Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-26T01:11:20.898Z Has data issue: false hasContentIssue false
  • English
  • Français

Dendritic growth from a melt in an external flow: uniformly valid asymptotic solution for the steady state

Published online by Cambridge University Press:  26 April 2006

Jian-Jun Xu
Jian-Jun Xu
Affiliation:
Department of Mathematics and Statistics, McGill University, Burnside Hall, 805 Sherbrooke Street West, Montreal, Canada H3A 2K6
Get access Rights & Permissions [Opens in a new window]

Abstract

This work is part of an investigation dealing with the effect of external flow in a melt on dendritic growth. In this paper, we will consider steady growth with zero surface tension. Assuming that the Prandtl number Pr is large, we are able to obtain a uniformly valid asymptotic solution for the steady state in the whole growth region.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 263 , 25 March 1994 , pp. 227 - 244
Copyright
© 1994 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramovitz, M. & Stegun, I. A. (ed.) 1964 Handbook of Mathematical Functions. National Bureau of Standards.
Ananth, R. & Gill, W. N. 1989 J. Fluid Mech. 208, 575.
Ananth, R. & Gill, W. N. 1991 J. Cryst. Growth 108, 173.
Ben Amar, M., Bouissou, Ph. & Pelce, P. 1988 J. Cryst. Growth 92, 97.
Bouissou, Ph & Pelce, P. 1989 Phys. Rev. A 40, 6673.
Canright, D. & Davis, S. H. 1990 Applied Mathematics Tech. Rep. 8982. Northwestern University.
Dash, S. K. & Gill, W. G. 1984 Intl J. Heat Mass Transfer 27, 1345.
Huang, S. C. & Glicksman, M. E. 1981 Acta Metall. 29, 701.
Ivantsov, G. P. 1947 Dokl. Nauk. SSSR 58, 567.
Kevorkian, J. & Cole, J. D. 1981 Perturbation Methods in Applied Mathematics. Applied Mathematical Sciences, Vol. 34. Springer.
McFadden, G. B. & Coriell, S. R. 1986 J. Cryst. Growth 74, 507.
Saville, D. A. & Beaghton, P. J. 1988 Phys. Rev. A 37, 3423.
Xu, J. J. 1990a Can. J. Phys. 68, 58.
Xu, J. J. 1990b Physica Status Solidi (b), 157, 577.
Xu, J. J. 1990c J. Cryst. Growth 100, 481.
Xu, J. J. 1991 Phys. Rev. A.
Xu, J. J. 1993 Effect of convection motion in melt induced by density change on dendritic growth. Can. J. phys. (to appear).Google Scholar