This paper examines the natural convection in an open cavity with a sinusoidal thermal boundary condition. The cavity is filled with a water-Al2O3 nanofluid and subjected to a magnetic field. Lattice Boltzmann method (LBM) is applied to solve the coupled equations of flow and temperature fields. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number of the base fluid, Ra =10(3) to 10(6), Hartmann number varied from Ha = 0 to 60, the phase deviation (gamma = 0, pi/4, pi/2, 3 pi/4 and pi) and the solid volume fraction of nanoparticles between phi = 0 and 6%. Results show that the heat transfer rate decreases with the increase of Hartmann number and increases with the rise of Rayleigh number. At Ha =30 and Ra = 10(3) to 10(5), for all phase deviations the addition of nanoparticles increases heat transfer rate. Also, at low Rayleigh number (Ra <= 10(4)) the highest heat transfer rate is obtained for gamma = pi/2. (c) 2015 The Institution of Chemical Engineers. Published by Elsevier BM. All rights reserved.