Stability of buoyancy-driven convection in directional solidification of a binary melt

In Gook Hwang; Chang Kyun Choi

Korean Journal of Chemical Engineering, Vol.26, No.4, 930-934, July, 2009

DOI10.1007/s11814-009-0156-0 Export Citation

Stability of buoyancy-driven convection in directional solidification of a binary melt

In Gook Hwang^†, and Chang Kyun Choi¹

Department of Chemical and Biochemical Engineering, The University of Suwon, Gyeonggi-do 445-743, Korea
¹School of Chemical and Biological Engineering, Seoul National University, Seoul 151-744, Korea

E-mail:

In directional solidification, compositional convection can be driven by an unstable density gradient in the melt. In this paper convective instabilities in liquid and mushy layers during solidification of a horizontal binary melt are analyzed by using the propagation theory. The self-similar stability equations are used to examine the boundarymode and mushy-layer-mode of convection. The effects of velocity conditions at the liquid-mush interface on the onset of convection are discussed. The critical Darcy-Rayleigh number for the convection in the mushy layer decreases with increasing the temperature of a cooled boundary.

Keywords:Directional Solidification;Buoyancy-driven Convection;Propagation Theory;Self-similar Stability Analysis

[References]

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Huppert HE, J. Fluid Mech., 212, 209 (1990)
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Chung CA, Chen CF, J. Fluid Mech., 408, 53 (2000)
Hwang IG, Choi CK, J. Cryst. Growth, 162, 182 (1996)
Hwang IG, Choi CK, J. Cryst. Growth, 220(3), 326 (2000)
Hwang IG, Choi CK, J. Cryst. Growth, 267(3-4), 714 (2004)
Kim MC, Yoon DY, Choi CK, Korean J. Chem. Eng., 13(2), 165 (1996)
Choi CK, Kang KH, Kim MC, Hwang IG, Korean J. Chem. Eng., 15(2), 192 (1998)
Yoon DY, Kim MC, Choi CK, Korean J. Chem. Eng., 20(1), 27 (2003)
Kim MC, Chung TJ, Choi CK, Korean J. Chem. Eng., 21(1), 69 (2004)
Chung TJ, Kim MC, Choi CK, Korean J. Chem. Eng., 21(1), 41 (2004)
Hwang IG, Choi CK, Korean J. Chem. Eng., 25(2), 199 (2008)
Choi CK, Park JH, Kim MC, Lee JD, Kim JJ, David EJ, Int. J. Heat Mass Transf., 47(19-20), 4377 (2004)
Choi CK, Park JH, Park HK, Cho HJ, Chung TJ, Kim MC, Int. J. Thermal Sci., 43, 817 (2004)
Beavers GS, Joseph DD, J. Fluid Mech., 30, 197 (1967)
Nield DA, Bejan A, Convection in porous media, Springer-Verlag, New York (1977)
Govender S, Transp. Porous Med., 67, 431 (2007)

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[4] Davis SH, J. Fluid Mech., 212, 241 (1990)

[5] Chen CF, Chen F, J. Fluid Mech., 227, 567 (1991)

[6] Worster MG, J. Fluid Mech., 237, 649 (1992)

[7] Tait S, Jaupart C, J. Geophys. Res., 97, 6735 (1992)

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[9] Emms PW, Fowler AC, J. Fluid Mech., 262, 111 (1994)

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