Magnetohydrodynamic nanofluid convective flow in a porous enclosure by means of LBM

•The influence of Lorentz force on nanofluid free convection inside a porous cavity is reported.•Simulations have been performed via Lattice Boltzmann Method (LBM).•KKL model is applied to consider Brownian motion impact on nanofluid properties.•Impacts of various parameters on heat transfer are evaluated and examined.

In this research, influence of Lorentz forces on nanofluid free convection inside a porous cavity is simulated. Simulations have been done via Lattice Boltzmann Method (LBM). Koo-Kleinstreuer-Li (KKL) model is applied in order to consider Brownian motion impact on nanofluid properties. Impacts of Darcy number (Da), Rayleigh number (Ra), nanofluid volume fraction (ϕ) and Hartmann number (Ha) on heat transfer treatment are illustrated. Outputs demonstrate that temperature gradient reduces with increase of Ha while it increases with augment of permeability of porous media and buoyancy forces.