## 3 Results
### The Effect of Protrusion Height
#### 3.1.1 Enhancement of Heat Transfer  
The overall \(\dot{Q}\) is the sum of those from the top and lateral faces of both CPs and from the base plate to the fluid in the computational domain presented in Figure 5a. For a \(D_{p}/D\) of 3.5, the overall \(\dot{Q}\) according to \(H_{p}/D\) is presented for various jet \(Re\) numbers in Figure 6. In Figure 6, \(H_{p}/D\) of 0 represents the flat target plate. The overall \(\dot{Q}\) increases with \(H_{p}/D\) for any jet \(Re\) number considered. As seen in Figure 6, the rate of change of the \(\dot{Q}\) according to \(H_{p}/D\) increases with the jet \(Re\) number. For any jet \(Re\) number, it decreases with \(H_{p}/D\) until an \(H_{p}/D\) of 3.0 and rapidly increases for \(H_{p}/D\) exceeding 4.0. For any jet \(Re\) number considered, the maximum \(\dot{Q}\) is obtained for an \(H_{p}/D\) of 4.5 where the top face of a CP is 0.5\(D\) below the jet orifice and the CGV almost touches the confinement plate. The ratio of the \(\dot{Q}\) of the protruding surface to that of the flat target plate (\(\dot{Q}_{o}\)) according to \(H_{p}/D\) for various jet \(Re\) numbers is presented in Figure 7. As seen in Figure 7, the \(\dot{Q}/\dot{Q}_{o}\) increases with \(H_{p}/D\) for all jet \(Re\) numbers considered. For a jet \(Re\) number of 5000, \(\dot{Q}\) enhancement compared with the flat target plate is 18.1% at \(H_{p}/D\) of 1, while it is 62.9% for \(H_{p}/D\) of 4.5. For a jet \(Re\) number of 10,000, the overall \(\dot{Q}\) is enhanced by 20.5% and 65% for \(H_{p}/D\) of 1 and 4.5, respectively. For a jet \(Re\) number of 15,000, the enhancement in \(\dot{Q}\) is calculated as 17.9% and 62.1% for \(H_{p}/D\) of 1 and 4.5, respectively. Furthermore, the corresponding enhancements in \(\dot{Q}\) are 16.2% and 58.8% for a jet \(Re\) number of 20,000. Therefore, the biggest improvement in \(\dot{Q}\) compared with that of the flat target plate is obtained for a jet \(Re\) number of 10,000 and \(H_{p}/D\) of 4.5. The \(\dot{Q}/\dot{Q}_{o}\) rapidly increases for \(H_{p}/D\) values ranging between 4 and 4.5 where the upper surface of a CP is at a smaller distance away from the jet orifice than \(D\), as seen in Figure 7. Another conclusion that can be drawn from Figure 7 is that as the jet \(Re\) number increases, \(\dot{Q}/\dot{Q}_{o}\) decreases except for a few \(H_{p}/D\) values on lower jet \(Re\) number curves. For instance, while the improvement in \(\dot{Q}\) for \(H_{p}/D\) of 3 is 47.2% at a jet \(Re\) number of 5000, it decreases to 46.3%, 41.4%, and 38.6% at jet \(Re\) numbers of 10,000, 15,000 and 20,000, respectively. In conclusion, \(\dot{Q}\) is significantly improved by CPs equipped with CGVs compared with that of the flat target plate, while the \(\dot{Q}/\dot{Q}_{o}\) has a decreasing trend as the jet \(Re\) number is increased. \(\overline{Nu}\) number according to \(H_{p}/D\) for various jet \(Re\) numbers is presented in Figure 8. For any considered \(H_{p}/D\), the \(\overline{Nu}\) number increases at a decreasing rate with the jet \(Re\) number. Contrary to the overall \(\dot{Q}\), the \(\overline{Nu}\) number decreases as \(H_{p}/D\) is increased for all considered jet \(Re\) numbers due to the bigger contribution of the less effectively cooled lateral surface of the CP to the enhanced heat transfer. In other words, the decrease in the \(\overline{Nu}\) number with increasing \(H_{p}/D\) is due to the increased contribution of ordinary convective heat transfer on the lateral faces of the CPs with smaller HTCs than the jet impingement cooling on the upper faces. It has been reported in the literature that the \(\overline{Nu}\) number of a MJICS decreases as the heat transfer surface is augmented by protrusions having various shapes [48,78]. [PERSON] and [PERSON] stated that the \(\overline{Nu}\) number of a MJICS may decrease due to changes in the flow field if the target surface is augmented by modifications and emphasized that the main indicator to consider is the overall \(\dot{Q}\)[54].