###### Abstract
For the premixed methane impinging flame jet (PMIFI), the peak heat flux is located near the reaction region, and both the velocity and temperature are found to reach the highest values in this region. This is due to the diffusion and exothermic recombination of dissociated substances in the boundary layer around the heated object, raising the convective heat transfer rate and heat flux [22]. [PERSON] [23] studied the effects of Reynolds number and equivalence ratio on premixed butane IFJs at a fixed nozzle-to-plate distance. The results indicate that the heat transfer to the impingement plate increases with the Reynolds number due to the turbulence enhancing the mixing of fuel and air, increasing the combustion rate. Furthermore, it is found that maximum heat transfer occurs under slightly fuel-rich conditions. Finally, it is proposed to match the flame length to the distance from the nozzle to the plate, which is crucial for achieving optimal heat transfer. [PERSON] and [PERSON] [24] experimentally studied the heat transfer performance of PMIFJs. The thermal efficiency was found to increase with increasing Reynolds number and equivalence ratio. The thermal efficiency decreases as the distance of nozzle-to-plate increases. They also established an empirical correlation between the stagnation point Nusselt number and three parameters (Reynolds number, equivalence ratio, and nozzle-to-plate distance). The maximum deviation is 12% compared to the experimental stagnation point Nusselt number. [PERSON] et al. [25] conducted experiments using premixed butane IFJs to establish empirical correlations between the average Nusselt number and Reynolds number, equivalence ratio, and nozzle-to-plate distance. Compared with the experimental average Nusselt number, the maximum deviation is 13.3%. In addition to using experimental methods for research, numerical simulation methods can provide an augmented understanding of the correlation between the flow field and heat transfer of IFJs. [PERSON] and [PERSON] [26] used the computational fluid dynamics (CFD) method and simplified methane chemical reaction mechanisms to study the flow field and heat transfer characteristics of PMIFJs. The results show that the local peak heat flux is away from the stagnation region, which is caused by the change of the peak axial velocity close to the plate. [PERSON] et al. [27] studied PMIFJs produced by square and rectangular burners through CFD and a simplified methane chemical reaction mechanism. The simulated results show that the vortices formed near the corner of the tube produce an axis-switching phenomenon, causing the heat flux distribution on the impingement plate to be rotated. [PERSON] et al. [28; 29] adopted the CFD and a methane-air two-step global reaction mechanism to simulate the behavior of the flow field and heat transfer of several double-swirling flames impinging a flat plate without simplifying complex geometries and gain insights into their correlations. [PERSON] et al. [30] used the CFD and the detailed chemical reaction mechanism of methane (GRI-Mech 3.0) to accurately capture the relevant phenomena that occur in the partially premixed flame of methane, such as the jet's velocity decay, the structure of inner premixed cone and diffusion zone, the temperature distribution on the wall, and pollutants emission. It further provides the factual standard for the design of natural gas burners. Numerical simulation has become an indispensable part of today's engineering. It provides a powerful tool that enables engineers to evaluate and analyze various engineering systems and processes more quickly and effectively [31; 32]. CFD is commonly utilized to optimize the design and operating parameters of practical engineering problems [33; 34; 35]. However, the difficulties in CFD optimization are high computational costs and time constraints due to the need to consider the complexity of the geometry, the number of meshes, the applicability of the model, and the complexity of the chemical reaction mechanism.