Control of solidification of non-conducting materials using tailored magnetic fields

The structure of fluid flow in a solidifying melt plays a critical role in the quality/properties of the solid. It follows that by controlling the flow behavior, the final solidified material can be suitably affected. Most of the magnetic control approaches used depend on the variation of the Lorentz force for suppression of flow and are limited to conducting materials alone. The application of a magnetic gradient gives rise to an additional force that can be used to affect the melt flow of any material. In this work, a computational method for the design of solidification of a non-conducting material is addressed such that diffusion-dominated growth is achieved by the suppression of convection. The control parameter in the design problem is the time history of the imposed magnetic field. The design problem is posed as an unconstrained optimization problem. The adjoint method for the inverse design of continuum processes is adopted. Examples of designing the time history of the imposed magnetic field for the directional growth of various non-conducting materials are presented to demonstrate the developed formulation.