This study considers numerical simulation of the combustion of methane with air including 21% oxygen and 79% nitrogen in a burner and the numerical solution of the local entropy generation rate due to the high temperature and velocity gradients in the combustion chamber for various fuel flow rates (from 5 to 10 lpm). Swirling air flow is also used to burn the methane more efficiently. The effects of equivalence ratio (phi) and swirl number (S) on the combustion and entropy generation rate are investigated for different (consecutive) equivalence ratios (from 0.5 to 1.0) and swirl numbers (from 0 to 0.3). The numerical calculation of combustion is performed individually for these cases with the help of the Fluent CFD code. The volumetric entropy generation rate distributions and the other thermodynamic parameters are calculated numerically by using the results of the combustion calculations. The maximum values of the rates of reaction-1 and -2 decrease with the increase of phi. In the case of phi < 1, complete combustion occurs, and the combustion in the case of phi = 1 is very close to the complete combustion state. In the case of no swirl, the entropy generation rate decreases exponentially with the increase of 0 in the cases of high Q(f), whereas they have quadratic profiles having their minimum values in cases of low Qf. In terms of the entropy generation rates, the optimum equivalence ratios for Q(f) = 5, 6, 7, > 7 lpm in the case of S = 0 and Q(f) = 10 lpm in the case of S = 0.3 are obtained as 0 = 0.66, 0.8, 0.86, 1.0 and 0.92, respectively. (c) 2004 Elsevier Ltd. All rights reserved.