An Experimental Study of Fluidic Coupling Between Multiple Piezoelectric Fans

An Experimental Study of Fluidic Coupling Between Multiple Piezoelectric Fans Mark Kimber, Suresh V. Garimella, and Arvind Raman Cooling Technologies Research Center School of Mechanical Engineering Purdue University 585 Purdue Mall, West Lafayette, IN 47907-2088 (765) 494-5621, sureshg@purdue.edu ABSTRACT Piezoelectric fans have been shown to provide large enhancements in heat transfer over natural convection while consuming very little power. These fans consist of a piezoelectric material attached to a flexible cantilever. When driven at resonance, large oscillations at the cantilever tip cause fluid motion, which in turn, results in improved heat transfer rates. In this work, the performance of two fans operating simultaneously is analyzed. A coupling phenomenon is observed which, for a given input, causes an increase in vibration amplitude of as large as 40 percent compared to an isolated single fan. Understanding this coupling is essential in order to create design tools for implementing piezoelectric fans in practical cooling systems. Mylar fans are analyzed, and multiple experiments performed in air and within a vacuum chamber to isolate the source of coupling and determine its magnitude. The results suggest that coupling is almost entirely due to fluid-structure interaction, and the impact on the characteristic vibration parameters is explored. The collective motion of the fans decreases the fluidic damping, and the coupling magnitude is determined for a range of fan pitches. KEYWORDS: Piezoelectric fan, fluidic coupling, cantilever INTRODUCTION A piezoelectric fan consists of a piezoelectric material bonded to a flexible cantilever blade. An alternating input signal causes the piezoelectric material to contract and expand, generating shear forces between itself and the blade. These forces produce oscillations at the free end of the cantilever blade, and when driven at the resonance frequency of the structure, the oscillations become large and serve to agitate and move the surrounding fluid, which enhances heat transfer when compared to natural convection alone. These fans consume very little power and can be built and modified to meet various geometric constraints for many applications. Because of this, piezoelectric fans have received much attention of late as a thermal management solution. Many aspects of the performance of piezoelectric fans have been studied. A detailed analysis of the two-dimensional flow field generated from a vibrating cantilever beam was presented by Kim et al. [1]. Vortices were observed to be shed each time the beam passed the position of zero displacement, i.e., at twice the vibration frequency. The maximum fluid velocity was found to be roughly four times that of the maximum tip velocity. The streaming flow induced by vibrating piezoelectric fans was modeled by Açıkalın et al. [2], and good qualitative agreement was found between the predicted flow patterns and experimental visualizations for small displacements. Açıkalın et al. [3] analyzed a single piezoelectric fan vibrating near a heat source to determine the conditions under which heat transfer could be optimized. The factors investigated included the fan length, amplitude, frequency offset and distance from heat source. Feasibility studies for implementing piezoelectric fans in electronic systems were conducted by Açıkalın et al. [4] and Wait et al. [5], where piezoelectric fans were placed within a laptop to further enhance the heat transfer performance of the rotary fan by increasing the fluid mixing in stagnant regions normally not accessed by the rotary fan. A simulated cell phone enclosure was also considered for which enhancements over natural convection were quantified for various piezoelectric fan orientations. Numerical modeling of the fluid flow and heat transfer induced by a piezoelectric fan has also been conducted [6]. The flow field generated from these fans is found to be extremely complex and highly dependent on the distance from fan tip to heater, as well as other boundary conditions. The flow field is also dependent on the vibration characteristics of the fan, which have been explored in [7, 8]. Much of the previous work has considered a single fan or cantilever beam, and very little research has been conducted to better understand the behavior of multiple fans. The twodimensional flow field generated from two flexible cantilevers was analyzed experimentally by Ihara and Watanabe [9]. They investigated the behavior for in-phase and out-of-phase vibration at three different fan separations. The cantilevers were sandwiched between two large plates, thereby approximating a two-dimensional flow field. The results were compared to the flow field generated by a single cantilever in the same experimental setup, and the volumetric flow rate for in-phase vibration was found to be approximately double that of a single cantilever. However, their work was exclusively dedicated to the fluid domain, and heat transfer characteristics were not considered. Mass transfer experiments on a vertical 0-7803-9524-7/06/$20.00/ 2006 IEEE 333

surface targeted by two piezoelectric fans were conducted by Schmidt [10] using the naphthalene sublimation technique. The fans vibrated out of phase and the separation distance between fans was kept constant. Power-law correlations were found to reasonably describe both maximum and surfaceaveraged Sherwood numbers for three separate distances from the vertical surface. In each case the Sherwood numbers formed contours symmetric about the midpoint of fan separation. However, the fan pitch was not treated as a variable and therefore any existing coupling between fans that could influence the performance was not characterized. The present work further addresses the complicated nature of the collective influence of multiple piezoelectric fans. Heat transfer experiments are conducted for two separate fan orientations. Coupling between fans is observed to cause an increase in vibration amplitude, which further augments the heat transfer obtained. The degree of coupling is more readily apparent when the fans vibrate in the same plane, and this orientation is further investigated to determine the source and magnitude of coupling. To exploit fan coupling in practical implementations, the coupling must be understood in terms of the details of vibration and its corresponding effect on heat transfer. This paper discusses the heat transfer investigation, followed by the fan coupling study. HEAT TRANSFER EXPERIMENTS Experiments are conducted to characterize the thermal performance of multiple piezoelectric fans. Of particular interest is the combined performance of two fans and the improvement observed relative to a single fan. Heat transfer characteristics are determined experimentally for a pair of piezoelectric fans oriented in two different ways as shown in Figure 1. The direction of vibration distinguishes each orientation, and is horizontal for orientation A, while it is vertical for orientation B. A B Figure 1. Two fan orientations analyzed during heat transfer experiments: horizontal vibration (orientation A), and vertical vibration (orientation B). Experimental setup The target being cooled is illustrated in Figure 2 and consists of a thin sheet of aluminum of dimensions 38.1 mm 38.1 mm 2.0 mm with a thin-film heater attached to its back, as described in [3]. Losses from the heat transfer surface are minimized by means of the insulation block on the back and along the sides of the aluminum sheet, such that only the front surface is exposed to air. Five thermocouples are mounted on the exposed aluminum surface to yield the average surface temperature of the heat source. An additional thermocouple is attached directly to the heater and another to the back of the insulation to estimate losses through the insulation. The ambient air temperature is also measured with a thermocouple (not shown). To accurately estimate radiation losses, the exposed surface of the aluminum block is painted with Krylon #1602, which has a known emissivity of 0.95 [11]. The setup is placed in a large transparent box to isolate it from extraneous convection currents in the room. The thin film heater is powered by a dc power supply; the input voltage and current are monitored and adjusted such that the power input (P in ) is held at 1.6 W for all the experiments with an estimated uncertainty of less than 1%. Typical heat losses through the insulation were around 0.03 W as revealed by a simple 1-D analysis. The heat transfer coefficient is calculated according to Equation 1, where the heat lost through the insulation (q ins ) and that due to radiation (q rad ) are subtracted from the power input. This calculation uses the exposed surface area (A s ) of the heater and temperature difference between ambient (T ) and average surface (T s ) temperatures. Therefore, all values reported in this paper represent area-averaged heat transfer coefficients with uncertainties smaller than 5%: P q h A T in ins rad s s q T The commercially available fans used in these experiments are illustrated in Figure 3, and have a length (L) of 64.0 mm, width (w) of 12.7 mm and a fundamental resonance frequency near 60 Hz. The flexible blade is made from Mylar and has a maximum vibration amplitude (b) of 12.7 mm. The two parameters varied during the heat transfer experiments are also shown and for each orientation, fan pitch (p) and the fan to heater separation distance (d) are the primary factors under investigation. During the experiments, the fans are driven with a 60 Hz sinusoidal signal at 120 V for all heat transfer experiments, yielding a vibration amplitude of roughly 10 mm for a single isolated (not coupled) fan. The effect of fan coupling for each orientation is different for particular types of vibration. In orientation A, the vibration amplitude increased dramatically for in-phase vibration, whereas a negative effect (i.e., decrease in vibration amplitude) is observed for out-of-phase vibration. It is also worthwhile to note that for this orientation, the limit on achievable fan pitch greatly depends on the phase difference between the two fans. This is shown in Figure 4, where the envelopes of vibration cannot overlap for out-of-phase vibration due to the physical collision of fan tips, thereby requiring the fan pitch to be larger than twice the vibration amplitude. For in-phase vibration, this is clearly not the case and the fan pitch can approach zero because the fans will never collide, enabling an overlap of vibration envelopes. To take advantage of this fact and fit two fans in as small a space (1) 334

as possible, only in-phase excitation (0 phase difference of driving signal) is considered during heat transfer experiments for orientation A. The opposite effect of fan coupling is observed for orientation B where out-of-phase vibration produces the highest vibration amplitude. Therefore for this orientation, only out-of-phase excitation (180 phase difference of driving signal) is considered. It is understood that any two fans cannot have identical resonance frequencies due to unavoidable variations during the manufacturing and assembly processes. Therefore, discrepancies are seen when comparing the output phase difference (actual motion of fans) to the input phase difference (driving signal). Although inphase (or out-of-phase) excitation does not guarantee in-phase (or out-of-phase) vibration, the inherent phase difference is measured to be less than 5 for heat transfer experiments and the magnitude of its impact on the results is considered minimal. w Piezoelectric Fan p L b d p Heat Source Orientation A Orientation B Heat Source Insulation Block Figure 3. Illustration of various geometric parameters: fan length (L) and width (w), vibration amplitude (b), and fan to heater separation distance (d). Also shown is the fan pitch (p) for the two different multiple-fan orientations considered for heat transfer experiments. Thin Aluminum Plate Thin Film Heater 2b 2b Thermocouples p p Figure 2. Illustration of heat source consisting of a thin film heater attached to a thin aluminum plate, all surrounded by an insulation block, leaving a single surface exposed where heat transfer characteristics are measured using five thermocouples mounted on the aluminum plate. Losses through the insulation are measured with two additional thermocouples mounted on the back sides of the thin film heater and insulation block. Out of phase Limit: p < 2b In phase No Limit: p 0 Figure 4. Limit of fan pitch (p) for orientation A of two piezoelectric fans. The solid lines depict a current location of each fan, while the dashed lines are included to show the overall vibration envelope for each fan. 335

Results from heat transfer experiments Results from six different fan pitches (2.54, 7.62, 10.16, 12.70, 17.78, and 22.86 mm) and two separate distances from the heat source (1.59 and 3.18 mm) are shown in Figure 5. For each fan pitch considered, the performance is greatest when the fan is closest to the heat source. There appears to be an optimum heat transfer rate at approximately a fan pitch of 13 mm for both distances from the heat source. It should be noted that although the same input signal drives both fans for all experiments, the vibration amplitude is dependent on the fan pitch due to the coupling effect, and is greatest at the smallest fan pitch. However, the increase in amplitude due to coupling at the smallest pitch does not necessarily yield the best operating conditions. From a heat transfer standpoint, the optimal conditions occur for a fan pitch of 12.70 mm, at which the corresponding vibration amplitude is 11.10 mm, yielding a non-dimensional fan pitch (pitch divided by amplitude) slightly larger than unity (1.14). It is emphasized that this performance is described by the average heat transfer coefficient. Presumably, the maximum local heat transfer coefficient will increase with vibration amplitude, or as the pitch is decreased. However, a smaller fan pitch also decreases the coverage area, or combined vibration envelope, as seen by the heater. Therefore the impact of a larger local heat transfer coefficient due to a small pitch decays after a shorter distance, and the result is a decrease in the average heat transfer coefficient. similar for both distances from the heater, and the heat transfer rate decreases as the fan pitch increases, ranging from 104.46 to 97.82 W/m 2 K with the fan closest to the heater (d = 1.59 mm) and 102.94 to 98.09 W/m 2 K with the fan farther from the heater (d = 3.18 mm). At the largest fan pitch considered (22.86 mm), the outside edge of each fan is near the geometric boundaries of the heat source. An important fraction of the fan cooling-area coverage is beyond the heat source size, and hence, wasted and not accounted for in the measured average heat transfer coefficient. Experimental results for heat transfer coefficients with both orientations are summarized in Table 1, where the best case amongst the multiple-fan experiments is compared to the performance of a single fan, as well as to results from natural convection experiments. Results from both multiple-fan configurations are comparable and represent a 19-21% increase over a single fan and over a 650% increase compared to natural convection. It is important to note that both multiple-fan configurations exhibited fan coupling to some degree, with the coupling being greater for in-plane than outof-plane vibration. Therefore, a part of the performance increase over a single fan is simply attributed to larger vibration amplitudes, while the remainder is due to the presence of the additional fan. Table 1. Summary of results from heat transfer experiments. All reported results are based on an average surface temperature and input heater power of 1.6 W. Configuration Best case convection coefficient [W/m 2 K] Natural Convection 16.18 Single Fan 88.03 Orientation A 106.51 Orientation B 104.46 Figure 5. Heat transfer performance for orientation A at six fan pitches and two distances from heat source (d = 1.59 mm and 3.18 mm). For each pitch considered the performance is greater when the fan is closest to the heat source. The optimal condition appears to be when the pitch is approximately equal to the vibration amplitude. For orientation B, the average heat transfer coefficient is determined for five fan pitches (12.75, 15.24, 17.78, 20.32, and 22.86 mm) and is reported at two distances from the heat source (1.59 and 3.18 mm). The maximum performance occurs at the smallest fan pitch of 12.75 mm, only slightly larger than the width of the fans (12.7 mm). The trends are It should be noted that these heat transfer results are all based on the average surface temperature of a 38.1 mm 38.1 mm heat source. Further research with an improved larger heater design is underway to more completely describe local heat transfer coefficients and their dependence on the collective influence of the two piezoelectric fans. However, the present work shows that fan coupling can indeed be exploited to improve the thermal performance obtained when multiple fans operate in close proximity. Such fan coupling is investigated in greater detail in the following section. FAN COUPLING EXPERIMENTS The observations from the heat transfer experiments suggest that two fans vibrating in close proximity influence the 336

vibration characteristics of the pair, and hence, the thermal performance. This fan coupling could be brought about by two mechanisms: i) Structural coupling, by which the two structures are coupled together through the clamping structure represented by a spring of finite stiffness, and ii) Fluid structure coupling, which is a more complicated problem and suggests that as the fans travel in a given direction, the leading fan removes some of the fluid resistance seen by the trailing fan, thereby decreasing the fluidic damping. Much like a cyclist decreasing fluid drag by traveling directly behind another, this effect is more pronounced as the fan pitch becomes smaller. Blade materials most able to exhibit large oscillations at the free end of a piezoelectric fan typically have a small modulus of elasticity and small density. For structures with these characteristics, as is the case with the fans under investigation in the current work, fluidic damping is of significance in describing the characteristic vibration parameters. It is therefore likely that the fluid structure interaction serves as the dominant source of the fan coupling observed. The impact of this type of coupling can be observed by looking at the characteristic vibration parameters, namely quality factor and resonance frequency. The quality factor (Q) is a dimensionless quantity, and is related to the damping coefficient ( ) according to [12] 1 Q (2) 2 and will increase if the fluid primarily serves as an additional source of damping through viscous drag. However, if the fluid primarily acts as an added mass, then a shift down in natural frequency should be apparent as the added mass is increased. To investigate fan coupling, experiments are first performed in a vacuum chamber, with the effect of fluid removed, and compared to identical experiments performed under atmospheric conditions. The two possible sources of coupling are isolated by this means. It will be seen below that fluid structure coupling indeed dominates the fan behavior. The second set of experiments focus on estimating the quality factor and resonance frequency at various voltage levels and fan pitches. Each of these experiments is now described in more detail, followed by results from both. Fan coupling experimental setup To isolate possible sources of coupling, two piezoelectric fans are mounted in a vacuum chamber as shown in Figure 6, with accommodations for electrical inputs to the fans. An optical viewport provides the capability to capture vibration signals. A laser displacement sensor (Keyence LK-G157) with an accuracy of 0.05% is used to obtain the displacement signal from the fan nearest to the viewport. A high vacuum pump (Edwards E2M2) is used to create near-vacuum conditions, where pressures within the chamber reach less than 10 Pa, or 10-4 that of ambient pressure. The fans are excited in-phase at a frequency of 60 Hz and at four discrete levels of input signal amplitude (20, 40, 80, and 140 V). Two fan pitches (9.6 mm and 18.3 mm) are analyzed under vacuum and atmospheric conditions, and the corresponding vibration amplitude is measured and compared to that from a single fan at the same input levels in vacuum and atmospheric conditions. Electrical Feedthroughs (a) Piezofans Optical Viewport Figure 6. Vacuum experimental setup to isolate sources of piezoelectric fan coupling: a) two fans and electrical feedthroughs, and (b) bell jar placement with optical viewport for vibration signal acquisition. Only the signal from the fan nearest the viewport is captured for each experiment. The experimental setup used to estimate natural frequencies and quality factors is shown in Figure 7 where two piezoelectric fans are mounted near each other and the vibration motion is captured for each fan via two laser displacement sensors. In order to accurately estimate the natural frequency and damping, a circle fit method is employed [12], which requires both magnitude and phase response at multiple points near a resonance frequency. For this experiment, data are captured simultaneously from the input signal to each fan as well as the two signals from the laser displacement sensors capturing the motion of each fan tip. The input frequency is varied in the range of 57 to 62 Hz in increments of 0.1 Hz, yielding amplitude and phase information at 51 frequencies for each different fan pitch. It is understood that the output phase of the two fans will vary depending on the driving frequency; therefore, a phase lock function generator is employed to control the phase difference of input signals between the two fans. This enables the output phase to be zero at each driving frequency considered. Three different fan pitches (2.54, 8.51, and 18.54 mm) and two input signal amplitude levels (60 and 140 V) are considered, and the natural frequency and quality factor are estimated for each unique configuration. Similar data at the same driving frequencies are also obtained for a single fan to enable a comparison of the results from coupled fans to those of a single, isolated fan. Results from coupling isolation experiments Results in vacuum and atmospheric conditions for both single and two-fan experiments are shown in Figure 8. In the absence of a fluid environment in vacuum, the single fan is seen to vibrate at much larger amplitudes for all reported input voltages than the corresponding amplitudes for vibration in air. The amplitudes are nearly double for most voltage inputs. (b) 337

However, the vibration amplitude is comparable in vacuum at a given voltage, regardless of whether a single fan or two fans are considered. In contrast, the vibration amplitude for two fans under atmospheric conditions is larger compared to that of the single fan. The percentage increase in vibration amplitude for the smaller fan pitch (p = 9.6 mm) for a given input signal is more pronounced for the smaller fan pitch, revealing the dependence of coupling magnitude on fan pitch. It is clear from these experiments that the most significant source of fan coupling is indeed fluid structure interaction. Results from the next set of experiments provide further insight on the magnitude of this coupling and its impact on vibration characteristics. Laser Displacement Sensors Piezofans Results from vibration experiments The quality factor results are shown in Figure 9, where the ratio of coupled and isolated quality factors is plotted as a function of fan pitch for both input signal levels in order to show the relative decrease in viscous drag. As the fan pitch is increased, the quality factor ratio approaches unity which indicates that the quality factor becomes uncoupled as the distance between fans increases. Also, the quality factor increases as the fan pitch becomes smaller, suggesting that fluidic damping is decreased for fans vibrating in close proximity. Notice that for the largest fan pitch considered (p = 18.54 mm), the ratio of quality factors is comparable for both input levels, and the same is true for the intermediate fan pitch (p = 8.51 mm). However, this is clearly not the case at the smallest fan pitch (p = 2.54 mm) where a large difference is seen between the two input levels. At this fan pitch, the smaller input signal (60 V) yields a larger increase in the ratio of quality factors when compared to the larger input signal (140 V). This suggests that for larger fan pitches, the desirable increase in quality factor is to some extent independent of the input signal, and therefore the vibration amplitude. This does not indicate the quality factor magnitude itself is comparable, only the ratio of coupled to isolated quality factors. Also, for a smaller fan pitch, the increase in quality factor is highly dependent on the input signal magnitude, and is greater for smaller input levels, or vibration amplitudes. Figure 7. Vibration parameter experimental setup using two laser displacement sensors to simultaneously measure vibration signals for two piezoelectric fans at various fan pitches. Figure 8. Vibration amplitude of single fan compared to two fans at pitches 9.6 mm and 18.3 mm both within vacuum chamber and in atmospheric conditions. Figure 9. Quality factor estimates for three different fan pitches and two input magnitudes. The coupled quality factor is higher than the isolated (hence a ratio > 1) for all experiments performed. In each case the quality factor is calculated using a circle fit method [12] from magnitude and phase data of a frequency sweep near the fundamental resonance frequency. For reference, the corresponding quality factors of isolated fans at the input levels of 60V and 140V are 19.58 and 14.92, respectively. The quality factor results, along with resonance frequency estimates, are summarized in Table 2 for all conditions in this work. It can be seen that the natural frequency, like the 338

quality factor, is also dependent upon the degree to which the fans are coupled. As the fan pitch is decreased, the frequency shifts up, suggesting that the added mass from the fluid has decreased. This trend supports the argument that the coupling can be understood as resulting from a portion of the fluid, and hence the effective mass, being removed by the leading fan for the trailing fan. The result is a smaller effective mass, causing an increase in the resonance frequency. However, the relative magnitude of this change (only about 1%) compared to typical changes of quality factors (10-60%) suggests that the fan coupling observed in this work is almost entirely described by the decrease in damping, or increase in quality factor, with the effect of the decrease in added mass being very small. Table 2. Summary of results from experiments estimating vibration characteristics for coupled and isolated fan conditions. Resonance frequency and quality factor are listed for each fan in isolated conditions and for the pair in coupled conditions at three separate fan pitches (d) and two input levels. Configuration Input = 60 V Resonance frequency [Hz] Quality factor Isolated Fan 1 59.5 19.13 Isolated Fan 2 59.5 20.03 d = 2.54 mm 60.1 31.02 d = 8.51 mm 59.8 25.16 d = 18.54 mm 59.5 21.19 Input = 140 V Isolated Fan 1 59.4 14.88 Isolated Fan 2 59.4 14.92 d = 2.54 mm 60.0 21.72 d = 8.51 mm 59.6 19.39 d = 18.54 mm 59.5 16.57 This understanding of fan coupling is beneficial in designing and optimizing the thermal performance for practical applications. When two fans operate in close proximity, only a small frequency shift occurs, which implies the major benefit from fan coupling, namely the increase in vibration amplitude, can be exploited without any extra control circuitry to account for changes in driving frequency. CONCLUSIONS A coupling phenomenon is observed for two piezoelectric fans oscillating in phase in close proximity. The coupling increases the vibration amplitude, which in turn influences the heat transfer rates achieved from the fan air flow impinging on a heated surface. Behavior of the pair of fans is compared during operation in vacuum and atmospheric conditions, which reveals that the source of fan coupling is fluid structure interaction. The changes in the characteristic vibration parameters from fan coupling are almost entirely explained by a decrease in fluidic damping, or an increase in quality factor. While the magnitudes of these changes are a function of the fan geometry and material properties, the results from the present work yield important insights into the behavior of multiple piezoelectric fans. More detailed heat transfer experiments are underway to better quantify the local and area-averaged convection coefficients on a larger heated surface subject to a controlled heat flux. Additional experiments are also being conducted for piezoelectric fans of different geometries and materials. Acknowledgements The authors acknowledge the financial support from members of the Cooling Technologies Research Center (www.ecn.purdue.edu/ctrc), a National Science Foundation Industry/University Cooperative Research Center and Purdue University. REFERENCES [1] Y. Kim, S.T. Wereley, and C. Chun, Phase-resolved flow field produced by a vibrating cantilever plate between two endplates, Physics Fluids, vol. 16, no. 1, pp. 145-162, 2004. [2] T. Açıkalın, A. Raman, and S.V. Garimella, Twodimensional streaming flows induced by resonating, thin beams, J. Acoust. Soc. Am., vol. 114, no. 4, pp. 1785-1795, 2003 [3] T. Açıkalın, S.V. Garimella, J. Petroski, and A. Raman, Optimal design of miniature piezoelectric fans for cooling of light emitting diodes, 2004 Inter Society Conference on Thermal Phenomena, pp. 663-671, 2004. [4] T. Açıkalın, S.M. Wait, S.V. Garimella, and A. Raman, Experimental investigation of the thermal performance of piezoelectric fans, Heat Trans. Eng., vol. 25, no. 1, pp. 4-14, 2004. [5] S.M. Wait, T. Açıkalın, S.V. Garimella, and A. Raman, Piezoelectric fans for the thermal management of electronics, XVII National and VI ISHMT/ASME Heat and Mass Transfer Conference, IGCAR, Kalpakkam, Jan. 5-7, 2004. [6] T. Açıkalın, B.D. Iverson, S.V. Garimella, and A. Raman, Numerical investigation of the flow and heat transfer due to a miniature piezoelectric fan, Proceeding of IMECE 2004: 2004 International Mechanical Engineering Congress & 339

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