## 3 Results and Discussion
### Temperature and Velocity Distributions  
A deeper insight into the mean behavior described above can be gained by analyzing the detail of temperature and velocity distributions. The temperature maps reported in Figure 8 reveal that, in the horizontal channels of Pass 3, rapid expansion and coalescence of the upper and lower boundary layers occurs across a wide portion of the channels. Hence, the hottest temperature is reached at this height of the pass, although more stagnant flow can be found at lower positions. This occurrence is more evident for the cases exhibiting oscillatory behaviors and is a direct consequence of the formation of thermal instabilities like the ones depicted in Figure 4.  
Another relevant aspect that can be inferred from the temperature maps, and which decisively affects thermal performance in the present case study, is the onset of flow reversals in some of the horizontal channels and, in particular, for the cases of Nytro Taurus and Midel 7131. The first trace of this phenomenon is the presence of a local minimum of the MFR fraction (see Figure 6b), which occurs in each pass for Nytro Taurus and only in Pass 4 for Midel 7131. A further hint of this feature is the formation and detachment of hot streaks along the vertical channel on the side of the pass inlet, as visible in Figure 8b. When the effect of flow reversal runs out, these hot streaks are conveyed to the opposite vertical channel contributing to the local temperature rise. A similar behavior can be \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & **Symbol/Formula** & **Unit** & **Ref. Oil** & \begin{tabular}{c} **Midel** \\ **1215** \\ \end{tabular} & \begin{tabular}{c} **Nytro** \\ **Taurus** \\ \end{tabular} & \begin{tabular}{c} **Midel** \\ **7131** \\ \end{tabular} \\ \hline Hot-spot temperature & T\({}_{\text{hs}}\) & \({}^{\circ}\)C & 113.7 & 103.5 & 124.8 & 120.0 \\  & & & \(\left(-15.2\%\right)\) & \(\left(+16.6\%\right)\) & \(\left(+9.4\%\right)\) \\ Hot-spot location & - & - & disc 71 & disc 51 & disc 54 & disc 74 \\  & - & \begin{tabular}{c} (Pass 4) \\ \end{tabular} & \begin{tabular}{c} (Pass 3) \\ \end{tabular} & \
\begin{tabular}{c} (Pass 3) \\ \end{tabular} &
\begin{tabular}{c} (Pass 4) \\ \end{tabular} \\ Average disc temperature & T\({}_{\text{ave,Cu}}\) & \({}^{\circ}\)C & 89.0 & 85.3 & 90.9 & 87.5 \\  & & \(\left(-8.7\%\right)\) & \(\left(+4.5\%\right)\) & \(\left(-3.5\%\right)\) \\ Bulk outlet oil temperature & T\({}_{\text{out,oil}}\) & \({}^{\circ}\)C & 80.3 & 82.0 & 79.0 & 80.4 \\ Average bulk oil temperature & T\({}_{\text{ave,oil}}\) & \({}^{\circ}\)C & 63.5 & 64.3 & 62.8 & 63.6 \\ Mean Cu-oil gradient & \(\Delta\text{T}_{\text{Cu-oil}}=\text{T}_{\text{ave,Cu}}-\text{T}_{\text{ave,oil}}\) & \({}^{\circ}\)C & 25.5 & 20.9 & 28.1 & 24.0 \\  & & & \(\left(-17.9\%\right)\) & \(\left(+10.1\%\right)\) & \(\left(-6.1\%\right)\) \\ Hot-spot factor & HSF = \(\left(T_{\text{hs}}-\text{T}_{\text{ave,oil}}\right)/\Delta\text{T}_{\text{Cu- oil}}\) & - & 1.96 & 1.87 & 2.21 & 2.36 \\  & & & \(\left(-5.0\%\right)\) & \(\left(+12.1\%\right)\) & \(\left(+19.7\%\right)\) \\ Overall heat transfer coefficient & U = q\({}^{\prime\prime}/\Delta\text{T}_{\text{Cu-oil}}\) & W m\({}^{-2}\)\({}^{\circ}\)C\({}^{-1}\) & 100.4 & 122.2 & 91.1 & 106.9 \\  & & & & \(\left(+21.7\%\right)\) & \(\left(-9.2\%\right)\) & \(\left(+6\%\right)\) \\ Overall pressure drop & \(\Delta\text{p}=\text{Pin}-\text{P}_{\text{out}}\) & kPa & 12.87 & 13.47 & 12.60 & 14.06 \\  & & & \(\left(+4.7\%\right)\) & \(\left(-2.1\%\right)\) & \(\left(+9.3\%\right)\) \\ Pumping power & \(\dot{\text{L}}\) & W & 11.5 & 11.6 & 11.5 & 11.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main integral thermal-hydraulic results for the four cases considered. noticed near the top of Pass 4 also with the synthetic ester Midel 7131 (Figure 8c). In this case, the combination of the hot streak with the coalescence of thermal boundary layers from two neighboring discs results in a hot-spot temperature as high as 120.0 \({}^{\circ}\)C at disc 74.