## 3 Results
### Effect of Protrusion Diameter
#### 3.2.1 Enhancement of Heat Transfer  
For \(H_{p}/D\) of 4, at various jet \(Re\) numbers, the effect of five different \(D_{p}/D\) of 2, 2.5, 3, 3.5, and 4 on the overall \(\dot{Q}\) is presented in Figure 14. The flat target plate case is represented by \(D_{p}/D\) of 0. Like \(H_{p}/D\), increasing \(D_{p}/D\) enhances the overall \(\dot{Q}\) for any jet \(Re\) number considered in this study. For a jet \(Re\) number of 20,000, the  
of the flat target plate. Among all considered cases, the highest enhancement in the overall \(\dot{Q}\), 62.8%, is obtained at \(D_{p}/D\) of 4 for a jet \(Re\) number of 10,000.  
For \(H_{p}/D\) of 4, \(\dot{Q}/\dot{Q}_{o}\) according to \(D_{p}/D\) at various jet \(Re\) numbers are presented in Figure 15. For any jet \(Re\) number considered, the \(\dot{Q}/\dot{Q}_{o}\) increases with \(D_{p}/D\). As seen in Figure 15, at any \(D_{p}/D\), for the jet \(Re\) numbers exceeding 5000, \(\dot{Q}/\dot{Q}_{o}\) decreases with increasing jet \(Re\) number. At \(D_{p}/D\) of 4, approximately the same heat transfer enhancement with respect to that of the flat target plate, 62.8%, is obtained for the jet \(Re\) numbers of 5000 and 10,000.  
Figure 14: For \(H_{p}/D\) of 4, the effect of \(D_{p}/D\) on the overall \(\dot{Q}\) at various jet \(Re\) numbers.  
For \(H_{p}/D\) of 4, the \(\overline{Nu}\) numbers according to \(D_{p}/D\) at various jet \(Re\) numbers are presented in Figure 16. For any \(D_{p}/D\), the \(\overline{Nu}\) number increases with jet \(Re\) number. As seen in Figure 8, the \(\overline{Nu}\) number decreases with increasing \(H_{p}/D\). Similarly, as \(D_{p}/D\) increases, the \(\overline{Nu}\) number decreases but at a slower pace. As \(D_{p}/D\) increases, both top and lateral face areas of CPs increase whereas the base plate area decreases. Since the heat fluxes are highest on the top faces of the CPs, the \(\overline{Nu}\) number obtained by increasing their diameter, hence both the top and lateral face areas, decreases more slowly than that obtained by increasing their height, hence the lateral face areas.  
For \(H_{p}/D\) of 4, the \(\overline{Nu}/\overline{Nu}_{o}\) according to \(D_{p}/D\) at various jet \(Re\) numbers are presented in Figure 17. The \(\overline{Nu}/\overline{Nu}_{o}\) decreases with increasing \(D_{p}/D\) and jet \(Re\) number. For \(D_{p}/D\) of 2, 2.5, 3, 3.5, and 4, the lowest--72.3%, 66.5%, 63.9%, 63.4%, and 60.6%-- and highest--78.2%, 73.5%, 70.3%, 66.7%, and 63.7%--\(\overline{Nu}/\overline{Nu}_{o}\)s are obtained for jet \(Re\) numbers of 20,000 and 5000, respectively.  
For \(H_{p}/D\) of 4, local \(Nu\) number contour plots on the top faces of CPs and on the flat base plate, as well as on the unrolled lateral faces of the CPs, at various \(D_{p}/D\) and jet \(Re\) numbers are presented in Figure 18. The \(\overline{Nu}\) numbers on the top and lateral faces of the CPs and on the flat base plate decrease with increasing \(D_{p}/D\). For instance, at a jet \(Re\) number of 20,000, for \(D_{p}/D\) of 3 and 4, the \(\overline{Nu}\) numbers on the top faces are 102 and 93.71, respectively; on the lateral faces, 31.29 and 25.60; and on the flat base plate, 30.21 and 26.71. For \(D_{p}/D\) of 3, the \(Nu\) number trace of the rising fountain formed by the collision of wall jets on the flat base plate between the two CPs clearly indicates a secondary stagnation zone. As the distance between the two CPs decreases due to an increase in \(D_{p}/D\), the \(Nu\) number contours on the lateral face of the outer CP for \(D_{p}/D\) of 4 take on a helical shape due to the peripheral diversion of the flow directed toward the flat base plate by the intensified crossflow.  
Figure 18: For \(H_{p}/D\) of 4, \(Nu\) number contour plots in the top view of the system and in the unrolled views of the lateral faces of the CPs, at various jet \(Re\) numbers, for \(D_{p}/D\) of (**a**) 2; (**b**) 2.5; (**c**) 3; (**d**) 3.5; (**e**) 4.