Abstract
The linear stability theory is used to investigate analytically the effects of gravity modulation on solutal convection in the mushy layer of solidifying binary alloys. The gravitational field consists of a constant part and a sinusoidally varying part, which is synonymous to a vertically oscillating mushy layer subjected to constant gravity. The linear stability results are presented for both the synchronous and subharmonic solutions. It is demonstrated that up to the transition point between the synchronous and subharmonic regions, increasing the frequency of vibration rapidly stabilizes the solutal convection. Beyond the transition point, further increases in the frequency tend to destabilize the solutal convection, but gradually. It is also demonstrated that the effect of increasing the ratio of the Stefan number and the solid composition (η 0 ) is to destabilize the solutal convection.
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References
G. Amberg G. M. Homsy (1993) ArticleTitleNonlinear analysis of buoyant convection in binary solidification with application to channel formation J. Fluid Mech. 252 79–98
D. M. Anderson M. G. Worster (1995) ArticleTitleA new oscillatory instability in mushy layers during the solidification of binary alloys J. Fluid Mech. 307 245–267
D. M. Anderson M. G. Worster (1996) ArticleTitleWeakly nonlinear analysis of convection in mushy layers during the solidification of binary alloys J. Fluid Mech. 302 307–331
C. F. Chen F. Chen (1991) ArticleTitleExperimental study of the directional solidification of aqueous ammonium chloride solution J. Fluid Mech. 227 567–586
F. Chen J. W. Lu T. L. Yang (1994) ArticleTitleConvective instabilities in ammonium chloride solution directionally solidified from below J. Fluid Mech. 276 163–187
S. M. Copey A. F. Giamei S. M. Johnson M. F. Hornbecker (1970) ArticleTitleThe origin of freckles in unidirectional solidified castings Metall. Trans. 1 2193–2204
A. C. Fowler (1985) ArticleTitleThe formation of freckles in binary alloys IMA J. Appl. Maths 35 159–174
Govender, S.: (2004a), Stability of convection in a gravity modulated porous layer heated from below, Transport Porous Media (in press)
Govender, S.: (2004b), Stability of convection in a gravity modulated porous layer heated from below: transition from synchronous to subharmonic solutions, Transport Porous Media (Under Review).
S. Govender P. Vadasz (2002) ArticleTitleModerate time linear stability of moderate Stefan number convection in rotating mushy layers J. Porous Media 5 IssueID2 113–121
N. W. McLachlan (1964) Theory and Application of Mathieu Functions Dover New York
D. A. Nield (1999) ArticleTitleModelling effects of a magnetic field or rotation on flow in a porous medium Int. J. Heat and Mass Tran. 42 3715–3718
S. Tait C. Jaupart (1992) ArticleTitleCompositional convection in a reactive crystalline mush and melt differentiation J. Geophys. Res. 97 IssueIDB5 6735–6756
P. Vadasz (1998) ArticleTitleCoriolis effect on gravity-driven convection in a rotating porous layer heated from below J. Fluid Mech 376 351–375
M. G. Worster (1992) ArticleTitleInstabilities in the mushy regions during solidification of alloys J. Fluid Mech. 237 649–669
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Pillay, S.K., Govender, S. Stability of Solutal Convection in a Gravity Modulated Mushy Layer During the Solidification of Binary Alloys. Transp Porous Med 60, 183–197 (2005). https://doi.org/10.1007/s11242-004-5129-5
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DOI: https://doi.org/10.1007/s11242-004-5129-5