## 3 Results and Discussion  
A dependence of the Nusselt number on the Reynolds number for the inline tube bank is shown in Figure 5, where the mentioned variants of the reference temperatures were used to compare the computed Nusselt numbers with the correlating equations of [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and ESDU standards. Except the variants \(T_{em}\), \(T_{cc}\), \(\Delta T_{em}\), \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Author** & **C\({}_{1}\)** & **C\({}_{2}\)** & **m** & **n** & **\(p\)** \\ \hline [PERSON] [11] & 0.482 & - & 0.556 & - & - \\ \hline \multirow{2}{*}{\(\check{Z}\)[PERSON] [20; 21; 22]} & \multicolumn{2}{c}{1.04 *} & 0.4 * & \multirow{2}{*}{-} & \multirow{2}{*}{-} \\  & & 0.71 \(\times\) & & 0.5 \(\times\) & \\  & & 0.35 \(\dagger\) & & & \\ \hline [PERSON] [29; 30] & - & 1.04 & 1.84 & 0.125 & 500 \\ \hline [PERSON] [23] & 1.18 & 0.35 & 0.57 & - & - \\ \hline [PERSON] [25; 26] & 0.567 & 1.61 & - & - & - \\ \hline ESDU [47] & - & 1.309 \(\Delta\) & 0.36 \(\Delta\) & & \\ \hline \multirow{2}{*}{\(\star\) for \(Re=0\)–\(5\cdot 10^{2}\); \(\times\) for \(Re=5\cdot 10^{2}\)–\(10^{3}\); \(\dagger\) for \(Re=10^{3}\)–\(2\cdot 10^{5}\); \(\wedge\) for \(Re=10\)–\(3\cdot 10^{2}\); \(\Diamond\) for \(Re=3\cdot 10^{2}\)–\(2\cdot 10^{5}\).} & \multirow{2}{*}{-} \\  & & 0.273 \(\Diamond\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The correlation factors for the staggered arrangement. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Author** & **C\({}_{1}\)** & **C\({}_{2}\)** & **m** & **n** & **\(p\)** \\ \hline [PERSON] [11] & 0.229 & - & 0.632 & - & - \\ \hline \multirow{2}{*}{\(\check{Z}\)[PERSON] [20; 21; 22]} & - & 0.52 * & 0.5 * & - \\  & & 0.27 \(\times\) & 0.63 \(\times\) & - & - \\ \hline [PERSON] [29; 30] & - & 0.9 & 5 & 0.5 & 290 \\ \hline [PERSON] [23] & \(1-0.0605\sqrt{\frac{1000}{R_{max}}}\) & 0.34 & 0.61 & - & - \\ \hline [PERSON] [25; 26] & 0.542 & 1.43 & - & - & - \\ \hline ESDU [47] & - & 0.742 \(\Delta\) & 0.431 \(\Delta\) & & \\  & & 0.211 \(\Diamond\) & 0.651 \(\Diamond\) & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The correlation factors for the inline arrangement. and \(\Delta T_{\alpha}\), the other methods, shown hatched, underestimate the experimental results in the investigated area. Although the former methods meet the value order, the course slope is not in agreement with the correlating equations for a significant part of the \(Re\) range. When considering the variant with the lowest discrepancies to any correlating equation, the temperature \(T_{\alpha}\) provides a suitable reference temperature for the Nusselt numbers that are in a good agreement with the Zukauskas correlating equation in the range of \(Re=10^{2}\)-\(10^{3}\) (Figure 6). The maximum discrepancies appear on the boundary Reynolds numbers (4.5%) due to the Zukauskas discontinuous correlations. The average and maximum discrepancies, within the correlation interval, are 0.8% and 1.9%, respectively. For the turbulent flow over \(Re=10^{3}\), the approach according to the Equation (15) was tested. As is shown in Figure 7, the results are in good agreement with the Zukauskas correlating equation, where the average and maximum discrepancies are 1.25% and 2.86%, respectively. Figure 5: Average Nusselt number for the inline tube bank. Figure 6: Average Nusselt number for the inline tube bank at \(Re=100\)–\(1000\). In the range of \(0<Re<10^{2}\), any constant reference temperature was found to meet the value order and course slope of the mentioned correlating equations, which confirms the hypothesis of the listed authors: that there is no reference temperature which is both representative and easy to compute or measure at low Reynolds numbers. A dependence of the Nusselt number on the Reynolds number for the staggered tube bank is shown in Figure 8, in the same way as for the inline tube bank. Almost all of the investigated reference temperature variants meet the error range and curve slope of any of the correlating equations.