In the present work, three-dimensional numerical investigations are carried out to study the influence of top wall confinement on unsteady flow and heat transfer characteristics of sinusoidal wavy channels. Different channel confinements considered in the present study are channels having sinusoidal bottom wall and plane, in-phase, and out-of-phase configurations of the top wall. Computations are carried out by using open-source computational fluid dynamics package OpenFOAM. Numerical results are validated against the experimental results reported in the literature. The onset of unsteady flow and three-dimensionality in the channel has been identified by monitoring velocity at a point in the domain. Steady and unsteady flow characteristics have been presented with the help of temporal variation of velocity signals, phase space trajectories, power spectral density, instantaneous streamlines, and iso Q-surfaces. Heat transfer characteristics have been presented with the help of instantaneous Nusselt number contours and time-averaged values of Nusselt number. © 2021 Taylor & Francis Group, LLC.