This paper details the numerical study of laminar natural convection in a square enclosure filled with a non-Newtonian fluid. Thermal boundary conditions of the Dirichlet type are applied on the vertical walls of the enclosure while the horizontal ones are assumed adiabatic. A Power-law model is used to characterize the viscous behaviour of the purely viscous non-Newtonian fluids. The governing differential equations have been solved by the standard finite volume method and the hydrodynamic and thermal fields were coupled together using the Boussinesq approximation.The effects of Power-law index ( ) in the range 0.50 ≤ ≤ 1.50 on the heat and momentum transport are investigated for the values of Rayleigh number ( ) in the range 10 1 ≤ ≤ 10 4 and a Prandtl number of Pr = 10.We report accurate results of a systematic study with a focus on the most important buoyancyinduced flow and heat transfer characteristics. It is shown that the mean Nusselt number values increases with the increasing values of Rayleigh number for Newtonian as well as Power-law fluids. However, shear-thickening fluids (n > 1) are characterised with smaller ̅̅̅̅ values. Finally, the onset of convection dominated heat transfer mechanism is shifted towards lower values of for the shearthinning fluids (n < 1).