Numerical simulations were utilized to examine a methane-fueled Y-channel combustor, focusing on non-premixed turbulent reacting flows, using Reynolds Averaged Navier Stokes (RANS) models. Within the context of the eddy dissipation concept (EDC), a local extinction strategy has been used to handle chemical reaction kinetics. Gaseous methane is considered as fuel to simulate the phenomenon of combustion using opensource solver OpenFOAM. The numerical model is validated using the available numerical simulations and experimental data. In addition, radiation models were used to enhance the precision of the obtained outcome in this study. To achieve a highly efficient Y-channel, numerous alterations in both parameters and geometry were implemented.