## 5 Multi Slot Jet Analysis
### H/B = 16  
The same analysis has been performed for a configuration with the jets with higher distance from the target wall defined by H/B = 16. Three or two jets have been considered. In Figure 16 the velocity contours and streamlines of the three slots configuration have been reported.  
The developed flow field in this case is clearly different with respect the closest jet-wall case. The external jets have more space to mix with the surrounding fluid and to lose  
Figure 16: Velocity contours and streamlines of three slot jets configuration with H/B = 16, Re = 5500 and realizable k-\(\epsilon\) model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Configuration** & **Model** & **Average h [W/m\({}^{2}\)K]** & **Percentage Error [\%]** \\ \hline \multirow{3}{*}{3} & experimental & 174.1 & - \\  & realizable k-\(\epsilon\) & 204 & 17.7 \\  & SST & 197.7 & 13.5 \\ \hline \multirow{3}{*}{2} & experimental & 160.3 & - \\  & realizable k-\(\epsilon\) & 166.4 & 3.8 \\ \cline{1-1}  & SST & 164.5 & 2.6 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Average heat transfer coefficient and percentage errors of the CFD models with respect the experiment of the multi slot jet configurations for H/B = 4.  
velocity before their impingement on the target surface. In addition, the central jet is subject to an even stronger mixing; the streamlines of the external wall jets curve upwards, affected by the pressure increase in the stagnation zone of the central jet. The central jet not only interacts with the surrounding fluid, but also with the wall jets that entrain it towards the upper outlet. This last phenomenon increases the turbulent kinetic energy in the upper zones significantly, as shown in Figure 17.  
Similar contours for the configuration with two slots are obtained. It is clear that the wall jets have a lower energy at a higher jet-wall distance and their interaction is weaker due to the higher distance between the jets. In Figure 18 the convective heat transfer coefficient distributions are compared with the experimental data; in Table 6 the average values are reported with the corresponding percentage error referred to in experimental values.  
Figure 17: Turbulent kinetic energy contours of three slot jets configuration with H/B = 16, Re = 5500 and realizable k-\(\varepsilon\).  
Figure 18: Comparison between numerical and experimental data of the convective heat transfer coefficients for the multi slot configurations with H/B = 16 and Re = 5500: 3 slots (**left**) and 2 slots (**right**).  
In the three jets configuration the k-\(\varepsilon\) turbulent model gives the best prediction of convective heat transfer coefficient, almost coincident with the experimental value for a large area, including the external jets regions. A larger deviation is detected in the central jet with both models (more evident for SST), due to the pressure gradient between the stagnation region and the surrounding fluid. Also, for the two slots configuration the overall match with numerical and experimental data is good except for the region where there is a strong streamlines curvature (caused by the overpressure of the wall jets that interact and merge). In this zone the jet interaction is weaker due to the larger distance from the wall and because of the jets' mutual distance. In the two slots configurations the percentage errors are quite small for both models, with an underestimation by the k-\(\varepsilon\) and an overestimation by the SST model.  
From the above results and discussion, the k-\(\varepsilon\) model is selected for the application of the CFD approach to a reference industrial case.