In the present work, the influence of non-uniform boundary conditions on natural convection in inclined rectangular cavities differentially heated is studied. The hot wall is wavy with three undulations. The aspect ratio of the cavities has also been changed. Various inclination angles were performed. The flow and the heat transfer are calculated by solving both Navier–Stokes and the energy equations with finite volume method in the primitive formulation.

The sinusoidal distribution of temperature is imposed at the vertical walls and was compared with isothermal boundary conditions. The flow and the heat transfer are also simulated for different wavelength of the sinusoidal distribution. It was found that this parameter has an effect on the trend of the local Nusselt number.

The results obtained show that the trend of the local Nusselt number is wavy for all inclination angles and for all the configurations tested. The mean Nusselt number decreases comparing with the Nusselt number of the square cavity. Non-uniform boundary conditions of the temperature distribution in both vertical walls increase the local and the mean Nusselt number comparing with the isotherm walls. The sinusoidal distribution seems to reduce the heat transfer rate for two wavelengths and increasing aspect ratio results in a decrease of the Nusselt number.