Abstract This work examines steady convection heat transfer and entropy generation in a wavy cubical container with Al2O3–water nanofluid and the solid cylinder. An isothermal embedded heater of finite width is located within the left vertical surface center of the container. All surfaces are insulated, except that the right wavy surface is kept cold, and the left wall is partially heated. The Boussinesq approximation is assumed, and three-dimensional simulations of governing equations have been applied to utilize the Galerkin weighted residual finite-element approach. Numerical results for the three-dimensional patterns of nanofluid flow, iso-temperature surfaces, and isentropic lines are given. The local Nusselt number adjacent to the left and interface surfaces within the container and solid cylinder and Bejan number have been examined for different values of the Rayleigh number, nanoparticle volume fraction, number of undulations and heater length, and cylinder radius. The results indicate that the optimal local heat transfer between the solid cylinder and container declines with the increased cylinder radius, which yields an imperfect nanofluid flow circulation.