Lattice Boltzmann simulation of natural convection heat transfer in an open enclosure filled with Cu–water nanofluid in a presence of magnetic field

•Convection very strong when Ra is high and Ha = 0.•Isotherms smooth when Ra is low and Ha is high.•Maximum stream function increases by adding nano-particle.•Flow circulation decreases when magnetic orientation angle increases.•Nusselt number ratio increases when Ra increases.

In this paper magneto hydrodynamic (MHD) natural convection flow of Cu–water nanofluid in an open enclosure is investigated numerically using lattice Boltzmann method (LBM) scheme. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell–Garnetts (MG) and Brinkman models, respectively. In addition, the MDF model was used for simulating the effect of uniform magnetic field. The influence of pertinent parameters such as Hartmann number, nanoparticle volume fraction, Rayleigh number and the inclination of magnetic field on the flow and heat transfer characteristics have been examined. The results indicate that the absolute values of stream function decline significantly by increasing Hartmann numbers while these values rise by increasing Rayleigh numbers. Moreover, the results show that the solid volume fraction has a significant influence on stream function and heat transfer, depending on the value of Hartmann and Rayleigh numbers.