## 4 Conclusions  
In the indoor unit of an air conditioner using low-GWP refrigerants, the optimization of the slit length, width, and height of wavy-slit fins did not yield any improvements in the objective functions [20]. To address this issue, we introduced the RSM to optimize the fin shape while taking into consideration the interactions that take place between different parameters. This approach enabled the determination of the optimal design for two objective functions: reduced pumping power and volume goodness factor. The flow and temperature fields were analyzed for each shape, and the performance metrics were evaluated. The key conclusions obtained from this analysis are as follows:  
(1) In the regression model for pumping power, a local minimum was observed near the boundary of the design range with respect to the relationship between slit length and height, while an optimal point was anticipated outside the design range with respect to the relationship between slit length and width. For the relationship between slit height and width, a stationary point was identified at the boundary of the design range. In contrast, the regression model for the volume goodness factor best predicted the optimal point through a quadratic interaction between slit length and height. Additionally, a stationary point was observed at the midpoint between slit length and width, while another stationary point was found between slit height and width. (2) In the model designed to minimize pumping power while maintaining a fixed heat transfer rate for the baseline configuration, the analysis of the flow and temperature fields revealed that the flow branching through the slits resulted in the vigorous mixing of the upper and lower surface flows, leading to a more uneven flow distribution. The largest separation zone was observed in the downstream flow of the duct. Although the pressure drop decreased, and the heat transfer rate declined to a minimal extent, under the design flow conditions, the heat transfer rate decreased by 0.55%, while the pumping power decreased by 2.05%. Additionally, the Colburn j-factor decreased by 2.11%, while the f-factor decreased by 1.78%. The reduction in pumping power was also maintained under partial load conditions. (3) In the Gv optimization model, which aimed to maximize the volume goodness factor, the flow was divided into upper and lower branches after the duct through the slits was relatively uniform. The separation zone in the downstream flow of the duct was the smallest. Although the volume goodness factor improved, additional pumping power was required. Under the design flow conditions, the volume goodness factor increased by 1.85%, while the Colburn j-factor increased by 3.87%, and the f-factor increased by 6.09%. Under partial load conditions, the increase in pumping power was more significant. Future work: The pumping power was not significantly influenced by the geometric parameter of slit width, resulting in only minor performance improvements. Moreover, the optimal point was found to be outside the geometric constraint range. This suggests the need for a study that includes the analysis of the effects of other dominant geometric variables, identifies the most influential parameters, and adjusts the experimental points using a sequential experimental design, such as the steepest ascent method, to develop a nonlinear model. **Author Contributions:** [PERSON] and [PERSON] carried out the simulations, analyzed the CFD data, and wrote the paper. [PERSON] supervised the research, analyzed the CFD data, and wrote the paper. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Ministry of Trade, Industry and Energy (MOTIE) of the Republic of Korea (No. 20212020800070). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.