# Enhanced Heat Transfer Study of Spherical Heat Storage Based on Response Surface Methodology
## 4 Conclusions  
In this study, by building an experimental system for melting spherical heat storage units, selecting the number of pin fins, water bath temperature, and the content of CuO nanoparticles added in paraffin as variables and the melting time of composite PCM as the target value, the following conclusions were obtained using the response surface methodology to optimize the target value:  
1. CCD was used to design the experimental conditions, and the data were imported into Design-Expert software to obtain the quadratic polynomial regression model of melting time. The analysis of variance showed that the regression model was significant, and the comparison analysis between the experimental and predicted values of melting time further proved that the obtained model had high reliability in fitting the melting time throughout the experimental design range.
2. The effect of the interaction between the factors on the melting time was analyzed using the response surface methodology. Among them, the water bath temperature has a large effect on the response value of PCM melting time in the spherical heat storage unit, and the interaction between the water bath temperature and the number of pin fins has the most significant effect on the melting time. The addition of CuO nanoparticles enhances heat transfer, but the effect is not particularly significant compared to the other two influencing parameters.
3. Using the optimal module of Design-Expert software, the optimal operating conditions of the system were obtained as follows: six pin fins were added to the spherical thermal storage unit, the water bath temperature was \(75\)\({}^{\circ}\)C, the mass fraction of CuO nanoparticles was 5 wt%, and the melting time of PCM was the shortest, 79.7 min. Using the response surface method, a model for predicting the melting time was further developed, and the results of this study are useful for the design of the spherical thermal storage unit. The results of this study will have a guiding significance for the design of spherical thermal storage units.  
Computational analysis using the RSM is used to improve and optimize the statistical properties of the optimization objective to some extent. This research has achieved some results; however, there is still some distance from the practical application. The spherical phase change heat storage unit is not used alone in practical applications, and subsequent research should continue to explore other influencing factors that may affect the heat storage and release performance of the spherical phase change heat storage unit for in-depth study.  
Conceptualization, R.T.; methodology, L.L.; software, L.L.; validation, X.G.; formal analysis, R.T.; investigation, Y.Z.; resources, R.T.; data curation, L.L.; writing--original draft preparation, L.L.; writing--review and editing, R.T.; visualization, X.G.; supervision, Y.Z.; project administration, L.L.; funding acquisition, X.G. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Inner Mongolia Autonomous Region Natural Science Fund, grant number 2023 QN05039 and the Scientific Research Projection of Higher Schools of Inner Mongolia, grant number NJZY23115.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
**Conflicts of Interest:** The authors declare no conflict of interest.