## 3 Results and Discussion  
Figure 3 shows the local circumference average normalized temperature profiles along the outer surface of a single square tube at various heat fluxes. The end effect is clear on the temperature profiles at the up and downstream of heat transfer. Therefore, the test section will be focused on the vertical distance between \(x/L\) = 0.2-0.8. Other tubes give similar temperature profiles. It should be noted that the temperature reaches a steady state after about 100 min, as shown in Figure 4 at different supplied heating powers. \begin{table}
\begin{tabular}{c c} \hline \hline
**Quantity** & **Uncertainty (\(\pm\)\%)** \\ \hline Electrical input power & 3.4 \\ \hline \(q_{r}\) & 9.0 \\ \hline \(q_{c}\) & 4.7 \\ \hline \(h_{x}\) & 4.8 \\ \hline \(Nu_{x}\) & 4.8 \\ \hline \(Ra_{x}^{*}\) & 4.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The maximum percentage uncertainties of the parameters. Figure 3: Local circumference average normalized temperatures along the vertical surface of the tube at different heat fluxes. Figure 5a-c shows a sample of the temperature readings in the middle of the tube at the three surfaces, namely: front (F), left (L), and right (R) at three different heat fluxes. Table 2 shows the surface temperature, the mean value, and the standard deviation between the three different readings for each tube. As indicated, as the heat flux increases, the surface temperature increases and the maximum overall standard deviation is 3.30. The percent of overall relative standard deviation is obtained at the three heat fluxes as 2.34, 3.46, and 4.23, as shown in Table 2.  
Figure 4: Steady-state temperature profiles at the outer surface of the tubes at three different supplied powers. Figure 5: Temperature measurements in the middle of the tube at different heat fluxes at the three circumference surfaces: front (F), left (L), and right (R); (**a**) 108.0 W/m\({}^{2}\), (**b**) 221.0 W/m\({}^{2}\), and (**c**) 341.0 W/m\({}^{2}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & & Heat Flux = 108.0 W/m\({}^{2}\) \\ \hline  & & & & Temperature, \({}^{\circ}\)C & \\ \cline{2-6}  & Left Surface (L) & Front Surface (F) & Right Surface (R) & Mean Value & Standard deviation \(S_{x}=\sqrt{\frac{\sum_{i=1}(x_{i}-\overline{Y})^{2}}{n-1}}\) \\ \hline Tube No. 1 & 48.51 & 50.84 & 47.73 & 49.03 & 1.62 \\ \hline Tube No. 2 & 49.55 & 48.90 & 48.39 & 48.95 & 0.58 \\ \hline Tube No. 3 & 47.40 & 47.21 & 49.15 & 47.92 & 1.07 \\ \hline Overall mean & & & & 48.63 & \\ \hline Overall standard deviation & & & & 1.14 \\ \hline Overall relative standard deviation percent = standard deviation \(\times\) 100/mean & & & & 2.34 \\ \hline  & & & & Heat flux = 221.0 W/m\({}^{2}\) & \\ \cline{2-6}  & & & & Temperature, \({}^{\circ}\)C & \\ \cline{2-6}  & Left surface (L) & Front surface (F) & Right surface (R) & Mean value & Standard deviation \(S_{x}=\sqrt{\frac{\sum_{i=1}(x_{i}-\overline{Y})^{2}}{n-1}}\) \\ \hline Tube No. 1 & 66.29 & 71.18 & 65.46 & 67.64 & 3.09 \\ \hline Tube No. 2 & 68.35 & 67.15 & 67.02 & 67.51 & 0.73 \\ \hline Tube No. 3 & 63.80 & 63.95 & 68.09 & 65.28 & 2.43 \\ \hline Overall mean & & & & 66.81 & \\ \hline Overall standard deviation percent = standard deviation \(\times\) 100/mean & & & & 2.31 \\ \hline  & & & & 3.46 \\ \hline \end{tabular}
\end{table} 
Table 2: Sample of the temperature measurements in the middle of the tubes at the three surfaces. It should be noted that the thermocouples have been calibrated using a platinum resistance thermometer made by Fluke Corporation (Model: 5609). The thermocouples along with the Fluke thermometer were immersed in a container full of distilled water, which was then heated up to the boiling temperature. Temperature readings were recorded using a data logger. A sample of such measurement/calibration is shown in Figure 6 for seven thermocouples, and the boiling temperature for each thermocouple is shown in Table 3. These results ensure a very good accuracy of the used thermocouples.