In this paper, a symmetric two-dimensional numerical model for premixed methane-air combustion in a porous medium has been developed. For this purpose, multi-step mechanisms and variable porosity have been used and the effects of them on the entropy generation rate have been investigated. This model solves the continuity, Navier Stokes, the solid and gas energy, the chemical species transport equations and entropy generation rate equations by using thefinite volume method and the pressure and velocity have been coupled with the SIMPLE algorithm. The results reveal that the entropy generation due to heat transfer has the highest contribution to entropy generation and after that are the chemical reactions, mass diffusion, and friction respectively. When used from porosity variation the entropy generation rate due to heat transfer, chemical reaction and friction are reduced and for the entropy generation due to mass diffusion is vice versa.

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