By employing the finite element method, thermophoresis and Brownian diffusion are studied numerically relating to the natural convection in a wavy cavity that is filled with an Al2O3-water nanofluid possessing a central heat-conducting solid block that is influenced by the local heater located on the bottom wall. An isothermal condition is established in the two wavy vertical walls, while adiabatic condition is for the top horizontal wall. Partial heating is applied to the bottom of the horizontal wall, while the remaining part remains in the adiabatic condition. Empirical correlations are employed for the thermal conductivity and dynamic viscosity of the nanofluid. The number of oscillations (1 <= N <= 4), Rayleigh number (10(3) <= 6 Ra <= 10(6)), nanoparticles volume fraction (0 <= phi <= 04) and dimensionless length of the bottom heater (0.2 <= H <= 0.8) govern the parameters in this study. The grid independency test, as well as experimental and numerical data from other published works, was employed to validate the developed computational code comprehensively. Based on the obtained results, it was found that the heat transfer inside the cavity is enhanced by introducing nanoparticles as well as a selection of optimal number of oscillations. (C) 2018 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.