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

The present paper is concerned with the single needle dendrite growth from a pure melt with arbitrary under-cooling parameter (−1 < T_ꝏ < 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.