Lattice Boltzmann Simulation of MHD Rayleigh–Bénard Convection in Porous Media

Abstract

Lattice Boltzmann method is used to investigate the Rayleigh–Benard convection of magnetohydrodynamic fluid flow inside a rectangular cavity filled by porous media. The Brinkman–Forchheimer model is considered in the simulation to formulate a porous medium mathematically, and the multi-distribution function model is considered to include the magnetic field effect with different inclination angles. The water is considered as the working fluid, which is electrically conducting. A comprehensive analysis of the impact of governing dimensionless parameters is performed by varying Rayleigh (Ra), Hartmann (Ha), and Darcy (Da) numbers, porosity ( $$\epsilon $$ ), and inclination angles ( $$\phi $$ ) of the applied magnetic field. Numerical results are evaluated in the form of streamlines, isotherms, and the rate of heat transfer in terms of the local and average Nusselt number as well as the entropy generation due to the irreversibility of the fluid friction, temperature gradient, and magnetic field effects. The results imply that increasing Ha and decreasing Da reduce the rate of heat transfer. The average Bejan number $$\hbox {Be}_\mathrm{{avg}}$$ increases for increasing the Hartmann number. On the other hand, augmenting Ra and $$\epsilon $$ improves the heat transfer rate. It is also found that the change of the magnetic field inclination angle $$\phi $$ changes the rate of heat transfer and entropy generation.