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Received August 23, 2023
Accepted August 23, 2023
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Onset of buoyancy-driven instability in a pure melt solidified from above
Department of Chemical and Biochemical Engineering, University of Suwon, Hwaseong-si, Gyeonggi-do 445-743, Korea 1Department of Chemical Engineering, Jeju National University, Jeju 690-756, Korea
mckim@cheju.ac.kr
Korean Journal of Chemical Engineering, March 2011, 28(3), 697-702(6), 10.1007/s11814-010-0406-1
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Abstract
When a pure liquid is solidified from above, convection may be induced in a thermally-unstable layer. The onset of buoyancy-driven convection during time-dependent solidification is investigated by using similarly transformed disturbance equations. The thermal disturbance distribution of the solid phase is approximated by WKB method, and the effects of various parameters on the stability condition of melt phase are analyzed theoretically. The present_x000D_
constant temperature cooling model gives more unstable results than the constant solidification velocity model of Smith [1].
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Brandeis G, Marsh BD, Nature., 339, 613 (1989)
Hwang IG, AIChE J., 47(7), 1698 (2001)
Hwang IG, Choi CK, J. Cryst. Growth, 267(3-4), 714 (2004)
Zhang X, Nguyen TH, Int. J. Numer. Methods Heat Fluid Flow., 9, 72 (1999)
Sparrow EM, Lee L, Shamsundar N, J. Heat Transfer., 98, 88 (1976)
Karcher C, Muller U, Fluid Dynamic Research., 15, 25 (1995)
Weaver JA, Viskanta R, Trans. ASME J. Heat Transfer., 108, 654 (1986)
Beckermann C, Viskanta R, Int. J. Heat Mass Transfer., 31, 35 (1988)
Boger DV, Westwater JW, Trans. ASME J. Heat Transfer., 89, 81 (1967)
Zhang X, Nguyen TH, Kahawita R, Int. J. Heat Mass Transfer., 34, 389 (1991)
Carslaw HS and Jaeger JC, Conduction of Heat in Solids, 2nd Ed., Oxford Univ. Press (1959)
Kim MC, Lee DW, Choi CK, Korean J. Chem. Eng., 25(6), 1239 (2008)
Kim MC, Park HK, Choi CK, Theoret. Comput. Fluid Dynamics., 16, 49 (2002)
Kim MC, Lee SG, Korean J. Chem. Eng., 26(1), 21 (2009)
Mathews J, Walker RL, Mathematical Methods of Physics, 2nd Ed., W.A. Benjamin Inc.
