Onset of buoyancy-driven convection in melting from below

Min Chan Kim; Dong Won Lee; Chang Kyun Choi

Korean Journal of Chemical Engineering, Vol.25, No.6, 1239-1244, November, 2008

DOI10.1007/s11814-008-0205-0 Export Citation

Onset of buoyancy-driven convection in melting from below

Min Chan Kim^†, Dong Won Lee¹, and Chang Kyun Choi²

Department of Chemical Engineering, Cheju National University, Cheju 690-756 Korea
¹Department of Mechanical Engineering, Cheju National University, Cheju 690-756 Korea
²School of Chemical and Biological Engineering, Seoul National University, Seoul 151-744 Korea

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When a horizontal homogeneous solid is melted from below, convection can be induced in a thermally unstable melt layer. In this study the onset of buoyancy-driven convection during time-dependent melting is investigated by using similarly transformed disturbance equations. The critical Rayleigh numbers based on the melt-layer thickness are found numerically for various conditions. For small superheats, the present predictions approach the well known results of classical Rayleigh-Benard problems, that is, critical Rayleigh numbers are located between 1,296 and 1,708, regardless of the Prandtl number. However, for high superheats the critical Rayleigh number increases with an increase in phase change rate but with decrease in Prandtl number.

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

[References]

Sparrow EM, Lee L, Shamsundar N, J. Heat Transfer, 98, 88 (1976)
Gau C, Viskanta R, Int. J. Heat Mass Transfer, 28, 573 (1985)
Chen CCF, Chen F, J. Fluid Mech., 227, 567 (1991)
Hwang IG, Choi CK, J. Cryst. Growth, 267(3-4), 714 (2004)
Goldstein RJ, Ramsey JW, in Studies in heat transfer, A. Festschrift, E. R.G. Eckert, J. P. Hartnet Eds., McGraw-Hill, Washington DC, pp. 199-208 (1978)
Ostrach S, Trans. ASME: J. Fluids Eng., 105, 5 (1983)
Feldman D, Shapiro MM, Banu D, Fuks CJ, Solar Energy Mater, 18, 201 (1989)
Smith MK, J.Fluid Mech., 188, 547 (1988)
Carslaw HS, Jaeger JC, Conduction of heat in solids, 2nd ed., Oxford Univ. Press (1959)
Hwang IG, AIChE J., 47(7), 1698 (2001)
Boger DV, Westwater JW, Trans. ASME: J. Heat Transfer, 89, 81 (1967)
Lowell RP, J. Volcanol. Geotherm. Res., 26, 1 (1985)
Kim MC, Chung TJ, Choi CK, Korean J. Chem. Eng., 21(1), 69 (2004)
Mathews J, Walker RL, Mathematical methods of physics, 2nd ed., W.A. Benjamin Inc. (1970)
Sparrow EM, Goldsetin RJ, Jonsson VK, J. Fluid Mech., 18, 513 (1964)
Kim MC, Park HK, Choi CK, Theoret. Comput. Fluid Mech., 16, 49 (2002)

[Referenced By]

[Related Articles]

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

[2] Gau C, Viskanta R, Int. J. Heat Mass Transfer, 28, 573 (1985)

[3] Chen CCF, Chen F, J. Fluid Mech., 227, 567 (1991)

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

[5] Goldstein RJ, Ramsey JW, in Studies in heat transfer, A. Festschrift, E. R.G. Eckert, J. P. Hartnet Eds., McGraw-Hill, Washington DC, pp. 199-208 (1978)

[6] Ostrach S, Trans. ASME: J. Fluids Eng., 105, 5 (1983)

[7] Feldman D, Shapiro MM, Banu D, Fuks CJ, Solar Energy Mater, 18, 201 (1989)

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

[9] Carslaw HS, Jaeger JC, Conduction of heat in solids, 2nd ed., Oxford Univ. Press (1959)

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

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

[12] Lowell RP, J. Volcanol. Geotherm. Res., 26, 1 (1985)

[13] Kim MC, Chung TJ, Choi CK, Korean J. Chem. Eng., 21(1), 69 (2004)

[14] Mathews J, Walker RL, Mathematical methods of physics, 2nd ed., W.A. Benjamin Inc. (1970)

[15] Sparrow EM, Goldsetin RJ, Jonsson VK, J. Fluid Mech., 18, 513 (1964)

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