References
- C. Vives and C. Perry, Effects of magnetically damped convection during the controlled solidification of metals and alloys, Int. J. Heat Mass Transfer, 30(1987), 479-496. https://doi.org/10.1016/0017-9310(87)90263-8
- S. Tait and C. Jaupart, The planform of compositional convection and chimney formation in a mushy layer, Nature, 359(1992), 406-408. https://doi.org/10.1038/359406a0
- C. F. Chen, and F. Chen, Experimental study directional solidification of aqueous chloride solution, J. Fluid Mech., 227(1991), 567-586. https://doi.org/10.1017/S0022112091000253
- C. F. Chen, Experimental study of convection in a mushy layer during directional solidification, J. Fluid Mech., 293(1995), 81-98. https://doi.org/10.1017/S0022112095001649
- M. G.Worster, Solidification of an alloy from a cooled boundary, J. Fluid Mech., 167(1986), 481-501. https://doi.org/10.1017/S0022112086002938
- A. C. Fowler, The formation of freckles in binary alloys, IMA. J. Appl. Math., 35(1985), 159-174. https://doi.org/10.1093/imamat/35.2.159
- M. G. Worster, Natural convection in a mushy layer, J. Fluid Mech., 224(1991), 335-359. https://doi.org/10.1017/S0022112091001787
- M. G. Worster, Instabilities of the liquid and mushy regions during solidification of alloys, J. Fluid Mech., 237(1992), 335-359.
- G. Amberg and G. M. Homsy, Nonlinear analysis of buoyant convection in binary solidifi- cation with application to channel formation, J. Fluid Mech., 252(1993), 79-98. https://doi.org/10.1017/S0022112093003672
- D. M. Anderson and M. G. Worster, Weakly nonlinear analysis of convection in mushy layers during the solidification of binary alloys, J. Fluid Mech., 302(1995), 307-331.
- B. S. Okhuysen and D. Riahi, On weakly nonlinear convection in mushy layers during solidification of alloys, J. Fluid Mech., 596(2008), 143-167.
- D. Riahi, On stationary and oscillatory modes of flow instability in a rotating porous layer convection during alloy solidification, J. Porous Media, 6(2003), 177-187. https://doi.org/10.1615/JPorMedia.v6.i3.30
- D. Bhatta, M. S. Muddamallappa, and D. N. Riahi, On perturbation and marginal sta- bility analysis of magneto-convection in active mushy layer, Transport in Porous Media, 82(2010), 385-399. https://doi.org/10.1007/s11242-009-9433-y
- D. Bhatta, M. S. Muddamallappa, and D. N. Riahi, On weakly nonlinear evolution of convective flow in a passive mushy layer, Nonlinear Analysis: Real World Applications, 11(2010), 4010-4020. https://doi.org/10.1016/j.nonrwa.2010.03.007
- L. D. Landau, On the problem of turbulence, C.R. Acad. Sci. U.R.S.S., 44(1944), 311-314.
- P. Drazin and W. H. Reid, Hydrodynamic Stability, Cambridge University Press, Cambridge, 1981.
- S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover Publication, New York, 1961.
- D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, American Mathematical Society, Providence, Rode Island, 2002.