The present paper is concerned with the single needle dendrite growth from a pure melt with arbitrary under-cooling parameter (−1 < Tꝏ < 1). The dendrite is supposed to grow under the effect of convection motion induced by an oscillating external source with magnitude U∞ and frequency ꞷ. 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.
|Journal||International Journal of Computational and Applied Mathematics|
|Publication status||Published - 2015|
CitationYee, 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.
- Asymptotic expansion method
- Dendritic growth
- Pattern formation