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Moderate Stefan Number Convection in Rotating Mushy Layers: A New Darcy Equation Formulation

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Abstract

The coriolis effect on a solidifying mushy layer is considered. A near-eutectic approximation and large far-field temperature is employed in the current study for moderate Stefan numbers. The linear stability theory is used to investigate analytically the Coriolis effect on convection in a rotating mushy layer for a new formulation of the Darcy equation. It was found that only stationary convection is possible for moderate Stefan numbers. In contrast to the problem of a stationary mushy layer, rotating the mushy layer has a stabilizing effect on convection. It was also discovered that fot Taylor numbers larger than three (i.e., Ta > 3),increasing the retardability coefficient (hence increasing the solid fraction) destablished the convection.

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References

  • G. Amberg G. M. Homsy (1993) ArticleTitleNonlinear analysis of buoyant convection in binary solidification to channel formation J. Fluid Mech 252 79–98

    Google Scholar 

  • D. M. Anderson M. G. Worster (1996) ArticleTitleA new oscillatory instability in a mushy layer during the solidification of binary alloys J. Fluid Mech 307 245–267

    Google Scholar 

  • S. M. Copley A. F. Giamei S. M. Johnson M. F. Hornbecker (1970) ArticleTitleThe origin of freckles in unidirectionally solidified castings Metall. Trans 1 2193–2205

    Google Scholar 

  • Govender, S.: 2002, On the linear stability of large Stefan number convection in rotating mushy layers for a new Darcy equation formulation, Transp. Porous Media (in press).

  • S. Govender P. Vadasz (2002) ArticleTitleWeak nonlinear analysis of moderate Stefan number oscillatory convection in rotating mushy layers, Transp Porous Media 48 353–372

    Google Scholar 

  • D. A. Nield (1998) ArticleTitleModelling effects of magnetic field or rotation on flow in a porous medium: momentum equation and anisotropic permeability analogy, Int J. Heat Mass Transfer 42 3715–3718

    Google Scholar 

  • P. Vadasz (1998) ArticleTitleCoriolis effect on gravity driven convection in a rotating porous layer heated from below J. Fluid Mech 376 351–375

    Google Scholar 

  • J. R Sarazin A. Hellawell (1988) ArticleTitleChannel formation in Pb-Sn Pb-Sb, and Pb-Sn-Sb alloy ingots and comparison with the system NH_4Cl–H_2O, Metall. Trans 19A 1861–1871

    Google Scholar 

  • B. Straughan (2000) ArticleTitleA sharp nonlinear stability threshold in rotating porous convection, Proc R. Soc. Lond. Ser. A 457 87–93

    Google Scholar 

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Authors and Affiliations

  1. School of Mechanical Engineering, University of Natal, King George V Avenue, Durban, 4041, South Africa

    Saneshan Govender

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  1. Saneshan Govender
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Correspondence to Saneshan Govender.

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Govender, S. Moderate Stefan Number Convection in Rotating Mushy Layers: A New Darcy Equation Formulation. Transp Porous Med 59, 127–137 (2005). https://doi.org/10.1007/s11242-004-0669-2

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  • DOI: https://doi.org/10.1007/s11242-004-0669-2

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