## 1 Introduction  
Nanofluids [1; 2; 3; 4] can be simply seen as nanometer-sized particles (such as metal and crystalline materials) suspended in a fluid (such as water). Hence, nanofluids benefit from both high energy storage per unit mass without considerable increase in temperature of the water, and high thermal conductivity of the metal material. The heat transfer of a nanofluid is all the more efficient as both its heat capacity and thermal conductivity were high, because the heat transfer between a wall and a fluid is carried via both conduction and convection. Some relevant and interesting numerical works have been carried out in the last three years in order to investigate the magnetohydrodynamic (MHD) natural convection within an enclosure filled with nanofluid. [PERSON] et al. [5] numerically investigated the MHD natural convection in a baffled U-shaped enclosure. The thermal conductivity and the viscosity of the nanofluid were obtained using the Koo-Kleinstreuer-Li correlations. The effects of the Rayleigh number, the Hartmann number, the solid volume fraction and the aspect ratio of the enclosure on the nanofluid flow and heat transfer were assessed. Results showed that the average Nusslet number augmented by the increasing of the Rayleigh number, the solid volume fraction and the enclosure aspect ratio. The effect of Rayleigh number on the average Nusselt number was more remarkable at lower Hartmann number. The effect of Rayleigh number on heat transfer was more prominent at higher enclosure aspect ratio. The effect of magnetic field on heat transfer was more pronounced at high Rayleigh number. [PERSON] et al. [6] numerically studied the effects of magnetic field and cavity inclination on the natural convection of a Cu-water nanofluid, assuming one hot and one cold source. The double multiple-relaxation-time thermal lattice Boltzmann method has been used to simulate the effects of Rayleigh number, Hartmann number, the solid volume fraction and the cavity inclination angle on the flow and the heat transfer performance of the nanofluid. Results showed that when the cavity inclination angle increased, the average Nusselt number decreased drastically first, and then subsequently increased continuously until approaching a maximum value at a certain cavity inclination angle for high values of Rayleigh number. Results also showed that for high Rayleigh number, the maximized average Nusselt number were obtained for lower cavity inclination angles when the Hartmann number increased. [PERSON] and [PERSON] [7] numerically investigated the natural convection heat transfer within 2D and 3D trapezoidal section channels filled with nanofluids with variable characteristics. The finite element method and the SIMPLER algorithm were used to simulate the effect of the Rayleigh number, the solid volume fraction, the side wall angle of the channel trapezoidal section and the channel axial slope on the heat transfer rate. The rate of heat transfer increased when the Rayleigh number increased for both 2D and 3D channels. For the 2D trapezoidal section channel, the increase in the solid volume fraction from 0% to 2% induced a decrease in the Nusselt number. For a solid volume fraction higher than 2%, the Nusselt number increased. For the 3D trapezoidal section channel, the increase in the channel axial slope provoked an increase in the Nusselt number. [PERSON] et al. [8] numerically studied the 3D MHD natural convection within a Cu/water nanofluid-filled cubic enclosure with one side wall sinusoidal temperature distribution and subjected to a horizontal magnetic field. A new double multiple-relaxation-time thermal lattice Boltzmann model was used to simulate the effects of the Rayleigh number, the Hartmann number, the solid volume fraction and the phase deviation on the heat transfer rate performance (Nusselt number) within the nanofluid. Results showed that the heat transfer rate was diminished when the Hartmann number increased and was improved when the Rayleigh number and the solid volume fraction increase.