## 1 Introduction
Therefore, CFD has been extensively utilized for the optimization of fin shapes for air conditioners [15]. [PERSON] et al. [16] optimized the geometric parameters of fins using CFD to enhance the heat transfer performance of the herringbone wavy-slit heat exchanger. The geometric parameters selected were waffle height, fin pitch, and wavelength, and the optimal design was determined based on these variables. [PERSON] et al. [17] simulated the heat transfer and fluid flow of a wavy fin-tube heat exchanger equipped with delta-winglet-type vortex generators (VGs). The corrugation height of the fins and the attack angle of the delta-winglet VGs were optimized using the CFD results, with the Colburn j-factor and f-factor as the respective objective functions. [PERSON] et al. [16] considered only the wavy shape in their study. However, for wavy-slit fins, the geometric parameters of the slits also affect heat transfer and flow characteristics. The variations that occur in recirculation zones and vortex generation due to these parameters directly impact heat transfer performance [14]. Additionally, the heat transfer area of the fins changes based on the height, width, and length of the slits. While research has been conducted on the effects of the geometric parameters of slits in wavy-slit fins [18], there have been no studies that have explored the notion of optimizing these fins by considering the comprehensive effects of their geometric parameters. An analytical validation of small-diameter wavy-slit fins was carried out by [PERSON] [19]. Subsequently, in the study by [PERSON] and [PERSON] [20], the effects of various factors were analyzed with the aim of improving performance. The impact of the three slit factors (length, width, and height) on heat and pressure indicated that as the slit height increased, both the j- and the f-factor initially increased and then decreased after reaching optimal values, whereas, as the slit width increased, the reduction in the j- and f-factor became less pronounced. Finally, as the slit length increased, the j-factor initially increased but then decreased, while the f-factor continued to increase, exhibiting a differing trend. No significant correlation was found between the shape factors and the j- and f-factor, and the shapes optimized based on their performance in each individual setting did not achieve optimal performance due to the interactions among the factors [19; 20]. Therefore, this study introduced the response surface method (RSM) [21; 22] to carry out optimization for two objective functions. As done in a previous study [20], the longitudinal pitch (\(P_{l}\)) and transverse pitch (\(P_{l}\)) of the wavy-slit fin (shown in Figure 1) were fixed, while the slit length (\(L\)), width (\(W\)), and height (\(H\)) were taken as geometric variables. Using the RSM, various shapes were generated by combining the geometric variables \(L\), \(W\), and \(H\), and a CFD analysis was performed. Two objective functions were considered for optimization. First, the reduced pumping power function was established, which minimizes pumping power while maintaining a fixed heat transfer rate, as suggested by [PERSON] et al. [23] and [PERSON] et al. [10]. Second, the volume goodness factor (Gv), defined by [PERSON] et al. [24] to achieve the maximum heat exchange rate for a given volume and pumping power [25], was set as the objective. In this study, the geometric variables of the slits in wavy-slit fins, which were intended for use in small-diameter indoor evaporators of air conditioners with low-GWP refrigerants, were optimized using the RSM. This paper presents two optimized shapes that were obtained using reduced pumping power and Gv as the objective functions. The flow and temperature fields of the reference shape and the two optimized shapes have been compared to review the mechanisms through which performance is improved according to the objectives.