Water based nanofluid free convection heat transfer in a three dimensional porous cavity with hot sphere obstacle in existence of Lorenz forces

H2O based nanofluid magnetohydrodynamic free convection in a porous cubic cavity with hot sphere obstacle is investigated by means of Lattice Boltzmann method. Influences of Darcy number (Da), Hartmann number (Ha), and Rayleigh number (Ra) on Al2O3-H2O nanofluid treatment is demonstrated. Thermal conductivity is considered as function of Brownian motion. Results indicate that Lorentz forces makes temperature gradient to decrease. Thermal boundary layer becomes thicker with augment of Hartmann number but opposite treatment is observed for Darcy number.