Steady Dendritic Growth with Natural Convection (I): The Case of PR = O(1) and Ḡ ≪ 1

  • Jian-Jun Xu
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 7)


In the following two chapters, we shall study the cases that the convection in the melt is induced by the buoyancy effect. The effect of buoyancy-driven convection on dendritic growth has been an important topic in micro-gravity research. The first important experimental work on this case was performed by Huang and Glicksman in 1981. They found that the buoyancy-induced convection has a profound effect on dendritic growth, especially in the small undercooling regime (see Fig. 1.3). Huang and Glicksman’s observation was later confirmed by Lee and Gill (1991). The later development of the experimental investigations on this subject was reviewed by Lee et al. (1996). The analytical work on this problem was first carried out by Canright and Davis in 1991 with perturbation method. Canright et al. obtained a local solution valid near the interface for the case of small Grashof number.


Natural Convection Interface Condition Buoyancy Effect Interface Shape Valid Asymptotic Expansion 


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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Jian-Jun Xu
    • 1
  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada

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