## 3 Result and Discussion
### Thermal Conductivity Analysis  
The thermal conductivity results of PEG and PEG/GNPs composites are shown in Figure 7. The thermal conductivity of PEG is only 0.316 W/mK, which fails to meet the requirements for efficient thermal storage application. Impressively, it is seen that the thermal conductivities of PEG/GNPs composites increase remarkably as the GNPs weight fraction increases. The thermal conductivity of the composite doped with 2.0 wt % GNPs (PEG/2 GNPs) is measured to be as high as 0.776 W/mK, exhibiting a relative increment of above 146%. Moreover, the figure illustrates that the thermal conductivity has a tendency to ascend, implying that GNPs are excellent additives for improving the thermal conductivity of PEG. GNPs dispersing in PEG matrix can form uniformly aqueous system when the mass fraction of GNPs is relatively low in aid of magnetic stirring and ultrasonic bath. Thus, at a certain filling rate, the different layers of graphene nanoplates interact effectively with each other, forming a high thermal \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mass Fraction** & **The Calculated Latent** & **The Measured Latent** & **The Relative Errors (\%)** \\
**of GNPs (\%)** & **Heat (J/g)** & **Heat (J/g)** & **The Relative Errors (\%)** \\ \hline
0.5 & 179.8 & 178.5 & 0.7 \\
1.0 & 178.9 & 175.2 & 2.1 \\
1.5 & 178.0 & 172.1 & 3.1 \\
2.0 & 177.1 & 169.3 & 4.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculated and measured values of the melting latent heat of composites. Figure 6: The latent heat and thermal conductivity of the composite as a function of GNPs contents. Figure 7: Thermal conductivity of the composites with different contents of GNPs. conductivity network. Moreover, the large specific surface area of GNPs greatly reduces the interfacial thermal resistance between the GNPs and PEG matrix materials, as a result, heat will rapidly transfer among GNPs instead of through the PEG matrix. [PERSON] et al. [35] and [PERSON] et al. [36] point out that the low interfacial thermal resistance provided by GNPs is ascribed to the reduced geometric contribution of phonon scattering at the interfaces. In this work, the polynomial fitting curve is aimed at demonstrating the relationship between thermal conductivity of the PEG/GNPs and the content of GNPs. The dotted red line in Figure 7 represents the polynomial fitting curve, and the relation is expressed as following:  
\[\gamma=0.3168+0.156x+0.036x^{2} \tag{2}\]  
where \(\gamma\) is thermal conductivity of the composites, \(x\) represents the content of GNPs. The coefficient of correlation of the Equation (2) is 0.998, which exhibits a high correlation between the thermal conductivity of composites and the content of GNPs. High thermal conductivity is a significant element considered for the advanced thermal energy and heat transfer of PCMs. Thus, the enhanced heat transfer rates of PEG/GNPs composites were further investigated. A temperature recorder with thermocouples was used to record the melting and solidifying times for the purpose of evaluating the temperature response behavior of the composites. Before the test, the sample was heated to 90 \({}^{\circ}\)C in the 20 mL tube, then the thermocouple was inserted into the middle of the sample, finally, the sample cooled down to room temperature and contacted closely with the thermocouple. The temperature-time profiles of the pristine PEG and composites for both the processes are illustrated in Figure 8. In the melting process, it can be vividly observed that the rising rate of temperature is significantly much faster in PEG/GNPs-2% composite. In addition, the peak temperature of PEG/GNPs-2% reaches 74.9 \({}^{\circ}\)C, higher than that of PEG. It is clearly revealed that the GNPs can accelerate the conductivity thermal transfer during the heating process.