Magnetic control of natural convection in the horizontal Bridgman configuration: symmetric and non-symmetric cross sections

This study deals with the electromagnetic damping of free-convective flows in cavities such as those used in the crystal growth horizontal Bridgman configuration. The cavities are filled with a dilute electrically conducting alloy and are subjected to a horizontal temperature gradient. The flow is steady and laminar under an external, vertical, transversal and uniform magnetic field. Several cross sections of the cavities were investigated and can either be centro-symmetric or not. The governing equations for such problems are two coupled partial differential equations, for the velocity and the induced magnetic fields, coupled with a third integral equation for mass conservation. A finite element method has been developed, and the numerical results for the variation of the velocity and the induced magnetic field in terms of the Hartmann number show a considerable decrease in convection intensity as the Hartmann number increases. Results also reveal the presence of the well-known Hartmann and parallel layers. For non-centro-symmetric sections, results show the way the flow reorganises into two cells as the Hartmann number increases.