Effects of Grashof number and volume fraction of Cu–water nanofluid on natural convection heat transfer and fluid flow inside a two-dimensional wavy enclosure has been investigated numerically. Also, in the presence of nanofluid, the second law of thermodynamics is applied to predict the nature of irreversibility in terms of entropy generation. Finite-Volume numerical procedure with non orthogonal body fitted collocated grid arrangement is used to solve the governing differential equations. Calculation were performed for the Grashof numbers from 104 to 106, nanoparticles volume fraction from 0% to 10% and surface waviness ranging from 0.0 to 0.4 for different patterns of wavy enclosure. Streamlines, isothermal lines, counters of local entropy generation and the variation of local and average Nusselt number are presented and compared with considering the effects of different parameters. The results show that the average heat transfer rate decreases as nanoparticles volume fraction and Grashof number increase. Also, besides decreasing heat transfer rate, the nanoparticles can be used for decreasing the entropy generation.