This paper concerns a numerical work on unsteady non-homogeneous modeling of natural convection of a nanofluid inside horizontal annular heat exchanger with two eccentric cylinders. The study is formulated in terms of the vorticity-stream function procedure. The Buongiorno model is used, and the governing equations were resolved by finite volume method. Results concern three eccentricity values and three Rayleigh numbers. The distribution of the nanoparticles displays a particular dependency to the low Rayleigh numbers in both eccentric and concentric annulus.