The computational study of natural convection within porous enclosures with curved (concave/convex) horizontal walls is carried out via the heatline and entropy generation approach. The numerical simulation has been carried out for air at Prandtl numbers, Prm = 0.7 for various Darcy numbers (10-5 ≤ Dam ≤ 10-2) at a high Rayleigh number, Ram=106 with different wall curvatures. The heatlines approach, (mathematically represented as heatfunction) is employed for the heat flow visualization. In addition, the localized entropy generation due to heat transfer and fluid friction are also illustrated for various wall curvatures. Finally, the optimal situation is recommended based on the less entropy production and high heat transfer rate. © 2016, Dalian University of Technology. All rights reserved.