In this study, the numerical investigation focused on the impact of incorporating porous fins within the inner region of a concentric cylinder. The inner part of the cylinder contains nano-liquid, and the outer surface is exposed to stagnant air. The natural convection heat transfer phenomenon has been systematically examined by varying dimensionless parameters, Rayleigh number (103 ≤ \(Ra\) ≤ 105), Hartmann number (0 ≤ \(Ha\) ≤ 40), and Darcy number (0.01 ≤ \(Da\) ≤ 100). In our analysis, a decrease in velocity is identified in correlation with an increase in the magnetic parameter, (i.e., Hartmann number). The discretized governing equations are solved using the finite volume method (FVM). The variation in dimensionless numbers results in reported values for the average Nusselt number \((Nu)\) and entropy generation. Specifically, at a constant Rayleigh number, an increase in the Hartmann number leads to an augmentation in entropy generation, while a decrease is noted with an increase in the Darcy number. The fluid dynamics and heat transfer phenomena in this investigation are visually represented through isotherms and velocity streamlines. The present investigation has many engineering applications, including oil separation, solar power collection, energy-efficient drying, porous heat exchangers, thermal insulation, food storage, and solidification processes. In the presence of a magnetic field, heat transfer is reduced by 4.35% at a fixed \(Ra\) and \(Da\) . However, the \(Nu\) increases up to 100% as the \(Ra\) increases from 103 to 105 for the constant value of the \(Da\) , and \(Ha\) .
