MHD Natural Convection in a Nanofluid-filled Enclosure with Non-uniform Heating on Both Side Walls

This study examines natural convection in a square enclosure filled with a water-Al2O3 nanofluid and subjected to a magnetic field. The side walls of the cavity have spatially varying sinusoidal temperature distributions. The horizontal walls are adiabatic. A Lattice Boltzmann method (LBM) is applied to solve the governing equations for fluid velocity and temperature. The following parameters and related ranges are considered: Rayleigh number of the base fluid, from Ra=10(3) to 10(6), Hartmann number from Ha=0 to 90, phase deviation (gamma=0, pi/4, pi/2, 3 pi/4 and pi) and solid volume fraction of the nanoparticles between phi = 0 and 6%. The results show that the heat transfer rate increases with an increase in the Rayleigh number but it decreases with an increase in the Hartmann number. For gamma = pi/2 and Ra=10(5) the magnetic field strengthens the effect produced by the presence of nanoparticles. For Ha=0, the most evident influence of nanoparticles is achieved at gamma = 0 and pi/4 for Ra=10(4) and 10(5) respectively.