# Enhanced Heat Transfer Study of Spherical Heat Storage Based on Response Surface Methodology
## 2 Experimental Procedure  
### Design of Experiments  
Paraffin mainly comprises straight-chain compounds. The latent heat and temperature of the phase transition of paraffin change with the growth of the carbon chain and increase with the growth of the carbon chain under normal circumstances. As the carbon chain grows and the melting point increases, the growth rate starts out fast, but it becomes slower and slower as the chain increases. However, the thermal conductivity of paraffin wax is low. Obviously, this lower thermal conductivity results in a low heat storage/release rate. In order to solve the problems of the low thermal conductivity, uneven temperature distribution, and low heat storage/release rate of pure paraffin PCMs, this study used composite PCMs to improve the thermal performance of paraffin PCMs. Paraffin wax was used as the phase change material. With the \"two-step\" method, a certain amount of paraffin wax was weighed into a beaker and then placed in a constant temperature water bath at 80 \({}^{\circ}\)C to melt the paraffin wax completely, while a certain amount of CuO nanoparticles were weighed and added to the melted paraffin wax. The CuO nanoparticles were added to the melted paraffin wax and stirred with a magnetic stirrer for 30 min to make them fully integrated and then treated with an ultrasonic shaker for 60 min to disperse the CuO nanoparticles evenly in the paraffin wax to prepare a CuO/paraffin wax composite phase change material. Figure 1 shows the variation curve of the latent heat of phase transition of CuO/paraffin wax composite phase change materials in the case of different mass fractions measured using DSC. Two 304 stainless-steel hemispherical vessels were selected and flanged externally, and the two hemispheres were encapsulated into a complete spherical vessel using bolts, resulting in the spherical shell of the phase change heat storage unit used in this study. The inner diameter of the sphere was 97 mm, the thickness was 1.5 mm, and the sphere was welded with 3 mm-diameter pin fins made of aluminum alloy in quantities of 2, 4, and 6, as shown in Figure 2.  
The composite phase change materials filled the heat storage sphere through small holes in the top of the sphere shell. The sphere shell was heated using an electric heating furnace to completely melt the composite phase change materials, which were added to the sphere in small quantities. Considering the thermal expansion of the phase change materials, the filling was terminated when the liquid phase change materials filled in the spheres reached a fixed height to ensure that no overflow would occur. The experimental test system for melting within a spherical heat storage unit is shown in Figure 3. It mainly consisted of a constant temperature water bath, TP700 multi-channel data logger, thermocouples, and a heat storage sphere. K-type thermocouples were used for temperature testing and were arranged inside the sphere to record the internal temperature changes of the phase change materials during the melting process in real time. The locations of the thermocouples are shown in Figure 3. The duration the temperature at all monitoring points took to reach a steady-state value of 0.99 was taken as the melting time. Figure 1: Curve of latent heat of phase change materials using DSC. Figure 2: Distribution of fins inside the phase change heat storage sphere. At a water bath temperature of 70 \({}^{\circ}\)C, the temperature variation of pure paraffin with three fin quantities is shown in Figure 4a. Figure 4b shows the temperature variation in the heat storage unit for different mass fractions of CuO. For all cases, at the beginning of melting, the heat in the water bath was transferred to the solid PCM, which absorbed heat and warmed up. When the temperature approached the phase change temperature, the solid PCM started to undergo phase change, and all the absorbed heat was used for latent heat. Thus, the temperature underwent a period of slower change.