The purpose of the current study is to numerically investigate the effects of shape factors of nanoparticles on natural convection in a fluid-saturated porous annulus developed between the elliptical cylinder and square enclosure. A numerical method called the control volume-based finite element method is implemented for solving the governing equations. The modified flow and thermal structures and corresponding heat transfer features are investigated. Numerical outcomes reveal very good grid independency and excellent agreement with the existing studies. The obtained results convey that at a certain aspect ratio, an increment in Rayleigh and Darcy numbers significantly augments the heat transfer and average Nusselt number. Further, enhancement of Rayleigh number increases the velocity of nanofluid, while that of aspect ratio of the elliptical cylinder shows the opposite trend.