Main aim of present research is to investigate the influence of wavy surface characteristics on natural convection heat transfer in a cosine corrugated square cavity filled with Cu-water nanofluid. Discretization of two dimensional governing equations is first carried out utilizing a finite volume method and then solved by simple algorithm. For achieving the maximum heat transfer in wavy cavity, optimization procedure is carried out by means of Response Surface Methodology for different wavy amplitudes, wavy wavelengths and volume fraction of nanoparticles. Impact of sundry parameters on flow quantities are discussed and displayed via graphs and tables. Results indicated that the mean Nusselt number declines by augmenting the wavy amplitudes and wavy wavelengths up to level (0) but afterward quite opposite behavior is noted that is that the mean Nusselt number increases as the wavy amplitudes and wavy wavelengths augment up to level (+1) with fixed Rayleigh number 10(4). It is also noted, that the mean Nusselt number improves with the escalation of volume fraction of nanoparticles. The sensitivity analysis is also taken into account. The increment in sensitivity of the mean Nusselt number is seen at low level (-1) for the wavy amplitude and wavy wavelength whereas the sensitivity remains independent for volume fraction of nanoparticles at all levels. (C) 2016 Elsevier Ltd. All rights reserved.