## 3 Results and Discussion  
### Thermal Conductivity  
Initially, the thermal conductivity of pure DI water was experimentally measured at temperatures ranging from \(-\)10 to 40 \({}^{\circ}\)C. Then, the experimental data were compared with the standard data to validate the measurement practice [30; 31; 32]. It was found that the measured values matched-up with the standard values. The average percentage deviation of measured values from the standard values of the base fluid was \(\pm\)2%. Figure 4 shows the variation in thermal conductivity of the nanocomposite in a liquid state, and it is observed that the graphene nanocomposite has higher thermal conductivity when compared to the base fluid. The dispersion of GnP significantly improved the thermal conductivity of the nanocomposite. The reason behind this enhancement of thermal conductivity is the nano-size of the GnP and the two-dimensional geometry of the GnP that increases the exposure to the base fluid. By increasing the volume percentage of the GnP, the thermal conductivity was found to increase. The average increase in thermal conductivity compared to base fluid were found to be 11.01%, 13.38%, 17.23%, 20.96%, and 23.95% respectively, for the considered volume percentages of the GnP in the liquid state. The thermal conductivity for the 0.5% volume percentage was 23.95% higher compared to that of the base fluid; whereas [PERSON] et al. (2016) obtained a thermal conductivity 16% higher than the base fluid at the same concentration. The superior thermal conductivity is due to the use of chemically functionalized GnP instead of dispersing surfactants in the base fluid for better stability. Whereas, in the solid state, as shown in Figure 3, the average surge in thermal conductivity compared to base fluid are 18.67%, 25.7%, 34.75%, 45.08%, and 53.05%, respectively, for the considered volume percentages of GnP. Thermal conductivity in the solid state was higher than in the liquid state. The reason for this sudden increase in thermal conductivity when the fluid changes to a solid state is due to the orderly solid structure that causes accelerated molecular vibrations. The sudden fall in thermal conductivity \begin{table}
\begin{tabular}{c c c c c c} \hline
**Volume Percentage** & **Initial** & **Bath** & **Sample** & **Bath** & **Sample** \\
**of Functionalised** & **Temperature** & **Temperatures** & **Temperature** & **Temperature** & **Temperature** \\
**GnP** & **of the Sample** & **for Freezing** & **after Freezing** & **for Melting** & **after Melting** \\ \hline
0\%, 0.1\%, 0.2\%, 0.3\%, & \multirow{2}{*}{32 \({}^{\circ}\)C} & \(-\)6 \({}^{\circ}\)C \& \multirow{2}{*}{\(-\)3 \({}^{\circ}\)C} & \multirow{2}{*}{31 \({}^{\circ}\)C \& 36 \({}^{\circ}\)C} & \multirow{2}{*}{30 \({}^{\circ}\)C} \\
0.4\% \& 0.5\% & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Freezing and melting test matrix. when the solid state changes to liquid state might be caused by the orderly stable microstructure in the solid turning into a disorderly structure in the liquid state. Table 2 shows the tabulated comparison of thermal conductivity of the nanocomposite with respect to temperature and % volume fraction. The reason for thermal conductivity enhancement is attributed to the high aspect ratio, 2-D geometry, and stiffness of graphene. The acid treatment of GnP plays a significant role in the enhancement of thermal conductivity in the nanocomposites. Instead of adding surfactant, nitric acid treatment was used to chemically modify the surface of GnP in order to increase the surface-active sites for electrochemical reactions and also to improve the stability. As surfactants not used, the effects of degradation in thermal conductivity while adding surfactant completely avoided in this nanocomposite. Figure 4 shows the variation in thermal conductivity of the nanocomposite in liquid state and it is observed that the graphene nanocomposite has higher thermal conductivity when compared to the base fluid.