# Enhanced Heat Transfer Study of Spherical Heat Storage Based on Response Surface Methodology
## 1 Introduction  
In recent years, phase change thermal storage technology has been used in areas such as waste heat recovery and solar energy storage to cover the differences in quantity, form, and space between energy supply and demand. Phase change thermal storage materials are widely used in latent heat storage because of their high heat storage density, almost constant temperature during the heat storage/exothermic process, wide melting point distribution, chemical stability, and corrosion resistance [1]. Paraffin waxes are stable as phase change materials, free from subcooling and phase separation, cheap, and non-toxic, but they also have drawbacks, such as low thermal conductivity. With the rapid development of nanotechnology, the addition of nanoparticles (e.g., CuO [2, 3], Al\({}_{2}\)O\({}_{3}\)[4, 5], Fe\({}_{3}\)O\({}_{4}\)[6, 7], SiO\({}_{2}\)[8, 9], etc.) with high thermal conductivity to paraffin wax has become an emerging means [10]. [PERSON] [11] prepared CuO/paraffin nanopowder composite phase change materials with mass fractions of 0.01-0.1%. The results showed that the addition of CuO nanopowder to paraffin wax could greatly improve the solar thermal conversion capacity by enhancing the light absorption capacity of the PCM. At low mass concentrations (0-0.1%), the steady-state temperature gradually increased with increasing mass fraction ofCuO nanoparticles, with a maximum increase of about 2.3 times. A nanocomposite for energy storage was prepared by [PERSON] [12] by adding 20 nm nanoparticles of Cu to paraffin wax. The addition of 2.0% Cu nanoparticles to paraffin wax was found to increase the thermal conductivity of the Cu/paraffin phase change material by 46.3%. [PERSON] [13] dispersed ZnO nanoparticles in paraffin and analyzed their thermal properties. The experimental results showed that ZnO nanoparticles distributed inside the paraffin wax without affecting its chemical structure greatly improved its thermal stability and increased its thermal conductivity to 41.67% at 2.0 wt%. [PERSON] [14] experimentally investigated the effect of hybrid nanoparticles containing SiO\({}_{2}\) and CeO\({}_{2}\) nanoparticles on the thermophysical properties of paraffin-based phase change materials (PCMs). The experimental results showed that the mixed nanoparticles spread uniformly in the paraffin matrix without affecting the chemical arrangement of paraffin molecules. When hybrid nanoparticles were dispersed in paraffin, the relative thermal stability and relative thermal conductivity of paraffin were increased synergistically, reaching 115.49% and 165.56%, respectively. In addition, the hybrid nanoparticles appropriately changed the melting point and crystallization point of the paraffin wax and reduced the degree of supercooling of the paraffin wax; the maximum degree of supercooling was reduced by 35.81%. [PERSON] [15] conducted an experimental study of the melting and solidification processes and the enhancement of thermal conductivity of PCM inside a sphere. The enhancement of the thermal conductivity of PCM by aluminum powder was investigated via homogeneous diffusion and sedimentation methods. The results showed that the addition of aluminum powder accelerated the melting and solidification processes of PCM within the sphere. However, the settling of the aluminum powder during the melting process was more conducive to accelerated heat transfer throughout the sphere than the uniform diffusion of the aluminum powder in the PCM. As the main component of a phase change heat storage system, the phase change unit is a key part of the heat transfer efficiency of the system, and the heat transfer performance is closely related to its shape and structure. Common geometries for phase change heat storage units include square, cylindrical, spherical, and toroidal. The spherical shape has the largest heat transfer area for the same volume of heat storage unit. [PERSON] [16] visualized the solid-liquid interface inside a spherical capsule through experiments and numerical simulations.