On Compositional Convection in Near-Eutectic Solidification System Cooled from a Bottom Boundary

In Gook Hwang

Korean Chemical Engineering Research, Vol.55, No.6, 868-873, December, 2017

DOI10.9713/kcer.2017.55.6.868 Export Citation

On Compositional Convection in Near-Eutectic Solidification System Cooled from a Bottom Boundary

In Gook Hwang^†

Department of Chemical Engineering, The University of Suwon, 17, Wauan-gil, Bongdam-eup, Hwaseong, Gyeonggi, 18323, Kroea, Korea

E-mail:

Natural convection is driven by the compositional buoyancy in solidification of a binary melt. The stabilities of convection in a growing mushy layer were analyzed here in the time-dependent solidification system of a neareutectic melt cooled impulsively from below. The linear stability equations were transformed to self-similar forms by using the depth of the mushy layer as a length scale. In the liquid layer the stability equations are based on the propagation theory and the thermal buoyancy is neglected. The critical Rayleigh number for the mushy layer increases with decreasing the Stefan number and the Prandtl number. The critical conditions for solidification of aqueous ammonium chloride solution are discussed and compared with the results of the previous model for the liquid layer.

Keywords:Compositional convection;Solidification;Mushy layer;Ammonium chloride solution

[References]

Fowler AC, IMA J. Appl. Math., 35(2), 159 (1985)
Glicksman ME, Coriell SR, McFadden GB, Ann. Rev. Fluid. Mech., 18, 307 (1986)
Jones DWR, Worster MG, J. Fluid Mech., 714, 127 (2013)
Wells AJ, Wettlaufer JS, Orszag SA, J. Fluid Mech., 716, 203 (2013)
Worster MG, J. Fluid Mech., 237, 649 (1992)
Shih YC, Tu SM, Chiu CC, Appl. Therm. Eng., 50(1), 1055 (2013)
O'Rourke JG, Riggs AJE, Guertler CA, Miller PW, Padhi CM, Popelka MM, Wells AJ, West AC, Zhong JQ, Wettlaufer JS, Phys. Fluids, 24(10), 103305 (2012)
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Choi CK, Park JH, Park HK, Cho HJ, Chung TJ, Kim MC, Int. J. Therm. Sci., 43(8), 817 (2004)
Kim MC, Choi CK, Korean J. Chem. Eng., 32(12), 2400 (2015)
Hwang IG, Choi CK, Proceedings of the 11th International Heat Transfer Conference, 7, 193-198 (1998).
Hwang IG, Choi CK, J. Cryst. Growth, 220(3), 326 (2000)
Hwang IG, Choi CK, Korean J. Chem. Eng., 25(2), 199 (2008)
Hwang IG, Choi CK, Korean Chem. Eng. Res., 47(2), 174 (2009)
Hwang IG, Korean J. Chem. Eng., 30(5), 1023 (2013)
Chung CA, Chen F, J. Fluid Mech., 408, 53 (2000)
Nield DA, Bejan A, Convection in porous media, 4th ed., Springer Science & Business Media, New York, NY(2013).

[Referenced By]

[1] Fowler AC, IMA J. Appl. Math., 35(2), 159 (1985)

[2] Glicksman ME, Coriell SR, McFadden GB, Ann. Rev. Fluid. Mech., 18, 307 (1986)

[3] Jones DWR, Worster MG, J. Fluid Mech., 714, 127 (2013)

[4] Wells AJ, Wettlaufer JS, Orszag SA, J. Fluid Mech., 716, 203 (2013)

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

[6] Shih YC, Tu SM, Chiu CC, Appl. Therm. Eng., 50(1), 1055 (2013)

[7] O'Rourke JG, Riggs AJE, Guertler CA, Miller PW, Padhi CM, Popelka MM, Wells AJ, West AC, Zhong JQ, Wettlaufer JS, Phys. Fluids, 24(10), 103305 (2012)

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

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

[10] Choi CK, Park JH, Park HK, Cho HJ, Chung TJ, Kim MC, Int. J. Therm. Sci., 43(8), 817 (2004)

[11] Kim MC, Choi CK, Korean J. Chem. Eng., 32(12), 2400 (2015)

[12] Hwang IG, Choi CK, Proceedings of the 11th International Heat Transfer Conference, 7, 193-198 (1998).

[13] Hwang IG, Choi CK, J. Cryst. Growth, 220(3), 326 (2000)

[14] Hwang IG, Choi CK, Korean J. Chem. Eng., 25(2), 199 (2008)

[15] Hwang IG, Choi CK, Korean Chem. Eng. Res., 47(2), 174 (2009)

[16] Hwang IG, Korean J. Chem. Eng., 30(5), 1023 (2013)

[17] Chung CA, Chen F, J. Fluid Mech., 408, 53 (2000)

[18] Nield DA, Bejan A, Convection in porous media, 4th ed., Springer Science & Business Media, New York, NY(2013).