###### Abstract  
In practical applications, rapid prediction and optimization of heat transfer performance are essential for premixed methane impinging flame jets (PMIFJs). This study uses computational fluid dynamics (CFD) combined with a methane detailed chemical reaction mechanism (GRI-Mech 3.0) to study the equivalence ratio (\(\phi\)), Reynolds number (\(Re\)) of the mixture, and the normalized nozzle-to-plate distance (\(H/d\)) on the heat transfer performance of PMIFJs. Moreover, the Kriging model (KM) was used to construct a prediction model of PMIFJ heat transfer performance. A genetic algorithm (GA) was used to determine the maximum likelihood function (MLE) of the model parameters for constructing KM and identify the points with the maximum root mean square error (RMSE) as the new infilled points for surrogate-based optimization (SBO). Combining these methods to analyze the simulation results, the results show that the global heat transfer performance of PMIFJs is enhanced with the increase in \(\phi\), the increase in \(Re\), and the decrease in \(H/d\). Sensitivity analysis points out that \(Re\) and \(\phi\) significantly affect enhanced heat transfer, while \(H/d\) has a relatively small effect. In addition, GA was also used to search for the optimal heat transfer performance, and the global heat transfer performance at specific conditions was significantly enhanced. This study deepens the understanding of the heat transfer mechanism of impinging flame jets and provides an efficient method framework for practical applications. premixed methane flame; impinging flame jet; computational fluid dynamics; Kriging model; genetic algorithm +
Footnote †: journal: Medical  
is much more complex than traditional isothermal impact jets. According to previous research reports, IFJ mainly uses forced convection as the heat transfer mechanism [10]. Previous studies have confirmed that in impinging flame jets that use air as the oxidant, forced convection heat transfer accounts for 70% to 90% of the total heat transfer in the impinging region [11; 12]. The thermal radiation from the flame can be ignored since the emissivity of the hot gas layer is very low [13]. [PERSON] et al. [14] pointed out that the TCHR mechanism is significant in hydrocarbon fuel flames under pure oxygen or oxygen-rich conditions and can reach up to 60% of the total heat transfer. However, the effect on heat transfer in premixed methane-air flames is minimal and, therefore, can be ignored. In addition, the interaction between the flame and the wall produces flame structures with different characteristics depending on the position of the collision flame [15; 16], and it plays a critical role in the near-wall combustion process of various combustion equipment and power engines [17; 18]. Many parameters affect the heat transfer performance of IFJs. These include the geometry and design of the burner, the flame type, the operating conditions (fuel composition, Reynolds number of the jet, and the equivalence ratio of the mixture), and the distance of nozzle-to-plate. [PERSON] and [PERSON] [19] studied the influence of different burner geometries (tube, nozzle, and orifice) on the heat transfer characteristics of IFJs. It was found that the heat flux in the stagnation and wall jet regions is different, resulting in different flame lengths and shapes due to different exit velocity profiles. Compared to the heat flux distribution of the nozzle and orifice burner, the tube burner is non-uniform. [PERSON] and [PERSON] [20] studied the heat transfer characteristics of diffusion and premixed methane flame impingement on cold steel plates. Compared with diffusion flame, the maximum heat flux of premixed flame is higher because premixed flames can increase the combustion rate and promote faster combustion completion. [PERSON] et al. [21] indicated that as the Reynolds number increases, the reaction region of the premixed methane flame will extend further downstream and become wider.