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Received November 26, 2012
Accepted January 30, 2013
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Stability analysis of compositional convection in a mushy layer in the time-dependent solidification system
Department of Chemical Engineering, University of Suwon, Gyeonggi-do 445-743, Korea
ighwang@suwon.ac.kr
Korean Journal of Chemical Engineering, May 2013, 30(5), 1023-1028(6), 10.1007/s11814-013-0013-z
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Abstract
Instabilities of convection in a mushy layer with a permeable interface underlying a liquid layer are studied in the time-dependent solidification system in which a binary melt cooled from below. The self-similar stability equations in the liquid and mushy layers are derived by propagation theory. The onset of mushy-layer-mode convection is examined considering the variation of permeability with porosity in the mushy layer. The numerical results show that the critical Darcy-Rayleigh number defined in terms of the mean permeability increases with increasing the concentration ratio and decreases with increasing the superheat. When the concentration ratio is small, a small convective cell appears in the vicinity of the liquid-mush interface. The influences of various non-uniform permeability models on the stability of compositional convection are discussed.
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Chen F, Chung CA, Lai MH, Phys. Fluids., 14, 1295 (2002)
Emms PW, Fowler AC, J. Fluid Mech., 262, 111 (1994)
Tait S, Jaupart C, J. Geophys. Res., 97, 6735 (1992)
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Kim MC, Yoon DY, Cho E, Korean J. Chem. Eng., 26(6), 1461 (2009)
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Choi CK, Park JH, Kim MC, Lee JD, Kim JJ, David EJ, Int. J. Heat Mass Transf., 47(19-20), 4377 (2004)
Bhatta D, Muddamallappa MS, Riahi DN, Transp. Porous Media, 82(2), 385 (2010)
Nandapurkar P, Poirier DR, Heinrich JC, Felicelli S, Metall. Trans., 20B, 711 (1989)
Happel J, Brenner H, Low reynolds number hydrodynamics, Martinus Nijhoff Publishers, Dordrecht, Netherlands (1986)
Katz RF, Worster MG, J. Comput. Phys., 22, 9823 (2008)
