## 3 Results and Discussion
The boiling temperature corresponds to Riyadh's atmospheric condition. Figure 7 shows a comparison between the natural convection heat transfer from the three single tubes and that of Vliet and Liu [1] and Ali [2] for natural convection from vertical plates and vertical square cross-section tubes, respectively. The comparison shows that the current results lie between the envelope of Vliet and Liu [1] and Ali [2], and close to [2] since the current tubes have a square cross-section area similar to that of [2]. Figure 8a,b shows the local circumference averaged Nusselt number \(Nu_{x}\) versus the modified local Rayleigh number \(Ra_{x}^{*}\) on a logarithmic scale for the left tube (number 1, \(\square\)) in an array of three tubes compared to that of the single tube \(\bullet\). The solid and the dashed lines present the curve fitting through the experimental data. Figure 8a shows that for center-to-center distance ratio \(S/D=1.75\). It is clear that the effect of small \(S/D\) is to reduce the Nusselt number at the same \(Ra_{x}^{*}\). This could be attributed to the existence of small \(S/D\) since in general, there is competition between the raising plume due to the buoyancy force, which tends to improve the heat transfer coefficient, and the accumulated thermal boundary layer, which tends to degrade it. This competition depends on the S/D ratio. Therefore, as \(S/D\) increases, the velocity effect of the raising plume overcomes that of the accumulated thermal boundary layer, which reduces the difference in \(Nu_{x}\) between the single tube and that of the array of three tubes, as shown in Figure 8b. Moreover, as \(S/D\) increases more, the \(Nu_{x}\) of the tube in the array approaches that of a single tube and may enhance it over that of a single tube, as shown in Figure 9 for \(S/D=4.25\). Solid and dashed \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Fluke** **PRT (\({}^{\circ}\)C)** & **TC1 (\({}^{\circ}\)C)** & **TC2 (\({}^{\circ}\)C)** & **TC3 (\({}^{\circ}\)C)** & **TC4 (\({}^{\circ}\)C)** & **TC5 (\({}^{\circ}\)C)** & **TC6 (\({}^{\circ}\)C)** & **TC7 (\({}^{\circ}\)C)** \\ \hline
97.65 & 97.49 & 97.48 & 97.49 & 97.40 & 97.35 & 97.36 & 97.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Recorded temperatures of the seven thermocouples against the platinum resistance thermometer at boiling state. Figure 6: Thermocouple calibration against a platinum resistance thermometer using samples of seven thermocouples. lines, which appear in Figure 9, present the curve fitting through the experimental data at different \(S/D\) ratios. The general correlation of the curve fitting is in the form  
\[Nu_{x} =\text{A }(Ra_{x}^{*})^{B} \tag{12}\]  
where A and \(B\) are constants. Table 4 shows these constants and the coefficient of determination R\({}^{2}\) of tube number one and the other tubes at different \(S/D\) ratios compared to that of a single tube. Figure 8: The effect of a small center-to-center distance ratio on the natural convection heat transfer from the left tube in an array of three tubes; (**a**) \(S/D=1.75\) and (**b**) \(S/D=2.75\). Figure 7: Comparison of natural convection heat transfer from the used single tubes and that of Vliet and Liu [1] and Ali [2]. Figure 9: Local Nusselt numbers versus the modified Rayleigh numbers for different \(S/D\) ratios of the left tube in the array of three tubes compared to that of the single tube. Figure 10a,b shows the effect of center-to-center distance on natural convection heat transfer, and it is clear that as the \(S/D\) increases, the effect of natural convection velocity presented by a rising plume overcomes the degradation effect by the accumulated thermal boundary layer on heat transfer from the tube. Figure 11a-c shows the Nusselt number profiles as a function of the \(S/D\) ratio for different Rayleigh numbers for the left tube (#1) in Figure 11a, the middle (#2) in Figure 11b, and the right (#3) in Figure 11c, respectively.