Advertisement

Transport in Porous Media

, Volume 48, Issue 3, pp 353–372 | Cite as

Weak Nonlinear Analysis of Moderate Stefan Number Oscillatory Convection in Rotating Mushy Layers

  • Saneshan Govender
  • Peter Vadasz
Article

Abstract

We consider the solidification of a binary alloy in a mushy layer subject to Coriolis effects. A near-eutectic approximation and large far-field temperature is employed in order to study the dynamics of the mushy layer with a Stefan number of unit order of magnitude. The weak nonlinear theory is used to investigate analytically the Coriolis effect in a rotating mushy layer for a new moderate time scale proposed by the author. It is found that increasing the Taylor number favoured the forward bifurcation.

rotating flows mushy layers free convection Taylor number solidification oscillatory convection 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amberg, G. and Homsey, G. M.: 1993, Nonlinear analysis of buoyant convection in binary solidification to channel formation, J. Fluid Mech. 252, 79–98.Google Scholar
  2. Anderson, D. M. and Worster, M. G.: 1995, Weakly nonlinear analysis of convection in mushy layers during the solidification of binary alloys, J. Fluid Mech. 302, 307–331.Google Scholar
  3. Anderson, D. M. and Worster, M. G.: 1996, A new oscillatory instability in a mushy layer during the solidification of binary alloys, J. Fluid Mech. 307, 245–267.Google Scholar
  4. Chen, F., Lu, J. W. and Yang, T. L.: 1994, Convective instability in ammonium chloride solution directionally solidified from below, J. Fluid Mech. 276, 163–187.Google Scholar
  5. Copley, S. M., Giamei, A. F., Johnson, S. M. and Hornbecker, M. F.: 1970, The origin of freckles in unidirectionally solidified castings, Metall. Trans. 1, 2193–2205.Google Scholar
  6. Drazin, P. G. and Reid, W. H.: 1981, Hydrodynamic Stability, Cambridge University Press.Google Scholar
  7. Fowler, A. C.: 1985, The formation of freckles in binary alloys, IMA J. App. Math. 35, 159–174.Google Scholar
  8. Newell, A. C. and Whitehead, J. C.: 1969, Finite bandwidth, finite amplitude convection, J. Fluid. Mech. 38, 297–303.Google Scholar
  9. Nield, D. A.: 1999, Modelling effects of a magnetic field or rotation on flow in a porous medium, Int. J. Heat and Mass Tran. 42, 3715–3718.Google Scholar
  10. Segel, L. A.: 1969, Distant side-walls cause slow amplitude modulation of cellular convection, J. Fluid. Mech. 38, 203–224.Google Scholar
  11. Vadasz, P.: 1998, Coriolis effect on gravity driven convection in a rotating porous layer heated from below, J. Fluid. Mech. 376, 351–375.Google Scholar
  12. Worster, M. G.: 1992, Instabilities of the liquid and mushy regions during solidification of alloys, J. Fluid. Mech. 237, 649–669.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Saneshan Govender
    • 1
  • Peter Vadasz
    • 1
  1. 1.School of Mechanical EngineeringUniversity of NatalDurbanSouth Africa

Personalised recommendations