30
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Abstract

Here we consider magneto-convection in a mushy layer which is formed during solidification of binary alloys. The mushy layer is treated as an active porous media with variable permeability. The equations governing the layer are conservation of mass, conservation of heat, conservation of solute, magnetic induction equation, momentum equation governed by the Darcy's law and Maxwell's equations for the magnetic field. To study the second order effects on the flow without solving the second order system, we need to obtain the adjoint system for the flow. This motivates the authors we derive the adjoint system analytically for the mushy layer case. Numerical results of the adjoint system are presented for passive and active mushy layers at the onset of the motion using a set of parameters experimentalists use.

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References

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