Conjugate Effects of Buoyancy and Magnetic Field on Heat and Fluid Flow Pattern at Low-to-Moderate Prandtl Numbers

Abstract

This study aims to present a numerical investigation of unsteady two-dimensional natural convection of an electrically conducting fluid in a square medium under externally imposed magnetic field. A temperature gradient is applied between the two opposing side walls parallel to y-direction, while the floor and ceiling parallel to x-direction are kept adiabatic. The coupled momentum and energy equations associated with the Lorentz ‘decelerating’ force as well as the buoyancy force terms are solved using the single relaxation lattice Boltzmann (LB) approach. The flow is characterized by the Rayleigh number Ra (103-106), the Prandtl number Pr (0.01-10), the Hartman number Ha (0-100) determined by the strength of the imposed magnetic field and its tilt angle from x-axis ranging from 0° to 90°. The changes in the buoyant flow patterns and temperature contours due to the effects of varying the controlling parameters and associated heat transfer are examined. It was found that the developed thermal LB model gives excellent results by comparison with former experimental and numerical findings. Starting from the values 105 of the Rayleigh number Ra and Ha=0, the flow is unsteady multicellular for low Prandtl number typical of liquid metal. Increasing gradually Pr, the flow undergoes transition to steady bicellular. The transition occurs at a threshold value between Pr=0.01 and 0.1. Increasing more the Prandtl number, the flow structure is distorted due to the viscous forces which outweigh the buoyancy forces and a thermal stratification is clearly established. For high Hartman number, the damping effects suppress the unsteady behaviour and results in steady state with extended unicellular pattern in the direction of Lorentz force and the heat transfer rate is reduced considerably.