The current study deals with the heatline-based analysis of natural convection in porous cavities with the curved top and bottom walls involving the Rayleigh–Bénard heating. The streamline cells are weak, and the wall-to-wall heatlines are observed for all the cases at the low Dam involving two test cases, Prm = 0.015 and 7.2. At the high Dam, the convective force takes the command, and multiple heatline cells are observed for all the concave (except for high wall concavity) and convex cases. The directions of the streamlines (for all Dam) and heatlines (at the high Dam) are exactly opposite for the concave and convex cases. The case 3 (concave) is the efficient case based on the largest heat transfer rate for Prm = 0.015 involving all Dam and for Prm = 7.2 involving the low Dam. At Prm = 7.2 and high Dam, the case 1 (concave or convex) may be the efficient cases compared with the cases involving high wall curvatures. © 2017 Taylor & Francis.