## 3 Results and Discussion
### Thermal-Hydraulic Performance  
In Figure 6, the average temperature (T) of the discs (Figure 6a) is displayed together with the mass flow rate (MFR) distribution of the oil in the horizontal channels (Figure 6b) for all the explored cases. As expected, the two distributions are interrelated: one or multiple local peaks of temperature are generated within each pass, associated, in general, to discs that are surrounded by a poor circulation of the oil. Exceptions to such a correspondence are encountered at the base of each pass, starting from the second one: in these regions, hot streaks are conveyed from a vertical channel to the opposite one by the oil flow, producing an increase in the temperature of the adjacent disc despite a relatively high MFR fraction. An example of such a phenomenon, also described in [17], is reported in Figure 7, which shows the thermal distribution in both fluid and solid regions in Pass 2 for the case of Midel 1215: the hot streak coming from the first pass is drawn by the flow into the first three channels and determines local hot spots in the first two discs, despite the relatively high flow rate. The same temperature levels are then observed in the central discs, for which the flow rate is significantly lower.  
For what concerns the thermal performance of the four oils, Table 2 reports the location and value of the hot spots for each case. It can be observed that the best cooling performances for the present case study are obtained with the natural ester Midel 1215. As shown in Figure 6b, the mass flow rate distributes more equally in the various channels for this fluid, with a minimum MFR fraction that never falls below 1.5%, against the minimum value of 1.2% reached by the reference oil. Consequently, the temperature of the discs is kept low along the whole winding (Figure 6a). A hot spot of only 103.5 \({}^{\circ}\)C is generated at disc 51 (Pass 3), which is nearly 15% lower than the hot-spot value obtained for the reference oil (113.7 \({}^{\circ}\)C, disc 71, Pass 4).  
Figure 5: Prandtl number versus temperature for the 4 oils investigated. The maximum temperature value reached for each of the oils is highlighted by a circular marker.  
Figure 6: (**a**) Average disc temperature (T) and (**b**) mass flow rate (MFR) distributions. Entry region not included.  
Figure 7: Time-averaged temperature colormaps in Pass 2 for the case of Midel 1215. Hot streaks are visible in the blow-up.  
On the contrary, by involving a hot-spot temperature of 124.8 \({}^{\circ}\)C at disc 54 (Pass 3), the mineral oil Nytro Taurus is the fluid that determines the worst thermal scenario. In particular, the occurrence of nearly zero flow across three consecutive horizontal channels in the third pass (MFR fraction \(\leq\) 0.4%) is at the origin of the large peak encountered in the T distribution of the discs.  
The superior performance of both natural and synthetic esters with respect to Nytro Taurus is also reflected in the lower average temperature of the copper conductors and, consequently, in the lower mean temperature gradient between copper and oil, resulting in a higher overall cooling effectiveness (i.e., a higher heat transfer coefficient; see again Table 2), whose increase with respect to the reference oil is particularly significant for the case of Midel 1215. Even more interestingly, such a performance increase comes at no additional cost from the point of view of hydraulic losses: as reported in Table 2, the required pumping power is substantially equal for all the considered coolants. Pressure losses are moderately higher for both Midel 1215 and 7131, but, in the frame of a constant imposed mass flow rate, they are compensated by the lower density of both Midel oils.