Effect on temperature and interface shape of dendritic growth with forced oscillation

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Abstract

The present paper is concerned with the single needle dendrite growth from a pure melt with arbitrary under-cooling parameter (−1 < T < 1). The dendrite is supposed to grow under the effect of convection motion induced by an oscillating external source with magnitude U and frequency . We formulated and discussed the problem by assuming that the Reynolds number Re and the frequency ω are both small. An asymptotic expansion solution can be obtained that involves the perturbed term dependent of the under-cooling T and the convection magnitude U, and with an error of Ο (Re / ln (1 /Re)). The solution differs from the classical Ivantsov solution with a correction term proportional to a parameter which is dependent of the Reynolds number Re, the flow parameter U and the under-cooling T. Copyright © 2015 Research India Publications.
Original languageEnglish
Pages (from-to)47-59
JournalInternational Journal of Computational and Applied Mathematics
Volume10
Issue number1
Publication statusPublished - 2015

Citation

Yee, T. L. (2015). Effect on temperature and interface shape of dendritic growth with forced oscillation. International Journal of Computational and Applied Mathematics, 10(1), 47-59.

Keywords

  • Asymptotic expansion method
  • Dendritic growth
  • Pattern formation

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