Lattice Boltzmann method for nanofluid flow in a porous cavity with heat sources and magnetic field

In this article, Lattice Boltzmann method (LBM) has been applied to investigate the influences of magnetic field and heat sources on water based nanofluid natural convection inside a porous cavity with three square heat sources. Koo-Kleinstreuer-Li (KKL) model is applied to study Brownian motion impact on nanofluid flow. Effects of Rayleigh number (Ra), Darcy number (Da), nanofluid volume fraction (ϕ), and Hartmann number (Ha) on heat transfer characteristics are analyzed. From the obtained results we observe a decrease in the temperature gradient with increasing Ha; while quite the opposite effect is true with increasing Da   and Ra. In the absence of magnetic field, for higher values of Darcy and Rayleigh numbers, thermal plumes are generated and the temperature gradient is enhanced. Moreover, small eddies are generated near the vertical centerline. However, in the presence of magnetic field, the number of thermal plumes decreases.