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In this paper, the work and performance of the premixed methane-air porous axisymmetrical burner have firstly been simulated numerically using the CFD tools. For this purpose the set of governing equations has been enriched by an additional energy equation in porous solid, and the chemical species transport has been extended onto the multi-step mechanism (GRI-2-11). This numerical model has been verified on the base of available benchmark experiments. Next, we have studied the local entropy generation problem taking into account not only classical contributions like viscous and turbulent dissipation but also, the porous combustion of gases. The results showed that the greatest portion of entropy generation in the porous medium burner is related to chemical reactions, followed by heat transfer, mass diffusion (mixing) and friction (viscous dissipation), respectively. According to the results, as the excess air ratio increases, the local entropy generation rate due to heat transfer and friction increases and the local entropy generation rate due to chemical reactions is decreased. Also, by increasing the volumetric heat transfer coefficient, the local entropy generation rate due to heat transfer decreases and the local entropy generation rate due to friction and chemical reactions increases. Also, the local entropy generation rate due to mixing does not show a significant change with the changing excess air ratio and volumetric heat transfer coefficient. [ABSTRACT FROM AUTHOR]