Steady natural convection cooling of a localized heat source at the bottom wall of an enclosure filled with Cu-water nanofluid for a variety of thermal boundary conditions at the sidewalls has been studied in the present paper. Finite difference method was employed to solve the dimensionless governing equations of the problem. The effects of governing parameters, namely, solid volume fraction, the different values of the heat source length and the different locations of the heat source on the streamlines and isotherms contours as well as maximum temperature, Nusselt number and average Nusselt number along the heat source were considered. The present results are validated by favorable comparisons with previously published results. The results of the problem are presented in graphical and tabular forms and discussed.