# Cooling Performance of Fresh and Aged Automatic Transmission Fluids for Hybrid Electric Vehicles
## 3 Results  
The results of the measurements of density, viscosity, thermal conductivity, and heat capacity are portrayed in Figure 2. As expected, density and viscosity showed decreasing values with temperature and the differences among the three ATFs were small. ATF A demonstrated slightly higher density values than ATFs B and C at all temperatures tested. This was also observed for viscosity but only at lower temperatures. Regarding thermal conductivity and heat capacity, the ATFs behaved differently. ATF A demonstrated the lowest thermal conductivity and the highest heat capacity values, whereas ATF C demonstrated the highest thermal conductivity values and similar heat capacity values to ATF B. The differences in the relative values of these properties, despite ATFs B and C being formulated with the same base oils belonging to API Group III, are related to the molecular structure of the distinct hydrocarbon chains of the base oils. Unlike electrical conductivity, which is greatly affected by the lubricant additives, thermal properties are closely related to base oil types and molecular structures [19]. In  
Figure 2: Thermophysical properties of the fresh ATFs (A0, B0, C0): (**a**) density (\(\rho\)), (**b**) dynamic viscosity (\(u\)), (**c**) thermal conductivity (\(k\)), and (**d**) heat capacity (\(C_{p}\)). base oils with a longer main chain, thermal vibration energy is transmitted by intermolecular heat transfer propagated through the main chain and collisions with neighbouring molecules [19; 22]. Contrastingly, base oils with a shorter chain and many methyl branches need more intermolecular collisions to transmit thermal vibration energy over the same distance. [PERSON] and [PERSON] [22] found a correlation for thermal conductivity and molecular structure (Equation (6)) from the analysis of the quantitative factors structure-property relationship (QSPR) of 74 compounds. Thermal conductivity at 353.15 \(K=0.368A-0.126B+0.0741C+0.133D-0.239\)  
where \(A\) is the length of the main chain, \(B\) is the number of shorter branches, \(C\) is the number of longer branches, and \(D\) is the number of aromatic rings. This equation highlights the influence on the thermal conductivity of not only the main chain length and the number of shorter branches but also the number of longer branches and the number of aromatic rings. Although ATFs B and C are composed of a mixture of the same two base fluids, the concentration of these base oils is different in each ATF and this led to a different concentration of the distinct hydrocarbon chains forming these base fluids, resulting in different thermal conductivities. However, the very similar heat capacity of these two ATFs (B and C) could be related to the presence of an equal number of chemical groups according to the estimation method of heat capacity from group contributions [23]. Figure 3 portrays the figures-of-merit used for the comparison of the cooling performance of the lubricant samples in fresh conditions. Generally, all the lubricant samples have a very similar cooling performance. ATF A0, however, demonstrates lower FOM\({}_{heat\ losses}\) values than the other ATFs, which is advantageous. Conversely, it has a slightly lower Mouromtseff number (\(M_{O}\)). The oxidation state of the oil samples after the aging process was studied in previous work [20] by using the Fourier transform infrared (FT-IR) spectroscopy technique. The FT-IR spectra obtained from the fresh and aged oil samples demonstrated very slight differences, so the oxidation process was in the \"induction phase\" according to [PERSON] et al. [24]. However, four clustering zones (Figure 4) were detected after a Principal Component  
Figure 3: Figures-of-merit (FOM) of the fresh ATFs (A0, B0 and C0). Analysis of the spectra, demonstrating that similar molecular changes occurred in the ATFs for determined \"temperature-air flow-time\" combinations coded as 0, 1, 2, 4, 6, and 8 (Table 2).