Computational study of natural convection within differentially heated enclosures with curved (concave/convex) side walls is carried out via entropy generation analysis. Numerical simulation has been carried out for various Prandtl numbers (Pr=0.015 and 1000) and Rayleigh numbers (103≤Ra≤105) with different wall curvatures. Results are presented in terms of isotherms (θ), streamlines (ψ), entropy generation due to heat transfer (Sθ) and fluid friction (Sψ). The effects of Rayleigh number on the total entropy generation (Stotal), average Bejan number (Beav) and global heat transfer rate (Nur) are examined for all the cases. Maximum values of Sθ (Sθ,max) are found at the middle portion of the side walls for concave cases, whereas, Sθ,max is observed near the top right and bottom left corner of the cavity for convex cases. On the other hand, Sψ,max is seen near the solid walls of the cavity for all concave and convex cases. At all Ra and low Pr, largest heat transfer rate and lesser entropy generation is found for case 3 (highly concave case). Overall, for convex case, case 1 or case 2 (lesser convex cases) are efficient for all Ra and Pr. On the other hand, case 3 of concave case (highly concave) offers larger heat transfer rate and lesser entropy generation compared to less concave and all convex cases at low Ra and all Pr. At high Ra and low Pr, case 3 (concave) may be the optimal case whereas, at high Ra and high Pr, case 1 (less concave) may be recommended based on higher heat transfer rate. A comparative study of the concave and convex cases also revealed that the concave cases with high concavity (case 3) may be chosen as the energy efficient case at high Ra and high Pr. © 2014 Elsevier Ltd. All rights reserved.