A Periodically Reversed Flow Driven by a Modulated Traveling Magnetic Field: Part II. Theoretical Model

A flow of liquid GaInSn, which has been investigated experimentally in a companion article, [1] is modeled analytically in this article. The role of this electromagnetically driven flow is to transport the solute rejected by the solidifying interface at significant distances in the melt, and to periodically reverse its circulation such that macrosegregation is minimized. First, we present an analytical derivation of the electromagnetic force, exhibiting its space and time variations, which are essentially legitimate in the central part of the fluid domain. A model for the recirculating fluid flow is also derived, assuming that in this central region the flow is quasiparallel to the main axis. The narrowness of the fluid domain must be taken into account, to achieve a satisfactory agreement with the measurements.