Onset of buoyancy-driven instability in a pure melt solidified from above

In Gook Hwang; Min Chan Kim

Korean Journal of Chemical Engineering, Vol.28, No.3, 697-702, March, 2011

DOI10.1007/s11814-010-0406-1 Export Citation

Onset of buoyancy-driven instability in a pure melt solidified from above

In Gook Hwang, and Min Chan Kim^{1, †}

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

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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 constant temperature cooling model gives more unstable results than the constant solidification velocity model of Smith [1].

Keywords:Buoyancy Driven Convection;Solidification;Stefan Problem;Similar Transform

[References]

Smith MK, J. Fluid Mech., 188, 547 (1988)
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.

[Referenced By]

[Related Articles]

[1] Smith MK, J. Fluid Mech., 188, 547 (1988)

[2] Brandeis G, Marsh BD, Nature., 339, 613 (1989)

[3] Hwang IG, AIChE J., 47(7), 1698 (2001)

[4] Hwang IG, Choi CK, J. Cryst. Growth, 267(3-4), 714 (2004)

[5] Zhang X, Nguyen TH, Int. J. Numer. Methods Heat Fluid Flow., 9, 72 (1999)

[6] Sparrow EM, Lee L, Shamsundar N, J. Heat Transfer., 98, 88 (1976)

[7] Karcher C, Muller U, Fluid Dynamic Research., 15, 25 (1995)

[8] Weaver JA, Viskanta R, Trans. ASME J. Heat Transfer., 108, 654 (1986)

[9] Beckermann C, Viskanta R, Int. J. Heat Mass Transfer., 31, 35 (1988)

[10] Boger DV, Westwater JW, Trans. ASME J. Heat Transfer., 89, 81 (1967)

[11] Zhang X, Nguyen TH, Kahawita R, Int. J. Heat Mass Transfer., 34, 389 (1991)

[12] Carslaw HS and Jaeger JC, Conduction of Heat in Solids, 2nd Ed., Oxford Univ. Press (1959)

[13] Kim MC, Lee DW, Choi CK, Korean J. Chem. Eng., 25(6), 1239 (2008)

[14] Kim MC, Park HK, Choi CK, Theoret. Comput. Fluid Dynamics., 16, 49 (2002)

[15] Kim MC, Lee SG, Korean J. Chem. Eng., 26(1), 21 (2009)

[16] Mathews J, Walker RL, Mathematical Methods of Physics, 2nd Ed., W.A. Benjamin Inc.