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A critical factor in the design of combustion systems for optimum fuel economy and emission performance lies in adequately predicting thermodynamic irreversibilities associated with transport and chemical processes. The objective of this study is to map these irreversibilities in terms of entropy production for methane combustion. The numerical solution of the combustion process is conducted with the help of a Fluent 6.1.22 computer code, and the volumetric entropy production rate due to chemical reaction, viscous dissipation, and mass and heat transfer are calculated as post-processed quantities with the computed data of the reaction rates, fluid velocity, temperature and radiative intensity. This paper shows that radiative heat transfer, which is an important source of entropy production, cannot be omitted for combustion systems. The study is extended by conducting a parametric investigation to include the effects of wall emissivity, optical thickness, swirl number, and Boltzmann number on entropy production. Global entropy production rates decrease with the increase in swirl velocity, wall emissivity and optical thickness. Introducing swirling air into the combustion system and operations with the appropriate Boltzmann number reduces the irreversibility affected regions and improves energy utilization efficiency.