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In this study, a numerical investigation on nanofluid flow and heat transfer is presented in a cavity under the effects of cross partial magnetic fields and a partial heater. The governing stream function-vorticity equations are solved by thin plate spline radial basis functions (Rbfs) in space derivatives and backward Euler method in time derivatives. The vorticity transport equation involves either only buoyancy force or both buoyancy and cross partial magnetic field force. The results are depicted as streamlines, isotherms and vorticity contours as well as mean Nusselt number. The convective heat transfer increases with the rise in the length of the partial heater, in the concentration of nanoparticles and in Rayleigh number while it decreases with the augmentation of the Lorentz force.