Effects of nanoparticles Brownian motion in a linearly/sinusoidally heated cavity with MHD natural convection in the presence of uniform heat generation/absorption

In this numerical work, natural convection of CuO–water nanofluid and pure water in a cavity submitted to different heating modes on its vertical walls, is analyzed using the Lattice Boltzmann Method (LBM). The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo–Kleinstreuer–Li) correlation. The influence of pertinent parameters such as Rayleigh number (Ra=103–106), Hartmann number (Ha=0–80), heat generation or absorption coefficient (q=−10, −5, 0, 5, 10) and nanoparticle volume concentration (ϕ=0–0.04) on the flow and heat transfer characteristics has been examined. In general, by considering the role of Brownian motion, the enhancement in heat transfer is observed at any Hartman and Rayleigh numbers. In addition, the heat generation or absorption influences the heat transfer in the cavity at Ra=103 more than other Rayleigh numbers as the least effect is observed at Ra=106. [Display omitted] •Lattice Boltzmann method is applied to the problem.•The effects of Brownian motion of nanoparticles have been examined.•The effects of heat generation or absorption coefficient are studied.•The effects of Hartmann number, Rayleigh number and solid volume fraction are examined.