In this paper, the effect of a magnetic field on natural convection flow in a nanofluid-filled cavity with sinusoidal temperature distribution on one side wall has been analyzed with a new attitude to Lattice Boltzmann method (LBM). The cavity is filled with water and nanoparticles of Cu at the presence of a magnetic field. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number of the base fluid, Ra = 10(3)-10(5), the volumetric fraction of the nanoparticles between 0 and 6%, phase deviation (theta = 0, pi/4, pi/2, 3 pi/4, and pi) and Hartmann number varied from Ha = 0 to 90 with interval 30 while the magnetic field is considered horizontally. Results show that the heat transfer decreases by the increment of Hartmann number for various Rayleigh numbers. The magnetic field augments the effect of nanoparticle at Rayleigh number of (Ra = 105) in contrast with Ra = 10(3)&10(4). At Ha = 0, the greatest effects of nanoparticles are obtained at theta = 3 pi/4, 0 & pi/2 for Ra = 10(3), 10(4) and 10(5) respectively. (C) 2013 Elsevier B.V. All rights reserved.