Solidification of a ternary melt from a cooled boundary, or nonlinear dynamics of mushy layers / Alexandrov D.V., Ivanov A.A. // International Journal of Heat and Mass Transfer. - 2009. - V. 52, l. 21-22. - P. 4807-4811.

ISSN:

00179310

Type:

Article

Abstract:

We present a mathematical model and its analytical solution describing directional solidification of a ternary (three-component) system cooled from below. We focus on the solidification theory in the presence of two distinct mushy layers: (1) solidification along a liquidus surface is characterized by a primary mushy layer, and (2) solidification along a cotectic line is characterized by a secondary (cotectic) mushy layer. We consider the case when the phase transition temperatures in two mushy layers represent arbitrary functions of the compositions. We obtain an exact analytical solution of the nonlinear set of equations and boundary conditions in the case of a self-similar solidification scenario. Model predictions are in good agreement with existing experimental data. © 2009 Elsevier Ltd. All rights reserved.

Author keywords:

Mushy layer; Solidification; Ternary alloy

Index keywords:

Analytical solutions; Arbitrary functions; Directional solidification; Exact analytical solutions; Experimental data; Liquidus surfaces; Model prediction; Mushy layer; Non-linear dynamics; Phase trans

DOI:

10.1016/j.ijheatmasstransfer.2

Смотреть в Scopus:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-68749099586&doi=10.1016%2fj.ijheatmasstransfer.2009.05.029&partnerID=40&md5=fad586f7f98616d1a27c76d2448b6d7e

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Поле	Значение
Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-68749099586&doi=10.1016%2fj.ijheatmasstransfer.2009.05.029&partnerID=40&md5=fad586f7f98616d1a27c76d2448b6d7e
Affiliations	Urals State University, Department of Mathematical Physics, Lenin Avenue 51, Ekaterinburg, 620083, Russian Federation
Author Keywords	Mushy layer; Solidification; Ternary alloy
References	Meirmanov, A.M., (1992) The Stefan Problem, , De Gruyter, Berlin; Ivantsov, G.P., Diffusive supercooling in binary alloy solidification (1951) Dokl. Akad. Nauk SSSR, 81, pp. 179-182; Flemings, M., (1974) Solidification Processing, , McGraw Hill, New York; Chalmers, B., (1964) Principles of Solidification, , Wiley, New York; Borisov, V.T., Matveev, Yu.E., Determination of temperature at the beginning of mushy region of binary melts (short letter) (1962) Fiz. Met. Metalloved., 13 (3), pp. 465-467; Borisov, V.T., (1987) Theory of Two-Phase Zone of Metallic Ingot, , Metallurgia, Moscow; Hills, R.N., Loper, D.E., Roberts, P.H., A thermodynamically consistent model of a mushy zone (1983) Q. J. Appl. Math., 36, pp. 505-539; Alexandrov, D.V., Solidification with a quasiequilibrium mushy region: exact analytical solution of nonlinear model (2001) J. Cryst. Growth, 22, pp. 816-821; Alexandrov, D.V., Malygin, A.P., Self-similar solidification of an alloy from a cooled boundary (2006) Int. J. Heat Mass Transfer, 49, pp. 763-769; Alexandrov, D.V., Malygin, A.P., Alexandrova, I.V., Solidification of leads: approximate solutions of non-linear problem (2006) Ann. Glaciol., 44, pp. 118-122; Alexandrov, D.V., Nizovtseva, I.G., To the theory of underwater ice evolution, or nonlinear dynamics of false bottoms (2008) Int. J. Heat Mass Transfer, 51, pp. 5204-5208; Buyevich, Yu.A., Alexandrov, D.V., Mansurov, V.V., (2001) Macrokinetics of Crystallization, , Begell House, New York and Wallingford; Aseev, D.L., Alexandrov, D.V., Directional solidification of binary melts with a non-equilibrium mushy layer (2006) Int. J. Heat Mass Transfer, 49, pp. 4903-4909; Aitta, A., Huppert, H.E., Worster, M.G., Diffusion-controlled solidification of a ternary melt from a cooled boundary (2001) J. Fluid Mech., 432, pp. 201-217; Anderson, D.M., A model for diffusion-controlled solidification of ternary alloys in mushy layers (2003) J. Fluid Mech., 483, pp. 165-197; Scheil, E., Bemerkungen zur schichtkiistallbildung (1942) Z. Metallkd., 34, pp. 70-72; Kerr, R.C., Woods, A.W., Worster, M.G., Huppert, H.E., Solidification of an alloy cooled from above: Part 1. Equilibrium growth (1990) J. Fluid Mech., 216, pp. 323-342; Alexandrov, D.V., Nonlinear dynamics of solidification in three-component systems (2008) Dokl. Phys., 53 (9), pp. 471-475
Correspondence Address	Alexandrov, D.V.; Urals State University, Department of Mathematical Physics, Lenin Avenue 51, Ekaterinburg, 620083, Russian Federation; email: Dmitri.Alexandrov@usu.ru
CODEN	IJHMA
Language of Original Document	English
Abbreviated Source Title	Int. J. Heat Mass Transf.
Source	Scopus