2.1.3. Wind Speed

The purpose of this experiment was to determine the optimal placement of the PAJ device and the heat source in order to enhance the heat dissipation effect. In general, the volume of air displaced by a rotary fan is inversely proportional to its placement and the wind speed of the fan will decrease with increasing distance. Moreover, when the fan is too close to the heat source, the jet resistance increases, and the heat dissipation effect may

be poorer than natural convection. Thus, the placement distance is an important parameter. A clamp was used to fix the device of PAJ and the distance between it and the hot wire anemometer was changed in increments of 5 mm. Wind speeds were measured at distances of 5, 10, 15, 20, and 25 mm, respectively. Figure 4 exhibits the hot wire anemometer named TES-1341(TES Co., Ltd., Taipei, Taiwan), which can measure wind velocity between 0 and 30 m/s with a resolution of 0.01 m/s and an error of ±3%.

**Figure 4.** Hot wire anemometer.

2.1.4. Thermal Resistance Network Analysis

The HI-LED as shown in Figure 5a with dimensions of 36 × 34 × 2.6 mm<sup>3</sup> and power of 10 W dissipation design used in this study primarily utilizes thermal resistance to evaluate the characteristics of the LED package. Additionally, it can be used to judge the dissipation capacity of a heat sink by observing the level of thermal resistance. That is, a greater thermal resistance indicates a weaker heat dissipation effect. Equation (2) reveals the definition of thermal resistance.

**Figure 5.** LED Module network. (**a**) HI-LED, (**b**) Thermal resistance network.

$$R\_T = \frac{T\_j - T\_a}{Q} \tag{2}$$

*RT*: Total thermal resistance, *Tj*: Temperature of the interface, *Ta*: Temperature of the environment, *Q*: Power consumption

Five devices of PAJ were fabricated using a variety of parameters, such as the piezoelectric sheet spacing, size, and the opening area, to establish performance test methods and to conduct cooling experiments in hopes that the PAJs can be applied to the heat dissipation of HI-LEDs. According to LED cooling modules, the thermal resistance of an LED can be analyzed in two parts. The first part is the thermal resistance of the heat

diffusion (*RL*,1). The second part is the thermal resistance of the natural convection (*Ra*,1), as shown in Figure 5b. The thermal resistance of the heat diffusion (*RL*,1): heat is transferred to the substrate by heat. Since the surface area of the heat radiation substrate is greater than that of the heat source, the rate of heat diffusion is affected by the thermal conductivity of the material, such that the diffusion resistance that is generated, which can be calculated according to Equation (3), is defined as the temperature difference between the center of the LED substrate temperature (*TL*,1) and the average temperature of the substrate interface (*TM*,1) divided by the total power (*Qin*).

$$R\_{L,1} = \frac{T\_{L,1} - T\_{M,1}}{Q\_{\rm in}} \tag{3}$$

The thermal resistance of heat convection (*Ra*,1): the energy transmission created by the density difference between the substrate temperature and the air is called natural convection. A fan can also be installed to enhance the convection effect, resulting in a phenomenon called forced convection. Heat is dispersed into the air via convection and this transfer process is called the thermal resistance of heat convection. Equation (4) defines the temperature difference between the average temperature of the substrate interface (*TM*,1) and the ambient temperature (*Ta*,1) divided by the power (*Qin*).

$$R\_{a,1} = \frac{T\_{M,1} - T\_{a,1}}{Q\_{in}} \tag{4}$$

To simplify, in the diagram of the network analysis *RL*,1 + *Ra*,1 = *RT*,1 of the thermal resistance; *RT*,1 is the total thermal resistance as shown in Equation (5).

$$R\_{T,1} = \frac{\left(T\_{L,1} - T\_{a,1}\right)}{Q\_{\rm in}} \tag{5}$$

#### *2.2. Structural Design-Two Patterns*

The device of PAJ composes of circular piezoelectric sheets and a PMMA plate. The material of the circular piezoelectric sheets is Lead Zirconated Titanite (PZT), which XRD (X-ray Diffraction) patterns reveal the chemical formula of Pb(Zr0.44Ti0.56)O3 as shown in Figure 6. The present study investigated different design patterns, including designs with differences in the piezoelectric sheet size, as well as differences in the spacing and the opening area of the piezoelectric sheet. The tested PAJs were divided into two types according to the design of the jet channels. The first type utilized a linear jet path, as shown in Figure 7a, in which the jet channel outlet has smooth, straight lines and a larger opening area. The second type utilized a flared jet channel, as shown in Figure 7b, the area of the outlet was reduced and the flaring was increased, directing the airflow around the shunt, and increasing the heat dissipation area. The materials of the two jet channels are the PMMA manufactured by the technology of the insert injection molding process with the local heating mechanism of the vapor chamber [34–36], which improves the final strength of the product. The product of PMMA strength can be enhanced outstandingly and reduce the defect of the welding lines with a yield rate of up to 100% through this fabricating procedure. The PMMA has a density of 1.16 g/cm3, a melting point of 135 ◦C, a glass temperature of 102 ◦C, the thermal conductivity of 0.23 W/mk, and tensile strength of 78 MPa in the present paper. Figure 7c exhibited the real PAJ of the second type. These three sets of parameters were used to create five devices with different specifications for comparison. The detailed specifications are shown in Table 1. In addition, the previous literature has indicated that increasing the height of the cavity will directly affect the performance of the jet strength and performance. Therefore, the case5 device served as the control for the case1 device because the two devices are made using piezoelectric sheets with the same diameter and the same opening length, but the spacing between the piezoelectric sheets increased from 2 mm to 3 mm.

**Figure 6.** XRD patterns of the present PZT.

(**a**)

**Figure 7.** *Cont.*

(**c**)

**Figure 7.** Schematic diagram of jet path. (**a**) Linear type (**b**) Flared type (**c**) Real PAJ.

**Table 1.** Specifications of devices of piezo actuation jet.

