In industrial furnace applications, the interaction between the flame plume and the surface of the heat exchanger plays a crucial role in heat transfer efficiency, particularly given the current emphasis on energy conservation. Traditional research methods require adjusting independent variables to observe changes in dependent variables, leading to a large amount of experimental conditions. Hence, the equivalent simplification of problem complexity and the establishing of predictive models are crucial for applying premixed flames in engineering fields. In the present study, the three-dimensional computational fluid dynamics (CFD) method was employed alongside the assumption of isothermal flow to conduct a numerical investigation into the methane premixed impinging flat flame. The Reynolds number \((\text{Re})\) , the distance from the normalized nozzle to plate \((H/d)\) , and the influence of the inlet temperature \({(T}_{\text{in}})\) on the high-temperature isothermal impinging jet and local heat transfer characteristics were explored. The results indicated that the spread rate of the jet increased with rising \(\text{Re}\) , while the inlet temperature exhibited minimal effect. Furthermore, it was observed that the local Nusselt number increased with increasing \(Re\) and decreasing \(H/d\) . When appropriate adiabatic wall temperatures were taken into account, the local Nusselt number distribution was found to be independent of the inlet temperature. Additionally, a close relationship was identified between the spread rate of the jet and local Nusselt number. The surrogate model, specifically the Kriging model (KM), was utilized to analyze the interactive effects of variable on global heat transfer performance. The findings demonstrated that the average Nusselt number increased with increasing \(\text{Re}\) and decreasing \(H/d\) , with a slight increase also observed with rising \({T}_{\text{in}}\) . Sensitivity analysis revealed that the influence level of variables on the average Nusselt number followed the order of \(\text{Re}>H/d>{T}_{\text{in}}\) . Moreover, KM with promising predictive capabilities was achieved through the infilled criterion aimed at minimizing maximum root mean square error (RMSE), thereby significantly reducing both maximum and average relative errors.
