Abstract In this study, the thermal performance of an unsteady, one-dimensional model, and irreversible of a CH4-air reacting process is investigated. Due to the fundamental differences between the free flame and porous structures such as flame thickness and the length of the preheated zone, it is necessary to employ a chemical kinetic which in accordance with the structure of a porous duct made of cellular ceramic, even if it is very simple. To achieve this aim, CH4 oxidation with the five-step reaction mechanism is considered to simulate the combustion phenomenon in the porous burner. In order to solve the governing equations, a finite volume method is used to discretize the governing conservation equations of the problem. Transient, displacement and diffusion terms were respectively solved using completely implicit schemes, Upwind, and discretized central difference and the resulting algebraic equations by the TDMA repeated procedure. In this research, the segregated method was used to solve the set of equations, in which the suitable convergence condition for the governing variables of the problem was used. After validation of the obtained results with available experimental data, the effects of the solid matrix porosity density, porosity, length, extinction coefficient as well as the effects of fire rate, equilibrium ratio, and inlet temperature are investigated. The results show any changes in solid matrix properties and inlet conditions lead to significant changes in combustion structure.