## 6 Industrial Jet Cooler Module Optimization  
The CFD model is applied to an existing vertical galvanizing industrial line to understand the effect of the slot impingement technique. The slot impingement technique has been optimized and compared to the existing round jet cooling solution. In a previous work [30] the same module has been described in detail. The module is responsible for the temperature control of a moving band trough HNX jets (a mixing of 95% nitrogen and 5% hydrogen) to avoid oxidation of the target metal. The existing jet cooler is composed of 16 plenums, with 16 jet round nozzles each (256 in total) and a length of the metal band of 1650 [mm]. In order to save computational resources a quarter sector of 32 jets has been considered. Periodic boundary conditions on side walls are set to focus the analysis on the central area module. The entire jet cooler is modeled along the axial direction of the band. The new jet cooler based on slot impingement is designed taking some geometrical dimensions as constraints from the existing plant, as reported in Table 7.  
From the above data, the slots number for the cooling sector have been optimized. The total mass flow rate of the 256 round jets has been fixed to the slots in order to compare the different configurations. Unlike the round jets model, in the slot model it is not possible to place a single suction mouth for the operating fluid, located in the end of the band. In fact, the slot geometry, characterized by a transversal development equal to the band, forces the outgoing flow to curve in the longitudinal direction. A suction mouth is required between one slot and another, otherwise the jets would be deviated with no impingement on the \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 & 153 & - \\  & realizable k-\(\varepsilon\) & 141.8 & \(-\)7.4 \\  & SST & 180.1 & 17.7 \\ \hline \multirow{3}{*}{2} & experimental & 148.9 & - \\  & realizable k-\(\varepsilon\) & 136.9 & \(-\)8.0 \\ \cline{1-1}  & SST & 161.5 & 8.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Average heat transfer coefficient and percentage errors of the CFD models with respect to experimental values of the multi slot jet configurations for H/B = 16. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline jet-band distance & 100 mm \\ total longitudinal length & 2960 mm \\ Transversal length & 220 mm \\ impingement length plane & 1600 mm \\ half thickness of band & 0.34 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Main parameters of the industrial model. band. For this reason, the plenum for each single slot must be designed accordingly. In Figure 19 the plenum geometry that feeds the slot is shown. The geometry is designed with a constant narrow channel to guarantee a fully developed velocity profile, equal for each slot. Two different multi slot jet configurations (Table 8) have been simulated and compared to the existing configuration with round jets. The actual jet cooler geometry was simplified and the domain includes only the fluid flow from the outlet nozzles to the band surface, as well as the solid domain of the band (band half thickness). The above main parameters were chosen in order to make the present configurations comparable to the previous one with round jets [30]. The parameters guarantee the same mass flow rate and similar jet velocity values from the plenum. In the second model the H/B ratio was nevertheless strongly reduced with respect to the reference value [30] to enhance the turbulence generation into the flow field. To decrease H/B, the slot width was increased, with same jet height (a constraint design parameter). The Discrete Ordinates radiation model was activated in the CFD model due to the high band temperature. A mesh of two million elements complies with wall refinement constraints to get a y+ value close to one.