In this study, the natural convection in a square enclosure filled with water-based aluminium oxide (Al2O3) under the influence of an externally applied inclined magnetic field is considered numerically. The flow is steady, two-dimensional and laminar; the nanoparticles and water are assumed to be in thermal equilibrium. The governing equations are solved in terms of stream function-vorticity-temperature using both the dual reciprocity boundary element method and the finite element method to see the influence of characteristic flow parameters, namely: solid volume fraction (phi), inclination angle (gamma), Rayleigh (Ra) and Hartmann (Ha) numbers. Numerical simulations are performed for 0 <= phi <= 0.2, gamma = 0, pi/4, pi/3, pi/2, and the values of Rayleigh and Hartmann numbers up to 107 and 300, respectively. The results show that the buoyancy-driven circulating flows undergo inversion of direction as Ra and Ha increase, and magnitudes of streamlines and vorticity contours increase as Ra increases, but decrease as Ha increases. The isotherms have a horizontal profile for high Ra values as a result of convective dominance over conduction. As Ha increases, effect of the convection on flow is reduced, thus the isotherms tend to have vertical profiles.