The natural convection is analyzed via the entropy generation approach in the differentially heated, porous enclosures with curved (concave or convex) vertical walls. The numerical simulations have been carried out for various fluids (Prandtl number: Prm = 0.015, 0.7, and 7.2) at various permeabilities (Darcy numbers: 10−5 ≤ Dam ≤ 10−2) for a high value of Rayleigh number (Ram = 106). The finite element method is employed to solve the governing equations and that is further used to calculate the entropy generation and average Nusselt number. The detailed spatial distributions of Sθ and Sψ are analyzed for all the wall curvatures. Overall, the case with the highly concave surfaces (case 3) is the optimal case at low Dam, whereas the cases with the less convex surfaces (cases 1 and 2) are the most efficient cases at high Dam. © 2017 Taylor & Francis.