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In this work, for the first time, a double multi-relaxation-time lattice Boltzmann method (2-MRT-LBM) is proposed to simulate MHD natural convection of nanofluid in a two-dimensional square cavity. The cavity is filled with TiO2-water nanofluid and is get under a uniform magnetic field at different angles  with respect to horizontal plane. The proposed numerical scheme is solved the flow field and the temperature field using MRT-D2Q9 and MRT-D2Q5 lattice model, respectively. So, the main objective of this work is to show the effectiveness of this model to predict the effects of pertinent parameters such as the Rayleigh number (10 < Ra < 10), the solid volume fraction (0 % <  < 5 %), the Hartmann number (0 < Ha < 60) and the magnetic field angle (0 <  < 90) on the flow field and temperature field and the heat transfer performance of the cavity. The obtained results indicate that the proposed method is a powerful approach to simulate the MHD natural convection of nanofluids in a square cavity. Also the numerical results show that for Ra = 10 and for the range of Hartmann number of this study, the heat transfer and fluid flow depend strongly upon the direction of magnetic field. Furthermore, the magnetic field influence on the effect of nanoparticles on the heat transfer enhancement is not significant.

A Double Multi-Relaxation-Time Lattice Boltzmann Method for Simulation of Magneto Hydrodynamics Natural Convection of Nanofluid in a Square Cavity