Three-dimensional control of crystal growth using magnetic fields

Two coupled systems of partial differential equations governing three-dimensional laminar viscous flow undergoing solidification or melting under the influence of arbitrarily oriented externally applied magnetic fields have been formulated. The model accounts for arbitrary temperature dependence of physical properties including latent heat release, effects of Joule heating, magnetic field forces, and mushy region existence. On the basis of this model a numerical algorithm has been developed and implemented using central differencing on a curvilinear boundary-conforming grid and Runge-Kutta explicit time-stepping. The numerical results clearly demonstrate possibilities for active and practically instantaneous control of melt/solid interface shape, the solidification/melting front propagation speed, and the amount and location of solid accrued.