*3.3. Data Processing Results and Performance Curve Analysis*

3.3.1. Analytical Comparison of the Total Heat Transfer Coefficient K Versus Flow Rate *v*

As shown in Figure 5, the heat transfer in the foam-filled electronic heat sink is significantly higher than that of the unfilled heat sink. In the case of a foam-filled electronic heat sink, the heat transfer differs for different pore densities of the metal foam. As the pore density increases, the contact area between the metal foam and the fluid increases, and the total heat transfer area of the heat sink increases. On the other hand, the heat transfer of an electronic heat sink is also related to the metal foam it is filled with. The thermal conductivity of the copper metal foam is higher than that of the aluminum metal foam. Hence, the heat transfer is higher in the same model for the heat sinks filled with copper metal foam material at the same speed conditions.

Equation (16) was used to obtain the relation curve of the heat transfer coefficient K and v of the radiator. As shown in Figure 6, the convective heat transfer coefficient increases by around 31.57% when the number of electronic radiator fins is increased from no fins to two fins. When the number of fins is increased from two to three, the convective heat transfer coefficient increases by about 26.08%. When the number of fins is increased from three to five, the convective heat transfer coefficient decreases, as shown in Figure 7. This is due to an increase in the number of fins accompanied by a decrease in fin spacing and interference in the thermal boundary layer between adjacent fins, resulting in a delay in heat transfer. As a result, there is a maximum number of fins that allows the radiator to

achieve optimum heat transfer. As can be seen from the graph, the overall heat transfer coefficient is best when the number of fins is three.

**Figure 5.** The relationship between heat transfer *Q* and *v* of radiator.

**Figure 6.** Relation curve of heat transfer coefficient *K* and *v* of radiator.

On the other hand, the convective heat transfer coefficients with and without metal foam filling are very different for the same number of finned electronic heat exchangers. The heat transfer coefficient is significantly higher for the foam-filled type of electronic heat

sink than for the unfilled type. Moreover, the convective heat transfer coefficient is also related to the pore density of the filled metal foam, which is related to the length of the pore diameter. The greater the pore density, the smaller the corresponding pore length, and the smaller the diameter of the metal foam skeleton. When the porosity of the metal foam is certain, the contact area between the fluid flowing through the metal foam and the solid also increases, thus strengthening the heat transfer capacity of the electronic heat sink. At the same time, the greater the density of the pores, the greater the disruption of the skeleton within the metal foam and the greater the disturbance caused to the fluid flow, which, in turn, enhances the convective heat transfer intensity. Based on the experimental results, it can be concluded that the highest convective heat transfer coefficient is obtained for copper metal foam with a filled pore density of 20 PPI at a fin number of three.

**Figure 7.** Curve of *k* versus *v* for radiators with different numbers of fins.

Equation (2) was used to obtain the heat transfer rate of the radiator. In Figure 8, the heat exchange increasing rate decreases with the increasing flow rate. This is due to the fact that the greater the fluid flow velocity, the greater the degree of turbulence. This results in a consequent decrease in the heat transfer rate. As can be seen from Figure 8, the greatest increase in the heat transfer is in the finless radiator. This is due to the specific surface area of the metal foam itself. The larger the area of contact between the fluid and the solid, the larger the heat transfer area will be, ultimately increasing the heat transfer effect.

**Figure 8.** Heat transfer rate of radiator.

Electronic heat sink components with different numbers of pieces are filled with materials of the same porosity and different porosity densities. The rate of increase in the convective heat transfer coefficient gradually decreases when the fluid flow rate is in the range from 10 to 30 L/h. The convective heat transfer coefficient improvement rate gradually increases when the fluid flow rate is in the range of 30–60 L/h. When the fluid flow rate is in the range of 30–60 L/h, the convective heat transfer coefficient improvement rate gradually increases. This indicates that after filling the electronic heat sink components with metal foam, the effect of the enhanced heat transfer is more pronounced at low turbulence and less effective at high turbulence. This is because the main effect of the filled metal foam is to create a cyclonic flow in the core part of the flow. At low flow rates, the metal foam promotes a degree of turbulence and thus enhances heat transfer more effectively. At high flow rates, however, turbulence is sufficiently developed, and the enhanced effect of filling with metal foam on the heat transfer in the flow is reduced.
