Nonlinear dynamics of directional solidification of ternary solutions with mushy layers / Alexandrov D.V., Ivanov A.A. // Heat and Mass Transfer/Waerme- und Stoffuebertragung. - 2009. - V. 45, l. 11. - P. 1467-1472.

ISSN:
09477411
Type:
Article
Abstract:
We present new analytic results relating to the nonstationary dynamics of Stefan-type problems for the unidirectional solidification of ternary solutions in the presence of two mushy layers. Explicit analytical solutions (thicknesses of mushy layers, growth rates of their boundaries, temperature and impurity concentration fields, solid fractions) of the nonlinear model under consideration are found. Model predictions are in good agreement with existing experimental data. © 2009 Springer-Verlag.
Author keywords:
Index keywords:
Analytical solutions; Directional solidification; Experimental data; Impurity concentration; Model prediction; Non-linear dynamics; Non-linear model; Non-stationary dynamics; Solid fraction; Ternary s
DOI:
10.1007/s00231-009-0524-7
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-70350539301&doi=10.1007%2fs00231-009-0524-7&partnerID=40&md5=363eb773d8ffc14c77703593fe155e59
Соавторы в МНС:
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Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-70350539301&doi=10.1007%2fs00231-009-0524-7&partnerID=40&md5=363eb773d8ffc14c77703593fe155e59
Affiliations Department of Mathematical Physics, Urals State University, Lenin ave. 51, Ekaterinburg 620083, Russian Federation
References Davis, S.H., (2001) Theory of Solidification, , Cambridge University Press, Cambridge; Yua, B., Alexandrov, D.V., Mansurov, V.V., (2001) Macrokinetics of Crystallization, , Begell House, London; Hurle, D.T.J., (1993) Handbook of Crystal Growth, 1-3. , North-Holland, Amsterdam; Kurze, W., Fisher, D.J., Fundamentals of solidification (1986) Trans. Tech., , Publications, Brookfield; McBirney, A.R., Mixing and unmixing of magmas (1980) J Volcanol Geotherm Res, 7, pp. 357-371. , 10.1016/0377-0273(80)90038-4; Huppert, H.E., Sparks, R.S.J., Double-diffusive convection due to crystallization in magmas (1984) Annu Rev Earth Planet Sci, 12, pp. 11-37. , 10.1146/annurev.ea.12.050184.000303; 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. , 0549.73002 10.1093/qjmam/36.4.505; Worster, M.G., Solidification of an alloy from a cooled boundary (1988) J Fluid Mech, 167, pp. 481-501. , 10.1017/S0022112086002938; Fowler, A.C., The formation of freckles in binary alloys (1985) IMA J Appl Math, 35, pp. 159-174. , 0606.76110 10.1093/imamat/35.2.159; Alexandrov, D.V., Solidification with a quasiequilibrium mushy region: Exact analytical solution of nonlinear model (2001) Journal of Crystal Growth, 222 (4), pp. 816-821. , DOI 10.1016/S0022-0248(00)00960-X; Alexandrov, D.V., Malygin, A.P., Alexandrova, I.V., Solidification of leads: Approximate solutions of non-linear problem (2006) Annals of Glaciology, 44, pp. 118-122. , DOI 10.3189/172756406781811213; Anderson, D.M., A model for diffusion-controlled solidification of ternary alloys in mushy layers (2003) Journal of Fluid Mechanics, 483, pp. 165-197. , DOI 10.1017/S0022112003004129; 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. , 0969.76505; Scheil, E., Bemerkungen zur schichtkiistallbildung (1942) Z Metalld, 34, pp. 70-72
Correspondence Address Alexandrov, D. V.; Department of Mathematical Physics, Urals State University, Lenin ave. 51, Ekaterinburg 620083, Russian Federation; email: Dmitri.Alexandrov@usu.ru
CODEN HMTRF
Language of Original Document English
Abbreviated Source Title Heat Mass Transfer
Source Scopus