## 3 Results and Discussion
### Thermal Properties of Electro-Insulating Liquids Modified by Fullerene C\({}_{60}\)
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Property**} & \multirow{2}{*}{**Kind of Liquid**} & \multicolumn{4}{c}{**Temperature**} \\ \cline{3-6}  & & **25 \({}^{\circ}\)C** & **40 \({}^{\circ}\)C** & **60 \({}^{\circ}\)C** & **80 \({}^{\circ}\)C** \\ \hline \multirow{4}{*}{Thermal conductivity [W-m\({}^{-1}\cdot\)K\({}^{-1}\)]} & MO & 0.133 & 0.130 & 0.128 & 0.126 \\  & MO + C\({}_{60}\) & 0.133 & 0.131 & 0.128 & 0.127 \\ \cline{2-6}  & SE & 0.158 & 0.156 & 0.153 & 0.151 \\  & SE + C\({}_{60}\) & 0.159 & 0.157 & 0.153 & 0.151 \\ \cline{2-6}  & NE & 0.182 & 0.180 & 0.178 & 0.175 \\  & NE + C\({}_{60}\) & 0.182 & 0.180 & 0.178 & 0.176 \\ \hline \multirow{4}{*}{Specific heat [J\({}^{\circ}\)kg\({}^{-1}\cdot\)K\({}^{-1}\)]} & MO & 1902 & 1974 & 2077 & 2187 \\  & MO + C\({}_{60}\) & 1945 & 2017 & 2121 & 2233 \\ \cline{2-6}  & SE & 1905 & 1964 & 2052 & 2149 \\  & SE + C\({}_{60}\) & 1962 & 2014 & 2094 & 2182 \\ \cline{2-6}  & NE & 2028 & 2082 & 2166 & 2259 \\  & NE + C\({}_{60}\) & 2040 & 2108 & 2210 & 2320 \\ \hline \multirow{4}{*}{Kinematic viscosity [mm\({}^{2}\cdot\)s\({}^{-1}\)]} & MO & 17.1 & 9.6 & 5.4 & 3.4 \\  & MO + C\({}_{60}\) & 17.4 & 9.9 & 5.5 & 3.6 \\ \cline{2-6}  & SE & 55.1 & 28.3 & 14.0 & 8.1 \\  & SE + C\({}_{60}\) & 55.5 & 28.5 & 14.4 & 8.3 \\ \cline{2-6}  & NE & 56.3 & 32.7 & 18.3 & 11.5 \\  & NE + C\({}_{60}\) & 56.4 & 32.7 & 18.3 & 11.5 \\ \hline \multirow{4}{*}{Density [kg\(\cdot\)m\({}^{-3}\)]} & MO & 867 & 857 & 845 & 832 \\  & MO + C\({}_{60}\) & 867 & 856 & 845 & 832 \\ \cline{2-6}  & SE & 964 & 953 & 940 & 926 \\  & SE + C\({}_{60}\) & 964 & 952 & 940 & 926 \\ \cline{2-6}  & NE & 917 & 908 & 892 & 880 \\  & NE + C\({}_{60}\) & 917 & 907 & 893 & 881 \\ \hline \multirow{4}{*}{Thermal expansion coefficient [K\({}^{-1}\)]} & MO & 0.00075 & 0.00076 & 0.00078 & 0.00080 \\  & MO + C\({}_{60}\) & 0.00075 & 0.00077 & 0.00079 & 0.00080 \\ \cline{2-6}  & SE & 0.00076 & 0.00077 & 0.00078 & 0.00079 \\ \cline{2-6}  & NE & 0.00074 & 0.00076 & 0.00078 & 0.00080 \\ \cline{2-6}  & NE + C\({}_{60}\) & 0.00074 & 0.00077 & 0.00078 & 0.00080 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Thermal properties of pure electro-insulating liquids and nanofluids based on fullerene C\({}_{60}\)[62; 63; 64]. The Prandtl number expresses the ratio of the viscosity of the fluid to its thermal conductivity. A high value of the Prandtl number indicates that the convection is dominant in the spread of heat in the liquid medium, whereas a low Prandtl value means that heat transport mainly occurs through thermal conductivity at a molecular level. In the case of the analyzed liquids, it can be seen that modification with fullerene C\({}_{60}\) did not cause significant changes in the value of the Prandtl number. On the basis of the obtained results, it can only be stated that in comparison with pure and modified mineral oil, and in the case of pure and modified esters, convection plays a greater role in heat transport. The greater role of convection in the case of esters and nanofluids is mainly due to their higher viscosity and density. The Nusselt number expresses the ratio of the heat transfer rate due to convection of the heat transfer rate, which is caused by thermal conductivity at the fluid boundary and the heat transfer surface. The closer the Nusselt number is to a value equal to 1, the heat transfer in the fluid (at the border of the centers) is more conducive to conduction. In turn, the higher the Nusselt number is, the higher the heat transfer takes place by convection. Analyzing the data in Table 4, it can be seen that the highest value of the Nusselt number is characterized by pure mineral oil and mineral oil modified with fullerene C\({}_{60}\). In turn, the lowest value of the Nusselt number is characterized by pure natural ester and natural ester modified with fullerene C\({}_{60}\). This means that in the case of mineral oil, the transfer of heat in the boundary layer will take place to a greater extent by convection.