Transition Thresholds and Routes to Unsteadiness of Magneto-Convective Flows in Tall Cavities at Low-PrandtlNumber Fluids

Abstract

The present study aims to investigate numerically the routes to unsteadiness behavior inside tall cavities at low Prandtl numbers (Pr=0.01- 0.1) under imposed horizontal magnetic field. The transition thresholds are marked under the variation of the cavity aspect ratio Ar=W/H (1/8, 1/4, 1/2), the Rayleigh number Ra (104 -5×107) and the Hartmann number Ha (0-150). The Lattice Boltzmann (LBM) approach is used to solve the governing equations. Horizontal temperature gradient is responsible of the convective motion and heat transfer. The changes in the convective flow patterns and temperature contours due to the effects of varying the controlling parameters and associated heat transfer are examined. It has been concluded that the flow is strongly unstable and presents multicellular structure at Pr=0.01 typical of liquid metal compared to Pr=0.1 cases. The same effect is observed by decreasing the cavity aspect ratio Ar. The Magnetic field magnitude necessary to control and stabilize the flow is the weaker for Pr=0.1. Increasing gradually the Rayleigh number Ra, the flow undergoes transition to steady state with fewer cells than at low Ra. the transition occurs at a threshold value showing weak growth rate in the Hacr compared to Ra variation. Increasing the Prandtl number to 0.1, the core flow structure is distorted due to the Lorentz forces which outweigh the buoyancy forces and a thermal stratification is clearly established. For high Hartman numbers and Rayleigh numbers, the stretching effects suppress the unsteady behaviour and results in steady state with extended unicellular pattern in the direction of Lorentz force.