3.3.2. Analytical Comparison of Nusselt Number Nu with Re and Pressure Drop Δ*p* with *v*

As shown in Figure 9, the pressure drop across the different models of radiators increases with increasing inlet flow, and the trend of increase can be seen as approximately linear. This is due to the fact that at low inlet flow rates, the dominant flow pattern within the radiator is the laminar flow. As the inlet flow rate increases, the flow pattern within the radiator gradually changes to turbulent flow. The filling of the metal foam increases the flow disturbance within the radiator. This ultimately leads to an increase in the resistance to fluid flow, which, in turn, increases the pressure drop between the inlet and the outlet. For the same inlet flow rate, the pressure drop in the electronic radiator increases with the number of fins contained. However, at a certain inlet flow rate, the difference in pressure drop between different types of electronic heat sink is not significant. This is because the pressure drop generated by the fluid flowing through the electronic heat sink depends primarily on the metal foam itself. Moreover, the increase in the number of fins in practice results in the decrease in the fin spacing, thus, in effect, changing the width of the contact cross-section of the fluid in the direction of movement. This ultimately leads to an uneven velocity distribution of the fluid at the inlet. The pressure drop generated by the electronic heat sink also depends on the pore density of the filled metal foam. The greater the pore density, the more chaotic the metal foam's own skeleton structure becomes, which, in turn, generates greater pressure losses.

Equation (11) was used to obtain the relation curve between the *Nu* and *Re* of the radiator. As shown in Figure 10, the Nusselt number of the electronic heat sink filled with metal foam is significantly higher than the Nusselt number of the electronic heat sink not filled with metal foam. This indicates that the heat transfer capability of the heat sink filled with metal foam is enhanced. The heat transfer strength of each type of heat sink also differs under different conditions of the Reynolds number. As it can be seen from Figure 10, the Nusselt number increases with the increasing Reynolds number. Additionally, the Nusselt number increases with the increasing pore density at different pore densities, while it increases and then decreases with the number of fins contained in the electronic heat sink. As can also be concluded from Figure 10 that the Nusselt number reaches a maximum when the number of fins is three. This trend is consistent with that shown by the convective heat transfer coefficient.

Equation (16) was used to obtain the radiator resistance coefficient *f* and *Re* relation curve. As shown in Figure 11, the frictional drag coefficient gradually decreases as the Reynolds number increases. As *Re* > 3000, the trend of the decreasing frictional drag coefficient becomes progressively slower. The coefficient of frictional resistance and the Reynolds number follow the same trend for electronic heat sinks with and without metal foam filling. The drag coefficient of the electronic heat sink with metal foam filling is significantly higher than that of the electronic heat sink without metal foam filling, due to the structure of the filling metal foam itself.

**Figure 9.** Radiator pressure drop Δ*p* and *v* curve.

**Figure 10.** Relation curve between *Nu* and *Re* of radiator.

**Figure 11.** Radiator resistance coefficient of *f* and Re relation curve.
