The Stefan problem of solidification of ternary systems in the presence of moving phase transition regions

Journal of Experimental and Theoretical Physics - Tập 108 Số 5 - Trang 821-829 - 2009
Dmitri V. Alexandrov1, А.А. Ivanov
1Gorkiy Ural State University, Yekaterinburg, Russia

Tóm tắt

Từ khóa


Tài liệu tham khảo

J. Stefan, Akad. Wiss. 98(2a), 473 (1889).

J. Stefan, Akad. Wiss. 98(2a), 965 (1889).

B. Chalmers, Principles of Solidification (Wiley, New York, 1964).

R. L. Parker, Crystal Growth Mechanisms: Energetics, Kinetics, and Transport (Academic, New York, 1970).

M. C. Flemings, Solidification Processing (McGraw-Hill, New York, 1974).

G. P. Ivantsov, Dokl. Akad. Nauk SSSR 81, 179 (1951).

W. W. Mullins and R. F. Sekerka, J. Appl. Phys. 35, 444 (1964).

D. J. Wollkind and L. A. Segel, Philos. Trans. R. Soc. London, Ser. A 268, 351 (1970).

D. V. Alexandrov, in Coupled Instabilities in Metal Structures, Ed. by M. Pignataro, J. Rondal, and V. Gioncu (Imprimeria Mirton, Timisoara, Romania, 2006), p. 537.

P. K. Galenko and V. A. Zhuravlev, Physics of Dendrites (World Scientific, Singapore, 1994).

A. V. Alyab’eva and V. V. Mansurov, Inzh.-Fiz. Zh. 3, 314 (1994).

Yu. A. Buyevich, D. V. Alexandrov, and V. V. Mansurov, Macrokinetics of Crystallization (Begell House, New York, 2001).

D. L. Aseev and D. V. Alexandrov, Dokl. Akad. Nauk 408(4–6), 609 (2006) [Dokl. Phys. 51 (6), 291 (2006)].

Ya. B. Zel’dovich, Zh. Éksp. Teor. Fiz. 12, 525 (1942).

V. T. Borisov, Dokl. Akad. Nauk SSSR 136, 583 (1961) [Sov. Phys. Dokl. 6, 74 (1961)].

V. T. Borisov and Yu. E. Matveev, Fiz. Met. Metalloved. 13, 456 (1962).

V. T. Borisov, Theory of the Two-Phase Zone of a Metal Ingot (Metallurgiya, Moscow, 1987) [in Russian].

R. N. Hills, D. E. Loper, P. H. Roberts, and Q. J. Mech, Appl. Math. 36, 505 (1983).

A. C. Fowler, SIAM J. Appl. Math. 35, 159 (1985).

D. V. Aleksandrov, Dokl. Akad. Nauk 375(1–3), 172 (2000) [Dokl. Phys. 45 (11), 569 (2000)].

D. V. Alexandrov and D. L. Aseev, J. Fluid Mech. 527, 57 (2005).

D. V. Alexandrov and A. P. Malygin, Dokl. Akad. Nauk 411(3), 390 (2006) [Dokl. Earth Sci. 411 (9), 1407 (2006)].

D. V. Alexandrov, A. P. Malygin, and I. V. Alexandrova, Ann. Glaciol. 44, 118 (2006).

D. V. Alexandrov and I. G. Nizovtseva, Dokl. Akad. Nauk 419(3), 262 (2008) [Dokl. Earth Sci. 419 (1), 359 (2008)].

D. T. J. Hurle, Handbook of Crystal Growth (North-Holland, Amsterdam, 1993), Vols. 1–3.

W. Kurze and D. J. Fisher, Fundamentals of Solidification (Trans. Tech., Aedermannsdorf, Switzerland, 1992).

C.-F. Chen and J. S. Turner, J. Geophys. Res. 85, 2573 (1980).

A. R. McBirney, J. Volcanol. Geotherm. Res. 7, 357 (1980).

H. E. Huppert and R. S. J. Sparks, Annu. Rev. Earth Planet. Sci. 12, 11 (1984).

A. Aitta, H. E. Huppert, and M. G. Worster, J. Fluid Mech. 432, 201 (2001).

D. M. Anderson, J. Fluid Mech. 483, 165 (2003).

W. J. Boettinger, U. R. Kattner, S. R. Coriell, Y. A. Chang, and B. A. Mueller, in Proceedings of the Conference on Modelling of Casting, Welding, and Advanced Solidification Processes VII, Warrendale, PA, United States, 1995, Ed. by M. Cross and J. Campbell (Warrendale, 1995), p. 649.

M. J. M. Krane, F. P. Incropera, and D. R. Gaskell, Int. J. Heat Mass Transfer 40, 3827 (1997).

R. E. Smallman, Modern Physical Metallurgy (Butterworths, London, 1985).

H. E. Huppert and M. G. Worster, Nature (London) 314, 703 (1985).

J. S. Wettlaufer, M. G. Worster, and H. E. Huppert, J. Geophys. Res. 105(C1), 1123 (2000).

E. Scheil, Z. Metallkd. 34, 70 (1942).

W. J. Boettinger, U. R. Kattner, and D. K. Banerjee, in Proceedings of the Conference on Modeling of Casting, Welding, and Advanced Solidification Processes VIII, Warrendale, PA, United States, 1998, Ed. by B. G. Thomas and C. Beckermann (Warrendale, 1998), p. 159.

R. C. Kerr, A. W. Woods, M. G. Worster, and H. E. Huppert, J. Fluid Mech. 216, 323 (1990).

S. Martin and P. Kauffman, J. Fluid Mech. 64, 507 (1974).

D. V. Alexandrov, Dokl. Akad. Nauk 422(1–3), 322 (2008) [Dokl. Phys. 53 (9), 471 (2008)].

M. Hort, J. Petrol. 39, 1063 (1998).