## 3 Results and Discussion
### Thermal Properties of Electro-Insulating Liquids Modified by Fullerene C\({}_{60}\)  
Table 3 presents the measured values of thermal properties of the analyzed electro-insulating liquids and nanofluids based on fullerene C\({}_{60}\). On the basis of the presented measurement results, it can be stated that doping the liquids with fullerene C\({}_{60}\) did not cause any changes in thermal conductivity, density, and thermal expansion. Synthetic ester and mineral oil have a similar value of specific heat, while natural ester has a higher value of specific heat. It is most probably associated with the presence of unsaturated bonds. The addition of fullerene caused an increase in the specific heat of all nanofluids. This increase is due to the presence of hydrophobic bonds between fullerene C\({}_{60}\) and hydrocarbon molecules contained in the analyzed electro-insulating liquids [64]. This also explains the obtaining of appropriate stable solutions on the basis of fullerene C\({}_{60}\) and the analyzed liquids. Hydrophobic bonds are important from the point of view of particle absorption on the surface of carbon nanotubes [86]. These bonds are so strong that, despite the small concentration of fullerene in the analyzed liquids (0.1 g\(\cdot\)L\({}^{-1}\)) and more than twice the lower values of specific heat [87; 88; 89], they manage to increase the specific heat of analyzed nanofluids. A minimal increase in kinematic viscosity of the nanofluids based on mineral oil and synthetic ester was also visible. This increase may negatively affect the heat transfer coefficient, which will consequently affect the cooling effectiveness of the device. Other researchers also observed the negative influence of nanoparticles on the viscosity of the analyzed nanofluids [59]. Table 4 presents the values of the criterion numbers of the analyzed liquids calculated on the basis of Equations (4), (6), and (7), which correspond to the numbers of Grashof, Prandtl, and Nusselt, respectively. As mentioned earlier, the Grashof number expresses the ratio of the buoyancy force to the fluid viscosity. This number defines the boundary between laminar and turbulent flow during natural convection. It is assumed that this limit occurs for around 10\({}^{9}\). As can be seen from the presented calculation results, for a temperature range of 40-80 \({}^{\circ}\)C and for both mineral oil and mineral oil modified with fullerene C\({}_{60}\), it is possible to have turbulent flows. On the other hand, in the case of synthetic ester, the occurrence of turbulent flows is possible in the temperature range of 60-80 \({}^{\circ}\)C. For the other analyzed insulating liquids (synthetic ester modified by C\({}_{60}\), natural ester, and natural ester modified by C\({}_{60}\)), turbulent flow will probably occur at temperatures above 80 \({}^{\circ}\)C. In the case of C\({}_{60}\) fullerene nanofluids, the occurrence of turbulent flows can also have its advantages--these flows are accompanied by a mixing phenomenon, which can have a positive effect on the uniform dispersion of fullerene in the base liquid. The modification of the liquids with fullerene C\({}_{60}\) does not significantly change the value of the Grashof number.