# Enhanced Heat Transfer Study of Spherical Heat Storage Based on Response Surface Methodology
## 1 Introduction
[PERSON] [17] performed a numerical analysis of the inward solidification of PCM in spherical capsules. The results show that large-diameter spherical capsules have longer solidification times than small-diameter capsules. The entropy generation increases with increasing spherical capsule diameter and decreases after reaching a maximum. The enhancement of heat transfer by adding fins to the heat storage unit has been investigated [18]. [PERSON] [19] installed fins on PCM shells in horizontal and vertical directions. The results showed that the triple fins in the vertical direction and double fins in the horizontal direction had the best melting enhancement for PCM with the best fire use efficiency. [PERSON] [20] inserted copper plates inside spherical capsules to improve the latent heat storage rate of solid PCM and found that the latent heat storage rate was significantly increased. [PERSON] [21] proposed a novel heat sink model consisting of nano-enhanced phase change materials and pin fins for the thermal management of electronic devices. The effects of fin thickness and fin number on the performance of PCM fins were investigated. The results showed that the increase in fin volume fraction and nanoparticle concentration did not improve the performance of the heat sink. Because of the high thermal conductivity of the fin, the dispersion of nanoparticles in the fin radiator had no significant effect on the thermal response. [PERSON] [22] investigated the heat transfer process of PCM-confined melting in spherical capsules through experiments and numerical simulations and found a 30% reduction in melting time when the largest fin height was used. [PERSON] [23] used Ansys CFX to simulate the heat storage and release of PCM encapsulated in spheres, using pins and copper plating to improve the heat transfer of PCM within the spheres. The results showed that copper-plated spheres with pins had a 37% reduction in phase transition time compared to normal PCM spheres. [PERSON] [24] experimentally investigated frozen water in stainless-steel spherical containers with inner fins of different lengths. The resultsshow that in a spherical vessel with a diameter of 75 mm, it is recommended to install four 13.5 mm-long heat sinks to achieve maximum heat flux.v. The highly conductive fins helped accelerate the phase change and obtain the best energy-saving effect. [PERSON] [25] investigated the melting process of PCM inside a spherical capsule using numerical simulation. The melting processes of regular fins and hollow fins at different angles were compared. The results showed that the fins and their geometry play a key role in the melting process. Changing the inclination angle of the fins does not always enhance the heat transfer. However, adding hollow fins is more effective than regular fins. [PERSON] [26] investigated the effect of fin position within a spherical capsule on melting time, with an enhancement of 107.28% when the fins were centrally located. [PERSON] [27] studied the strengthening effects of metal foams and fins on ice storage spheres through numerical simulations. The temperature field, ice front evolution, solidification fraction, total solidification time, and cold storage capacity under four different strengthening modes (plane, fins, metal foam, and metal foam composite fins) were analyzed, and the optimal porosity was obtained. [PERSON] [28] studied the enhanced heat transfer of a single PCM sphere in TES systems. The results showed that adding pins to the sphere reduced the charging time by 34%. [PERSON] [29] proposed a new double-layer spherical phase change heat storage structural unit and investigated the effect of fins on its melting behavior by numerical simulation to elucidate the mechanism of enhanced heat transfer coupling between dual local natural convection and heat conduction in the spherical heat storage unit. Combining factors such as complete melting time and entropy production, the optimal installation position of the fins was determined as the outer side of the inner sphere.