Heat transfer due to laminar natural convection in a differentially heated square cavity using copper-water nanofluid has been studied numerically. The nanofluid is Non-Newtonian. The shear stresses have been calculated using Ostwald-de Waele model (power law model). The transport equations for a non-Newtonian fluid have been discretised using finite volume approach and solved following SIMPLER algorithm through ADI method. The thermal conductivity of the nanofluid has been calculated from the model proposed by Patel et al. Study has been conducted for Rayleigh number (Ra) varying from 10⁴ to 10⁷ while solid volume fraction (ø) of copper particles in water have been varied from 0.05% to 5%. Study has been conducted for different particle size of copper ranging from 50 nm to 100 nm. The general trend is that for a particular Rayleigh number and particular solid volume fraction of the nanoparticles, the heat transfer increases with decreases in particle size at higher Ra. For lower Ra the heat transfer first decreases and then increases.