An exact solution for the shape of a crystal growing in a forced flow

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Abstract

We determine an exact solution for the shape of an isothermal needle crystal growing in a forced flow. The shape is a parabola (respectively a paraboloid) in a two-dimensional (respectively axisymmetric) model. For a given undercooling, the Peclet number related to the velocity of the needle crystal is a function of the Peclet number associated to the flow.

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