Thermo-solutal growth of a dendritic crystal in the form of an elliptical paraboloid with forced convection

The steady-state analytical solutions describing the thermo-solutal growth of a dendritic crystal in the form of an elliptical paraboloid with allowance for a forced convective flow are found. The system of transcendental equations consisting of the undercooling balance and the stability criterion that describes a stable mode of growth of sections of elliptical dendrites is formulated and analyzed. It is shown that the temperature distributions in the melt, the growth and flow Peclet numbers as well as the dendrite tip diameter and tip velocity in the case of elliptical crystals essentially differ from their analogs in the case of symmetric shapes of dendrites in the form of paraboloids of revolution.