Asymptotic solutions of dendritic crystal growth in external flow

The present thesis is concerned with the effect of external fluid flow on steady axisymmetric dendrtic growth from a undercooled pure melt with zero surface tension. We consider two limiting cases: (1) the weak flow case, where the velocity of the forced external floe is much less than dendrite tip growth velocity; (2) the strong flow case, where the velocity of the forced external flow is much larger than dendrite tip growth velocity, and obtain uniformly valid asymptotic expansion solutions in terms of the generalized Laguerre series representation. For the case of weak external flow, we have a regular perturbation problem. The solution is obtained by using the regular perturbation expansion method. For the case of strong external flow, we have a singular boundary problem. The solution is found by using matched asymptotic expansion technique