The present study deals with the finite element based numerical simulations of heat transfer and entropy generation rates during natural convection for fluid saturated porous media in enclosures involving curved walls (case 1: lower curvature and case 2: higher curvature) with various thermal boundary conditions. The differential heating (isothermally hot left wall and cold right wall and adiabatic horizontal walls) and Rayleigh-Bénard heating (isothermally hot bottom wall and cold top wall involving adiabatic left and right walls) are considered. The locations and magnitudes of the entropy generation due to heat transfer (Sθ) and fluid friction (Sψ) are presented and discussed based on the spatial distributions of isotherms and streamlines, respectively. The magnitudes of local entropy generation (Sθ,Sψ), total entropy generation (Stotal) and average heat transfer rates (Nur‾ and Nut‾) are significantly lesser for the Rayleigh-Bénard heating compared to the differential heating for all the cases involving all Dam and Prm. The Rayleigh-Bénard heating is the optimal strategy for all Dam and Prm involving both the concave cases except for 10-3⩽Dam⩽10-2,Prm=10 and case 1 (concave) domain. The Rayleigh-Bénard heating is also the optimal strategy compared to the differential heating involving the convex cases at 10-5⩽Dam⩽10-4 whereas the differential heating is the optimal heating strategy for Dam⩾10-3 involving both Prm for the convex cases. © 2018