Abstract The free convective flow of a Nano-Encapsulated Phase Change Material (NEPCM) suspension in an eccentric annulus is investigated numerically. The inner cylinder is heated and kept at a temperature higher than that of the outer cylinder. The core of the NEPCM particles is made of nonadecane while the shell is made of Polyurethane. The nanoparticles are dispersed in water as the base fluid. The equations governing the flow and heat transfer of the NEPCM suspension in the annulus are developed and written in the non-dimensional form. The numerical solutions of these equations are obtained using the finite element method. The validity of the numerical method is ensured by comparing its predictions to the results of previously published studies. The main outcomes point out to the impact of the volume fraction of the NEPCM particles and Stefan number on the thermal and hydrodynamic characteristics of the suspension. A 5% volume fraction represents the optimal value for heat transfer enhancement. Heat transfer is also enhanced when the fusion temperature of the NEPCM core is far from the temperatures of the hot and cold walls. Furthermore, increasing the annulus eccentricity and moving the inner cylinder towards the top tends to inhibit heat transfer in the annulus.