In this work, the performance of an eccentric annular finned tube heat exchanger under natural convection conditions has been investigated numerically. The objective of the study is to analyse the effect of eccentric coefficient on the rate heat flux as a function of the fin material, diameter, spacing and thicknesses. To perform the numerical simulations, 3D ANSYS FLUENT computational fluid dynamics has been used. The study has been conducted in laminar flow across the single annular finned tube with Rayleigh numbers within of (4 × 10⁴−7 × 10⁴). It is concluded that the eccentricity effect appears better in high thermal conductivity materials with small fin diameter. Regardless of the fin eccentricity, thick fins produce the best heat transfer.