## 3 Results
### The Effect of Protrusion Height
#### 3.1.3 Pec  
Since measures to improve heat transfer may increase \(\Delta P\), an important indicator of the thermo-economic performance of an enhanced cooling system is the \(PEC\), which is the ratio of the proportional improvement in the overall \(\dot{Q}\) to the proportional increase in \(\dot{W}\). Therefore, the greater the \(PEC\), which is calculated by dividing the ratio of the improved \(\dot{Q}\) of the protruding surface to that of the flat target plate by the ratio of the corresponding \(\dot{W}\) requirements, the better the thermo-economic performance of the system. The \(PEC\) is calculated as  
\[PEC=\frac{\frac{\dot{Q}}{\dot{W}}}{\dot{W}_{o}}, \tag{15}\]  
\[\dot{W}_{o}=\Delta P_{o}.\dot{V}, \tag{16}\]  
\[\dot{W}=\Delta P.\dot{V}, \tag{17}\]  
where \(\dot{Q}_{o}\), \(\dot{W}_{o}\), and \(\Delta P_{o}\) are the overall heat transfer rate, fluid pumping power, and pressure drop, respectively, for an MJICS with a flat target plate, and \(\dot{Q}\), \(\dot{W}\), and \(\Delta P\) are those of a CMJICS with a protruding surface for the same fluid volume flow rate \(\dot{V}\). For various jet \(Re\) numbers, the \(PEC\) according to \(H_{p}/D\) is presented in Figure 13. For any jet \(Re\) number,  
Figure 12: For \(D_{p}/D\) of 3.5, \(\Delta P\) according to \(H_{p}/D\) at various jet \(Re\) numbers.  
the \(PEC\) increases with \(H_{p}/D\), reaching its peak value at \(H_{p}/D\) of 4. For jet \(Re\) numbers exceeding 10,000, at any considered \(H_{p}/D\), both \(\dot{Q}/\dot{Q}_{o}\) and \(PEC\) decrease with increasing jet \(Re\) number as seen in Figures 7 and 13, respectively. However, as seen in Figures 7, 9 and 13, for lower jet \(Re\) numbers between 5000 and 10,000, due to the varying effects of the formation and advection of vortices generated by Kelvin-Helmholtz instabilities, effects of the coherence of the core velocity profile of each jet, and effects of the steepness of its adjacent shear layer velocity gradients on local HTCs and \(Nu\) numbers, the trends of \(\dot{Q}/\dot{Q}_{o}\), \(\overline{Nu}/\overline{Nu}_{o}\) and \(PEC\) vary according to \(H_{p}/D\). For \(D_{p}/D\) of 3.5, among the \(H_{p}/D\) and jet \(Re\) numbers considered, the largest \(PEC\) of 1.47 is obtained for \(H_{p}/D\) of 4 and a jet \(Re\) number of 5000, while the smallest \(PEC\) of 1.39 occurs for the same \(H_{p}/D\) at the highest jet \(Re\) number of 20,000. Since the \(PEC\) is greater than unity for all \(H_{p}/D\) and jet \(Re\) numbers studied, enlarging the target surface with CPs equipped with CGVs in a hexagonal configuration is a robust and highly effective design, given the enhanced thermo-economic performance. For an \(H_{p}/D\) of 4.5, where the top face of a CP is only 0.5\(D\) away from the corresponding orifice, although the \(\dot{Q}/\dot{Q}_{o}\) increases rapidly for any jet \(Re\) number, \(PEC\) decreases sharply due to excessive \(\Delta P\) since the potential core of the jets prevail in the impingement zones. For \(H_{p}/D\) of 4.5, the highest and lowest \(PEC\) values of 1.15 and 1.05 are obtained at jet \(Re\) numbers of 5000 and 20,000, respectively. Therefore, for any jet \(Re\) number considered, the thermo-economic performance of the system having \(H_{p}/D\) of 4.5 significantly deteriorates compared with the peak \(PEC\) values obtained at \(H_{p}/D\) of 4.