## 6 Industrial Jet Cooler Module Optimization
The following boundary conditions were set: at the inlet the velocity and turbulence profile obtained in the preliminary simulation on the plenum model (Figure 19) have been set. Due to the band movement, the transverse input surface was modeled by activating the Frame Motion option with a velocity of 180 [m/min] in the appropriate direction. The temperature of 660 [\({}^{\circ}\)C] was fixed on this transverse input surface of the band. The band solid domain (with half thickness) is equipped with meshes and the conjugate heat transfer option is considered. The moving wall option with a speed equal to that of the band has been activated for the band upper surface. On the lower band surface a symmetry condition was used to correctly simulate the cooling on both band sides. An outlet relative pressure condition of 150 [Pa] (pressure value controlled in the cooling chamber) was set on the boundaries of flow domain between one slot and the other. The periodicity condition on the lateral surfaces of the band and on the transversal surfaces of the flow is imposed (the model represents only a sector of the complete jet cooler in the middle of the line). The fluid is a nitrogen-hydrogen mixture, therefore the transport equations for each species were introduced. An ideal gas mixture with thermo-physical properties varying with the temperature according to the ideal gas mixing law is considered. Figures 20 and 21 \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Configuration \#1** & **Configuration \#2** \\ \hline slot jets number & 8 & 5 \\ step [mm] & 228 & 400 \\ slot width [mm] & 4 & 9 \\ H/B & 25 & 11 \\ u\({}_{\text{outlet}}\) [m/s] & 58.5 & 41.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Main parameters of the two industrial configurations tested. Figure 19: Plenum configuration upstream of each slot. show the development of the streamlines in the flow domain for both configurations. The flow structure, already described in the previous paragraphs, is evident with the wall jets at the target surface; they interact and deviate towards the upper outlet, due to the induced pressure. Figure 22 shows the temperature patterns along the band, for the slot jet configurations compared to the existing one with round jets. Figure 21: Streamlines in the configuration #2 with 8 slots. Figure 20: Streamlines in the configuration #1 with 5 slots. The temperature gradients along the sliding direction are stronger in the slot jet configurations, with peak values close to 700 [K] in the jet area. In fact, with the same global cooling mass flow rate, in the round jets model the impinging jet is distributed over 32 nozzles, a much higher number than in the configurations with slot jets. In the two slot jet configurations, it should be noted that for eight slots a lower minimum temperature value is reached than that for five slots, due to a local speed difference of 20 [m/s]. As for the transverse temperature distribution, the slot configuration has a more uniform trend than the round jet nozzles. This feature offers a mechanical advantage by limiting transverse deformations, which could jeopardize the product quality. Figure 23 shows the surface temperature distributions along the flow direction and Table 9 reports the main quantities needed to evaluate the heat exchange of the different configurations. Figure 23: Temperature contours on the tape surface along its movement direction. Figure 22: Temperature contours on the tape for the different cooling configurations. The results obtained from the simulations show that the lowest temperature at the tape outlet is found with eight slot jets. In fact, in this case a higher average convective heat transfer coefficient is obtained over the entire band surface with respect to the other configurations. The heat transfer coefficient has been evaluated according to Equation (2), with the radiant heat flux subtracted from the overall. On the other hand, the round jets configuration gives the maximum value of the heat transfer coefficient on the target surface only.