In this work, a theoretical study of phase equilibrium in mixtures of a calamitic nematic liquid crystal and hard spherical nanoparticles is presented. A mean-field thermodynamic model is used, where the interactions are considered to be proportional to the number of contacts, which in turn are proportional to the areas and area fractions of each component. It is shown that, as the radius of the particle is increased, the effect of the particles on the isotropic-nematic transition is less pronounced, and that for a large radius the miscibility increases as the particle radius increases.