In the present study, various tangential angles of effusion hole configurations were investigated to evaluate their effects on the cooling performance and combustion characteristics of a can-type combustor model. Numerical simulations were conducted using the Reynolds stress model for turbulence modeling and the steady flamelet approach within the non-premixed combustion framework to model methane combustion. The results indicated that the effusion hole configuration with a tangential angle of 0° enhanced the liner wall cooling effectiveness by approximately 340.28%. This configuration also blocked 77.71% of the absorbed radiation flux, resulting in a 47.81% reduction in wall temperature. Furthermore, the lowest pattern factor value was observed when the liner wall was designed with effusion holes at a tangential angle of ±30°, compared to other configurations. Similarly, injecting cooling air into the combusted region through effusion holes at a tangential angle of 0° led to an approximate 20.23% reduction in thermal NOx emissions.