**1. Introduction**

With the advances in integrated circuit packaging technology and the miniaturization process, the density of the circuit packages embedded in electronic components and the speed of such circuits have improved. In addition, the frequency of operation and heat generation have been relatively increased. If electronic components operate under high temperatures over a long period of time, their lifetimes may be shortened and their efficiency may be reduced. The use of piezoelectric sheets with polymeric materials for the purpose of heat dissipation was first proposed by Toda [1,2] in 1978. He presented a piezoelectric fan which was produced by using polyvinylidene fluoride resin 2 (PVF2) to make the fan blades, which were combined with the piezoelectric ceramics to generate a swayable cantilever beam structure. The result was a piezoelectric fan that could be compared with other small fans in terms of their effectiveness when used for heat dissipation in electronic products. In recent years, there has been significant interest conveyed in the polymer of PVDF (PVF2 or polyvinylidene difluoride) due to it revealing the strongest piezoelectric properties among these merchant polymers. PVDF (homo- and co-polymers) is generally synthesized and polymerized under the emulsion or suspension between 5 and 160 ◦C and between 5 and 350 atm. This contains generating the biaxially aligned film of PVF2 via admixing in changing capacities of polymethyl methacrylate

**Citation:** Chang, Y.-T.; Wang, R.-T.; Wang, J.-C. PMMA Application in Piezo Actuation Jet for Dissipating Heat of Electronic Devices. *Polymers* **2021**, *13*, 2596. https://doi.org/ 10.3390/polym13162596

Academic Editors: Vijay Kumar Thakur and Arunas Ramanavicius

Received: 3 July 2021 Accepted: 2 August 2021 Published: 5 August 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

(PMMA), which is miscible with PVDF. PVDF has extreme pureness and a semi-crystal thermoplastic fluoropolymer, which can be used in chemical manufacturing facilities and has high mechanical strength, electronics and electricals, wonderful chemical resistance, specialized fields, good processability, energy-related applications, and piezoelectric and thermoelectric properties [3–8]. Chen et al. [9] demonstrated the wonderful performance for practical electrowetting and energy storage applications of the P(VDF-TrFE)/PMMA (PVT/PMMA)-blended films synthesized by a facile solution-blending method. Moreover, the PVT/PMMA blend containing 20 wt% PMMA with significantly enhanced energy storage capability and reduced remnant polarization even turned out to be a superior material for capacitor applications. Mahapatra et al. [10] investigated the latest development in piezoelectric (smart) materials for various applications in energy harvesting and self-powered sensors including vibrations, human motion, and mechanical loads, etc., in detail. They indicated that the enhancing efficiency of light and temperature-based piezoelectric energy harvesting provides endless future possibilities to fulfill growing energy requirements. Furthermore, the technical advancements in materials, device integration, and fabrication procedures in the piezoelectric energy sector will play a major role in dealing with the global energy crisis by exploiting sensors and self-sufficient batteries. Yoo et al. [11,12] employed dual-piezoelectric sheets to improve the vibration behaviors of piezoelectric and polymeric materials. Several types of dual-piezoelectric sheets were designed and then tested with different voltage levels in order to examine the effects of heat exchange by measuring the amplitude of the materials and the wind speed. The findings showed that when the length of a dual-piezoelectric sheet is increased, the harmonic vibration frequency will be reduced. Moreover, when the mezzanine is made from aluminum materials, it can reduce the amount of energy wasted and the cost.

Kalel and Wang [13] studied the integration of a PVDF-based un-bimorph actuator with a layer of one-way shape memory polymers (1W-SMPs) to achieve maximum bending of the piezoelectric cantilever actuator. The results exhibit a maximum bending angle of 40◦ at a DC field of 20 V/μm after 60 s between the SMP layer mounted at the center of the actuator and a length half of the PVDF layer, in which structure could be utilized for high unidirectional bending piezoelectric microactuators. Wu et al. [14] discussed using the jet airstream of a piezoelectric synthetic jet generator to enforce heat convection effects. A synthetic jet enhances the cooling effect of its components. When the surface temperature reaches 100 ◦C, the natural power of the convection dissipation is 2 W, whereas when synthetic jet actuators are employed, the maximum dissipation effect can reach 17 W. When the same power is supplied to the actuator, its dissipation power can be three times bigger than that of the common means of dissipating heat. Ko et al. [15] investigated a piezoelectric fan in motionless air utilizing the CFD and observations with an IR camera. The results showed that the temperature of the heat source is regionally lowered by 28 ◦C and it is very valid to cool it regionally. Ebrahimi et al. [16,17] studied the vortex advancement on all sides of the tips of vibrational cantilever plates with different structures and oscillating behavior. The vortex regimes depended on the length of the cantilever and Reynold number (Re). The results showed that conquering damping can occupy over 50% of the total power input to a piezoelectric fan and exploit it for heat transfer purposes. Smith et al. [18,19] investigated the influence of the Re and the height of the cavity on the synthetic jet flow field. For the same Reynolds number of 2000, as a near flow field of a synthetic jet can generate vortex pairs, it can create a greater jet stream than a continuous jet flow. A distant flow field was similar to a continuous jet flow. Influences of freestream on the piezoelectric fans were carried out to analyze the inlet velocities (from 0 to 7 m/s) at the side of the fan [20]. The influence of the freestream on the tip vortex is major in that the freestream reduces the vortex intensity just after separation from the fan tip. The side vortex is also affected slightly by the freestream. Both vortices are yet deducted by the freestream and drift away from the fan after separation from the fan edge. Wu et al. [21] used piezoelectric sheets in the heat dissipation of electronic components and used the ANSYS software package for experiments and comparison. The simulation results and comparison found

few differences. They also discussed the factors that influence the harmonic frequency and harmonic amplitude, including the length of the piezoelectric materials, placement and distribution, and fixed boundary conditions. The analysis was conducted by changing previous parameters to design four different patterns as alternatives in order to determine the optimal construction. Kercher et al. [22] used synthetic jet technology to manage the heat dissipation of electronic components. Their experimental findings indicated that a piezoelectric synthetic jet had two times better cooling efficiency than the fans presently used as cooling technology.

Many research studies have focused on the aerodynamic performance of oscillating piezoelectric fans with flexible beams composed of polymeric materials because of their potential as active cooling mechanisms for thermal management applications. Conway et al. [23] investigated the influence of crossbeam thickness (1 and 3.7 mm) on the flow field generated by an oscillating crossbeam composed of polymeric materials using a custom-designed particle-image velocity (PIV) facility and numerical analysis. The results inform the design for use in thermal management applications and beneficial for thermal applications where there are constricted environments of oscillating cooling solutions. Liu et al. [24] studied the vibration and cooling performances of the piezoelectric cooling fan using finite element and experimental methods. The numerical results have good agreements with the experimental measurements. Additionally, for the cooling purpose, the piezoelectric cooling fan needs to work under the natural frequency. The aspect ratio of the optimal geometry of the fan blade is 2:3. Jalilvand et al. [25] evaluated the cooling performance of various configurations of synthetic jet-based thermal solution modules based on thermal resistance analysis. The results display that more than 12 W of heat can be dissipated by a DCJ (Dual Cooling Jet). Zhou et al. [26] explored and examined an active enhanced impingement cooling of a circular jet using a piezoelectric fan with low power consumption. The results show that the impingement cooling of the jet enhances as the Re increased. Usually, the new jet can supply superior performance of heat transfer at a small gap and a high Re. A circular enclosure divided by a movable barrier has been numerically investigated inside a separated circular attachment in the presence of a flexible wall [27]. The results verify that the degree of distortion of the plate is straightly dependent on the number of forces. A broad scope of PMMA (PolyMethyl MethAcrylate) polymers is regularly employed for various applications in engineering. The distinct properties of PMMA including the low density, cheap, esthetics, suitable physical and mechanical properties, ease of manufacture, and readily melt-processible technique can be fabricated into parts by injection and compression molding. Accordingly, PMMA is frequently applied in chemical processing equipment (e.g., tubes, valves, pumps, pipes, and fittings), sensors, and actuators, etc. Some chemical modifications and mechanical reinforcement techniques involving adding various types of nanofibers, nanoparticles, nanofillers, nanotubes, and hybrid materials (nanoparticles) are made known to enhance the functions of thermal and dielectric properties and tensile strength of PMMA-based materials in recent decades [28–33]. The present study utilizes the piezo actuation jet (PAJ) with the PMMA plate for dissipating heat of electronic devices. The polymeric material of PMMA in the present paper is manufactured through a thermoplastic injection molding and rapid-uniform heating and cooling cycle system associated with a vapor chamber technology, which can improve the tensile strength and decrease the deficiency of the welding lines of a plastic product [34,35]. Tsai et al. [36] exhibited that the plastic products with two opposite gates were found to enhance by 6.8 ◦C and 10 ◦C of tensile strength compared with the traditional one, and the other plastic product with eight holes plate is reduced from 12 μm to 0.5 μm of the depth of the welding line.
