Three-dimensional instability of thermal convection in a vertical Bridgman growth configuration under traveling magnetic field

Thermal convection in a vertical Bridgman growth configuration under the effect of a traveling magnetic field (TMF) is investigated numerically. The vertical Bridgman growth configuration is approximated by convection in a cylinder with a parabolic heated sidewall and isothermal-cooled end walls. The TMF effect is introduced as a usual approximation under low frequency and a low induction assumption to use the analytical expression for the Lorentz force applied in the fluid volume. The strength of the TMF force is measured by the parameter Ft. The cylinder aspect ratio (height/radius) is fixed to , and the Prandtl number considered is fixed to Pr = 0.02. The base flow simultaneously excited by buoyancy and TMF is axisymmetric. Our primary goal is to determine how the flow loses stability to three-dimensional flow. An extremely multiple valued stability curve in the (Ft,Ra) plane is revealed by linear stability analysis. Three distinct flow regimes are classified, i.e., buoyancy dominated regime, buoyancy and TMF-counterbalanced regime, and TMF-dominated regime. Typical steady and unsteady three-dimensional flows are illustrated.