Further results on dendritic growth with forced oscillation and pattern formation

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Abstract

We first recall the results on the asymptotic theory for a mathematical model of dendritic crystal solidification. A single needle dendrite is growing 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 ω. We formulated and discussed the problem by assuming that the Reynolds number Re and the frequency ω are both small. We then present the further results for the generated globally valid asymptotic expansion solutions of both the temperature field and the interface shape function in the whole physical domain. This enables us to finally explore the effect of the externally applied convection motion on the crystal growth and pattern formation. Copyright © 2014 Research India Publications.
Original languageEnglish
Pages (from-to)173-188
JournalAdvances in Theoretical and Applied Mathematics (ATAM)
Volume9
Issue number2
Publication statusPublished - 2014

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forced vibration
dendrites
convection
dendritic crystals
shape functions
needles
solidification
crystal growth
Reynolds number
mathematical models
temperature distribution
cooling
expansion

Citation

Yee, T. L. (2014). Further results on dendritic growth with forced oscillation and pattern formation. Advances in Theoretical and Applied Mathematics, 9(2), 173-188.

Keywords

  • Asymptotic expansion solutions
  • Dendritic growth