Dendritic growth from a binary system in an external flow: Steady state solution with zero surface tension

The influence of convective flow on the dendritic growth in the binary system is studied. We obtain a uniformly valid asymptotic solution in the whole growth region for steady dendrite growth in the external flow for the case of the zero surface tension and the large Schmidt number. With the effect of the external flow, the interface shape is nearly parabolic. Via affecting the normalization parameter of the system, the external flow affects the Peclet number of growth which is a function of undercooling temperature at the far field, the Schmidt number, the constitutional undercooling parameter, and the external flow parameter. Compared with the pure melt, the external flow has more significant effect on the dendritic growth in the binary system.