## 4 Results and Discussion
### Thermal Characteristics  
Figure 12 shows the dimensionless temperature contours of different heat sink arrays when Reynolds number \(Re=500\) and \({X_{T}}^{*}={X_{L}}^{*}=1.5\). First, the dimensionless fluid temperature and dimensionless solid temperature in the heat sink area are compared, there is significant difference, the dimensionless solid temperature is higher than the dimensionless fluid temperature, meaning in the present numerical simulation, the solid and fluid have not yet reached local thermal equilibrium. Therefore, the two-equation model meets the thermophysics in the current test system better than one-equation model. Secondly, the dimensionless solid temperature distributions of different heat sink arrays are compared (as shown in Figure 12a-c). It is observed that among the heat sink arrays with the same number of pin fins (Sample 1, Sample 2 and Sample 3), the heat sink array with higher porosity has lower overall dimensionless solid temperature, suggesting that the heat is transferred to the fluid effectively. This is because in the present cooling system, the heat considering fin efficiency radiates in each unit volume of heat sink, and then it is transmitted to the fluid by convection heat transfer. Therefore, it is basically conjugate heat transfer of thermal conduction and convection. When the porosity of heat sink is low, the upward thermal conduction capability of pin fins is better and the fin efficiency is good, thus contributing to overall heat transfer (Equation (13)). However, as shown in Figure 8, the heat sink array with lower porosity generates higher flow resistance, so that less fluid flows into the heat sink, thereby reducing the convection heat transfer of heat sink. Therefore, the heat sink Sample 1 with the smallest porosity accumulates heat in the pin-fins, so that it has the highest  
Figure 11: Dimensionless pressure drops for different heat-sink arrays with various \({X_{T}}^{*}\) and \({X_{L}}^{*}\). overall dimensionless solid temperature. The heat sink Sample 3 with the largest porosity has more cold inflow, and the dimensionless solid temperature is lower. In addition, the heat sink arrays with the same porosity (Sample 3, Sample 4 and Sample 5) are compared, as shown in Figure 12c-e. The overall dimensionless solid temperature of the Sample 3 heat sink array with more pin fins is lower than that of the Sample 4 and Sample 5 heat sink arrays with fewer pin fins, especially in the first row and the second row of heat sink array. In other words, Sample 3 with more pin fins has more heat carried away, so it is unlikely to accumulate heat. However, according to the conjugate heat transfer principle stated in Figure 12a-c, as Sample 3, Sample 4 and Sample 5 have the same porosity, they have the same upward thermal conduction capability of pin fins. However, according to Figure 10, the Sample 5 heat sink array with fewer pin fins has lower flow resistance, and it is supposed to have higher air inflow. The reason that the dimensionless solid temperature of heat sink is slightly higher than that of Sample 3 is explained below. First, the heat exchange area in unit volume of Sample 3 with more pin fins is far larger than that of Sample 4 and Sample 5 (see Table 1). This makes up the air inflow during convection heat transfer. Secondly, as shown in Equations (7) and (8), [PERSON] _et al._[24] indicated that the heat  
variable \({X_{T}}^{*}=1.25\), 1.5 and 2, the dimensionless solid temperature of heat sink increases with \({X_{T}}^{*}\). As the increase of \({X_{T}}^{*}\) amplifies the bypass effect of air flow, the air flow entering the heat sink decreases, and the heat removed decreases, so the solid part of heat sink accumulates heat and has higher temperature. Relatively, when the \({X_{T}}^{*}\) is larger, as the air flowing into the heat sink is lower, the fluid has larger temperature rise though the pin fins transfer less heat to the fluid. This result is reflected in the dimensionless fluid temperature contours.