Analysis of natural convection within inclined porous square cavities for various inclination angles (φ=15°, 30° and 60°) is carried out via the heatline and entropy generation approaches. The cases 1 and 2 correspond to the isothermal and non-isothermal heating of the bottom wall, respectively, involving the cold side walls and adiabatic top wall. The governing equations are solved via the Galerkin finite element method to obtain the results in terms the isotherms (θ), streamlines (ψ), heatlines (Π), entropy generation maps (Sθ and Sψ), total entropy generation (Stotal), average Bejan number (Beav) and average Nusselt number (Nu¯AB) at various Darcy numbers (10−5≤Dam≤10−2), Prandtl numbers (Prm=0.025 and 998.24) at Rayleigh number, Ram=106. The locations of Sθ,max and Sψ,max are identified and the magnitudes of Sθ,max and Sψ,max are larger for the case 1 compared to those for the case 2 involving all Dam, Prm and φ. Also, the magnitudes of Stotal, Beav and Nu¯AB are larger for the case 1 compared to the case 2. The case 2 is the efficient heating strategy with the optimal thermal management compared to the case 1 based on significantly lesser Stotal for all Dam, Prm and φ. The optimal φ involving the lesser Stotal and larger Nu¯AB is highly influenced by Dam and Prm. Various ranges of the optimal φ involving the higher thermal efficiency are identified for different Dam and Prm for each of the cases (cases 1 and 2). © 2016 Elsevier Ltd