In this paper, the natural convection of water-Al2O3 nanofluid in a square enclosure exposed to a magnetic field is numerically investigated. The enclosure is bounded by two isothermal vertical walls at different temperaturesof Th and Tc.The two horizontals walls of the enclosure are thermally insulated. A vertical plate (membrane separator) with a negligible thickness and a variable height is located in the middle of the chamber. Discretization of the governing equations are achived through a finit method and are solved using the SIMPLE algorithm. Based on the results of the numerical solution, the effects of the relevant parameters such as the dimensionless height of the membrane separator, Rayleigh number, the solid volume fraction and the Hartmann number on the flow field and the heat transfer rate are investigated. The results show that the heat transfer rate decreases with an increase of the dimensionless height of the membrane separator and an increase of the Hartmann number. The heat transfer rate, however, increases as the Rayleigh number increases. Depending on the Rayleigh number, the thermal performance of the enclosure is either improved or deteriorated as the solid volume fraction is increased.