THERMAL RADIATION AND HALL CURRENT EFFECTS IN A MHD NON-DARCY FLOW IN A DIFFERENTIALLY HEATED SQUARE ENCLOSURE -LATTICE BOLTZMANN SIMULATION

Abstract

A computational study of radiative-convection flow on incompressible magnetohydrodynamic (MHD) convection in a heated square enclosure containing a non-Darcy square cavity with Hall currents and heat generation/absorption is presented. The Rosseland algebraic flux model is deployed for radiative heat transfer. The equations of conservation for mass, momentum, and energy with associated boundary conditions are rendered non-dimensional with suitable transformations. The results dimensionless nonlinear boundary value problem is then solved with the D2Q9-based lattice Boltzmann method (LBM) in MATLAB. A grid independence test is included for validation of the D2Q9-LBM code accuracy. A parametric study of the impact of the Hartmann number (magnetic body force parameter), heat generation (<i>Q</i>), thermal radiation (<i>Rd</i>), Darcy number (permeability parameter), and Rayleigh number (thermal buoyancy force) on the temperature contours, streamline, and Nusselt number distributions with Prandtl number (Pr &#61; 0.71) is conducted.