Two-dimensional numerical simulations were conducted to investigate the natural convection heat transfer induced by the temperature difference between cold walls of the tilted square enclosure and a hot inner circular cylinder for different Prandtl numbers (10(-2) <= Pr <= 10(2)) and Rayleigh numbers (10(3) <= Ra <= 10(6)). The numerical solutions are obtained using an accurate and efficient immersed boundary method. The outer square enclosure is tilted from gamma = 0 degrees to gamma = 45 degrees by each 5. Detailed analysis results including the distribution of streamlines, isotherms and Nusselt numbers are presented. The entropy generation and corresponding Bejan number in the enclosure are analyzed to estimate the thermo-dynamic irreversibility accompanied by the natural convection in the system. (C) 2016 Elsevier Ltd. All rights reserved.