Solidification with a quasiequilibrium mushy region: Exact analytical solution of nonlinear model / Alexandrov D.V. // Journal of Crystal Growth. - 2001. - V. 222, l. 4. - P. 816-821.

ISSN:

00220248

Type:

Article

Abstract:

A set of nonlinear equations describing solidification of a binary melt in the presence of a quasiequilibrium mushy region is solved analytically in the case of an arbitrary dependence of effective coefficients of heat and mass transfer. Concentration, temperature distributions and a bulk fraction of the solid phase in a mushy region are found as functions of a spatial coordinate for unidirectional quasistationary regime of solidification. An algebraic equation for the bulk fraction of the solid phase at the solid-mushy region interface is also deduced. The mushy region width is found as a function of given physical and operating parameters of solidification. On the basis of obtained solutions the regime of solidification with the quasiequilibrium mushy zone is replaced by equivalent discontinuity surface (frontal) regime with new boundary conditions.

Author keywords:

Index keywords:

Algebra; Binary mixtures; Boundary conditions; Heat transfer; Mass transfer; Mathematical models; Nonlinear equations; Phase interfaces; Phase transitions; Solidification; Temperature distribution; Qu

DOI:

10.1016/S0022-0248(00)00960-X

Смотреть в Scopus:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-0035250753&doi=10.1016%2fS0022-0248%2800%2900960-X&partnerID=40&md5=c85d637ec38f135019acfa01cf234928

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Поле	Значение
Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-0035250753&doi=10.1016%2fS0022-0248%2800%2900960-X&partnerID=40&md5=c85d637ec38f135019acfa01cf234928
Affiliations	Department of Mathematical Physics, Urals Stt. Univ., Lenin A., Ekaterinburg, Russian Federation
References	Ivantsov, G.P., (1951) Sov. Phys. Dokl., 81, p. 179; Flemings, M., (1974) Solidification Processing, , McGraw Hill, New York; Chalmers, B., (1964) Principles of Solidification, , Wiley, New York; Borisov, V.T., Matveev, Yu.e., (1962) Fizika Metallov I Metallovedenie, 13, p. 456; Webb, B.W., Viskanta, R., Heat transfer 1986 (1986) Proceedings of the Eighth International Conference, 4. , San Francisko, California, August 17-22, General papers.-Wash. e. a; Borisov, V.T., (1987) Theory of Two-Phase Zone of Metallic Ingot, , Metallurgia, Moscow; Borisov, V.T., (1961) Sov. Phys. Dokl., 6, p. 74; Buyevich, Yu.a., Iskakova, L.yu., Mansurov, V.V., (1990) Zhurnal Prikl. Mechan. I Techn. Phisiki, 4, p. 46; Iskakova, L.yu., Mansurov, V.V., (1994) Rasplavy, 1, p. 82; Alexandrov, D.V., Ivanov, A.O., (2000) J. Crystal Growth, 210, p. 797; Hills, R.N., Loper, D.E., Roberts, P.H., (1983) Q.J. Mech. Appl. Math., 36, p. 505; Fowler, A.C., (1985) IMA J. Appl. Math., 35, p. 159; Czapelski, M., (1998) J. Crystal Growth, 187, p. 138; Engel, A.H.H., Incropera, F.P., (1989) Warme - Und Stoffubertragung, 24, p. 279; Buyevich, Yu.a., Iskakova, L.yu., Mansurov, V.V., (1990) Can. J. Phys., 68, p. 790; Iskakova, L.yu., Mansurov, V.V., (1994) Rasplavy, 1, p. 82
Correspondence Address	Alexandrov, D.V.; Urals State Univ, Ekaterinburg, Russian Federation
Publisher	Elsevier Science B.V., Amsterdam, Netherlands
CODEN	JCRGA
Language of Original Document	English
Abbreviated Source Title	J Cryst Growth
Source	Scopus