###### Abstract
Surrogate models are proposed as solutions to solve the above problems of CFD optimization. Therefore, this method is called surrogate-based optimization (SBO). Common surrogate models include the response surface method (RSM) [36], support vector regression (SVR) [37], radial basis function (RBF) [38], and Kriging model (KM) [39]. In these surrogate models, KM takes values from regionalized variables in finite regions and makes optimal and unbiased estimates from the perspective of the correlation and variability of variables. In addition, KM provides predicted mean and variance and establishes various learning functions to estimate failure probability and uncertainty accurately. Therefore, compared with other models, KM has higher fitting accuracy and can better approximate complex functions [40; 41; 42]. Surrogate models must cautiously be used due to the possible impact of new errors, although they can quickly obtain analytical results. Hence, the suitability of surrogate models must be carefully evaluated to ensure valid and accurate results, allowing for correct decisions to be made [43]. According to the previous literature review, empirical correlation was used to predict the heat transfer performance of unknown points for IFJs in the past, and the predicted values were found to deviate significantly from the actual values. In addition, since the optimization method for the heat transfer performance of IFJs has yet to be given, the optimal operating parameters of PMIFJs are worth exploring. This study uses experimental and numerical simulation methods to study PMIFJs. This study used the equivalence ratio, Reynolds number, and nozzle-to-plate distance, which are common in the previous literature, as research parameters. The experimental data serve as a validation of the numerical simulation to ensure its reliability. In terms of numerical simulation, obtaining the global heat transfer behavior and optimal solution using the CFD method and the detailed GRI-Mech 3.0 mechanism is quite challenging because of the complexity of the mechanism and the large number of computational resources required to consider all three parameters. Therefore, the SBO method is used to solve this problem, which is also the main contribution of this paper. The KM is chosen as the surrogate model. Its Gaussian basis function has independently different variance values in different dimensions, which enables the model to capture changes in the parameter space more accurately, thereby obtaining more accurate and optimized response surfaces. Hence, global information within specific parameters can be gained by fewer simulations, and target values at unknown parameters can be further predicted. Furthermore, the genetic algorithm (GA) is used to determine three optimization problems: maximizing the likelihood function in KM, the new infilled points according to maximizing root mean square error (RMSE), and the operating parameters of optimal heat transfer performance. The subsequent sections of this paper are structured as follows. Section 2 introduces the experimental setup and measurement methods. Section 3 provides the working process of the CFD method, mesh independence testing, and model validation results. Section 4 introduces the principles and working process of the SBO method and further elaborates on the details of each process. Section 5 provides optimized KM results and discusses the effect of operating parameters on heat transfer performance and the results of sensitivity analysis and optimization. Finally, Section 6 provides the conclusions of this study.