The present paper reports numerical results of the melting driven natural convection in an inclined rectangular enclosure filled with nano-enhanced phase change material (NePCM). The enclosure is heated from the bottom side by a flush-mounted heat source (microprocessor) that generates heat at a constant and uniform volumetric rate and mounted on a substrate (motherboard). All the walls are considered adiabatic. The purpose of the investigation is analyzing the effect of nanoparticles insertion by quantifying their contribution to the overall heat transfer. Combined effects of the PCM type, the inclination angle and the nanoparticles fraction on the structure of the fluid flow and heat transfer are investigated. A 2D mathematical model based on the conservation equations of mass, momentum, and energy was developed. The governing equations were integrated and discretized using the finite volume method. The SIMPLE algorithm was adopted for velocity–pressure coupling. The obtained results show that the nanoparticles insertion has an important quantitative effect on the overall heat transfer. The insertion of metallic nanoparticles with different concentrations affects the thermal behavior of the heat sink. They contribute to an efficient cooling of the heat source. The effect of nanoparticles insertion is also shown at the temperature distribution along the substrate.