- Email: [email protected]
Investigation of a piezoelectric fan embedded in a heat sink
International Communications in Heat and Mass Transfer 39 (2012) 603–609
Contents lists available at SciVerse ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Investigation of a piezoelectric fan embedded in a heat sink☆ H.K. Ma ⁎, H.C. Su, C.L. Liu, W.H. Ho Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan
a r t i c l e
i n f o
Available online 29 March 2012 Keywords: Piezoelectric fan Cooling Heat sink Force convection
a b s t r a c t Previous studies show that the performance of a piezoelectric (PZT) fan is strongly affected by length, vibrating frequency, and fan amplitude. This study examines a cooling system, which is composed of a heat sink made of aluminum and a piezoelectric fan. An oscillating airflow can be generated and induced by the fan deformation. The piezoelectric fan between two fins may break the thermal boundary layer and enhance the heat dissipation rate of the cooling system with forced convection. In order to estimate the optimum design of the cooling system, 2 the effects of operating frequency, fan amplitude, fan arrangement, Ri (Gr/Repzt ), and power consumption are analyzed. Moreover, the relationship between the dimensionless PZT-convection number (Mp) and Ri has been investigated to analyze the performance of the cooling system. A three-dimensional, transitional model has been built to account for the flow field of the cooling system. The optimum cooling system shows the Mp reaches 2.3. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction LEDs (light-emitting diodes) have become a popular lighting source due to its advantages of low power consumption, small size, and long life. However, the operating temperature has an extreme effect on the performance of the LEDs. The brightness and the lifetime may decay rapidly under high operating temperatures [1]. In general, the heat dissipation problem of LEDs is solved by natural convection. However, natural convection is insufficient for the high-power LED lighting equipment of today. Although rotary fans can improve heat convection by forced convection, it requires high-power input and produces loud noise. A number of studies on the piezoelectric actuators used for cooling applications are presented recently, including liquid cooling [2,3] and air cooling [4,5]. Toda and Osaka [6,7] proposed the concept of piezoelectric fans for cooling systems because of their small size, lower power consumption, and long life [8]. A piezoelectric fan is manufactured by attaching a cantilever beam to a piezoelectric plate. An alternating current is applied at the resonant frequency of the piezoelectric fan. Thus, the piezoelectric fan can operate at a high ratio of fan tip deflection to power consumption [9]. The vibrating cantilever beam can operate with enough air-moving capability to cool electronic equipment as small fans. The theoretical vibration model of a piezoelectric bimorph with a thin elastic plate was derived from a lumped-mass system [10], which indicated that the damping effect could not be ignored on the mechanical wobbling of the attached elastic plate.
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (H.K. Ma). 0735-1933/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2012.03.003
Acikalin et al. [11] presented a piezoelectric fan mounted to a constant heat flux surface. Several experimental parameters, including configuration, fan amplitude, fan length, and frequency, as well as the distance between the fan and the heat source, were explored to assess the cooling ability of the piezoelectric fan. The results showed that the fan frequency offset from resonance and fan amplitude were the crucial parameters of the design. Kimber et al. [12] presented experimental methods of pressure and flow rate measurements for piezoelectric fans and the Reynolds number was also defined to evaluate their performance. Yoo et al. [13] researched the influences of the dimensions and the material on a vibrating fan. Their study indicated that phosphor bronze and aluminum were also good choices for a vibrating fan. Before 2010, most of studies were concerning a piezoelectric fan used to cool a heated surface. In 2010, Petroski et al. [14] proposed a cooling system combining two piezoelectric fans with a heat sink. This cooling system has a five times heat transfer rate than that of a typical naturalconvection. Ma et al. [15] examined an innovative design of a vibrating fins cooling system. A three-dimensional simulated model for the cooling system was built to investigate its performance. Simulated results showed that the performance of the vibrating fins cooling system was strongly affected by dimensions, operating frequency, pitch, and amplitude of the fins. In this study, the piezoelectric fan is placed inside the heat sink, thus allowing it to cool the inner surfaces of the heat sink. The effects of operating frequency, fan amplitude, fan arrangement, the importance of natural convection relative to the 2 forced convection (Ri (Gr/Repzt ), and power consumption of the fan are analyzed to assess the performance of the cooling system. Moreover, the relationship between the dimensionless PZT-convection number (Mp) and the importance of natural convection relative to the forced convection (Ri) are also investigated. A three-dimensional, transitional
604
T1:1
Nomenclature
T1:2 T1:3 T1:4 T1:5 T1:6 T1:7 T1:8 T1:9 T1:10 T1:11 T1:12 T1:13 T1:14 T1:15 T1:16 T1:17 T1:18 T1:19 T1:20 T1:21 T1:22 T1:23 T1:24 T1:25 T1:26 T1:27 T1:28 T1:29 T1:30 T1:31 T1:32 T1:33
Ri
H.K. Ma et al. / International Communications in Heat and Mass Transfer 39 (2012) 603–609
Importance of natural convection relative to the forced convection. Gr Grashof number of the PZT fan cooling system. Repzt Reynolds number of the PZT fan cooling system. Nupzt Nusselt number of the PZT fan cooling system. Lpzt Characteristic length of the PZT fan cooling system y Vertical orientation. XPZT Length of the fan inside the heat sink. LFIN Length of the heat sink. XPZT/LFIN Horizontal orientation. θ Inclined angle of the cooling system. ω Vibrating frequency. α Fan tip amplitude. QH Input heat from the heat source. QFIN, Total Total dissipated heat from the fin surface by convection. QFIN, i Dissipated heat from each section. AFIN Total area of the inner fin surface. T s Average temperature of the inner surface. T∞ Ambient air temperature. h PZT Forced convection coefficient with the PZT fan h 0 Natural convection coefficient Tbase, i Temperature of each section at the bottom fin surface. Tside, i Temperature of each section at the side fin surface. Abase, i Area of each section at the side bottom surface. Aside, i Area of each section at the side fin surface. y Vertical orientation. k Conductivity of air. ν Dynamic viscosity w Width of the piezoelectric fan. Mp Dimensionless PZT-convection number
model has been successfully built to account for the flow field of the cooling system. This study provides a comprehensive technique to analyze the piezoelectric fan cooling system. By taking advantage of this technique, the performance of a cooling system can be assessed conveniently.
2. Design and experimental set-up The schematic view of the experimental set-up is shown in Fig. 1(a). The dimensions of the fin base were 100 × 30 × 1 (mm) and the dimensions of the extruded fin were 100 × 20 × 1 (mm). Fifteen thermocouples were pasted on the inner surfaces of the heat sink. A heat source device, which could dissipate 1 W–3 W power was attached to the outer surface of the heat sink. The outer surfaces of the heat sink were covered by insulation block. The piezoelectric fan was driven in the range between 60 V–100 V by an AC power supply. The system was placed in an acrylic box to prevent perturbation from external convective currents. A thermal meter was used to record the temperature data. The fan amplitude could be observed by a high-speed camera (JVC-HM550). Thus, the power consumption, the operating frequency, and the fan amplitude could be recorded to analyze the performance of the cooling system. The piezoelectric fan, composed of a rectangular piezoelectric plate and a polyvinyl chloride (PVC) sheet, was placed inside the heat sink. As shown in Fig. 1(b), the parameters included the vertical orientation y, the horizontal orientation XPZT/LFIN, the inclined angle of the cooling system θ, the vibrating frequency ω, and the fan amplitude α.
Fig. 1. Arrangement of (a) experimental devices, (b) piezoelectric fan, and (c) thermocouples.
3. Theoretical analysis In order to calculate the overall convection heat transfer coefficient, the fin surface was divided into fifteen equal sections. The thermocouples were arranged in each section as shown in Fig. 1(c). Eq. (1) shows the energy balance of the cooling system where QH is the input heat from the heat source, QFIN, Total is the total dissipated heat from the fin surfaces by convection, and QFIN, i is the dissipated heat from each section. 15
Q H ¼ Q FIN;Total ¼ ∑i¼1 Q FIN;i
ð1Þ
Eq. (1) can be taken to be the following Eq. (2) by substituting the notations. Q FIN ¼ h AFIN T S −T∞
ð2Þ
H.K. Ma et al. / International Communications in Heat and Mass Transfer 39 (2012) 603–609
It is denoted that AFIN is the total area of the inner fin surface, T S is the average temperature of the inner surface, T∞ is the ambient air temperature, and h is the overall convective heat transfer coefficient. Thus, the overall convective heat transfer coefficient can be computed by Eq. (3). h ¼
Q FIN AFIN TS −T∞
ð3Þ
By dividing the bottom and the side fin surface equally into five sections, as shown in Fig. 1(c), the central temperature of a section can be assumed the average temperature of the section. Thus, the average temperature of the inner surface can be derived by using the weighting method, as shown in Eq. (4), ∑5i¼1 Tbase;i Abase;i þ 2∑5i¼1 Tside;i Aside;i T S ¼ AFIN
ð4Þ
where Tbase, i is the temperature measured by the thermocouples of each section at the bottom fin surface, and Tside, i is the temperature measured by the thermocouples of each section at the side fin surface; Abase, iis the area of each section at the bottom fin surface, and Aside, i is the area of each section at the side fin surface. According to Eq. (4), the overall convective heat transfer coefficient of the heat sink with the vibrating piezoelectric fan can be calculated as Eq. (5) and the overall heat convection coefficient of the heat sink with natural convection can be calculated as Eq. (6). h PZT ¼
¼ h 0
Q FIN AFIN T S;PZT −T∞
Q FIN AFIN T S;0 −T∞
Repzt ¼
ωαLpzt ν
ð8Þ
Nupzt ¼
L h PZT pzt k
ð9Þ
where ν is the dynamic viscosity, α is the fan tip amplitude, ω is the vibrating frequency,k is the conductivity, and Lpzt is the characteristic length. The characteristic length is chosen by employing the hydraulic diameter of the vibrating fan envelope as shown in Eq. (10) [17], 4αw 2ðα þ wÞ
Gr Re2pzt
ð11Þ
By replacing the notations of Gr and Repzt, Ri can be expressed as Ri ¼
3 gβ T S;PZT −T∞ Lc
ð12Þ
V2 Lpzt 2
In Eq. (12), the characteristic length (Lc) is defined as the height of the fin (H) for buoyancy effect and β is the expansion coefficient. For an ideal gas, the thermal expansion coefficient β is expressed as 1/T, where T is assumed as 273 K. Therefore, Ri can be rewritten as Eq. (13).
Ri ¼
gβH3 T S;PZT −T∞ ω2 α2 Lpzt 2 T
:
ð13Þ
4. Flow field simulation Using CFD-GEOM and CFD-ACE+, a three-dimensional, transitional model was built to account for the flow field of the cooling system. In order to simplify the model, the vibrating motion of the piezoelectric fan was defined as an equation of sine wave, and expressed as Eq. (14), α x2 sinð2πωtÞ; 2 L
ð14Þ
where ω is the vibrating frequency and L is the length of the piezoelectric fan. The vibration period is divided into ten equal time steps. The time step is set as Eq. (15). Δt ¼
1 10ω
ð15Þ
Other major assumptions of the model are as follows: ð7Þ
The Reynolds number and the Nusselt number are also calculated to estimate the convective ability of the cooling system. In this study, the fan amplitude is used as the length scale. The velocity terms of the Reynolds number and the Nusselt number are based on the maximum fan tip velocity. Thus, the Reynolds number and the Nusselt number can be expressed as Eqs. (8) and (9) [16],
Lpzt ¼
Ri ¼
y¼
In order to demonstrate the convection ability improved by the piezoelectric fan, the dimensionless PZT-convection number(Mp) is defined as shown in Eq. (7) to assess the convection ability. h Forced convection coefficient with the PZT fan Mp ¼ PZT ¼ Natrual convection coefficient h0
to the forced convection (Ri) is defined as Eq. (11) by the Grashof number (Gr) and the Reynolds number (Re) [18].
ð5Þ
ð6Þ
605
ð10Þ
where w is the width of the piezoelectric fan. In addition, the cooling effect of this cooling system is the combination of natural convection and forced convection. The importance of natural convection relative
(1) The stable temperature of the cooling system without a piezoelectric fan is set as the initial condition of simulation. (2) The isothermal temperature of 340 K is set as the boundary condition of the heat source. (3) The density and the viscosity of fluid are constants. (4) There is no slip condition on the wall. (5) The effect of gravity is considered. (6) The inlet and outlet pressures of control surfaces are fixed pressures. In the simulation model, the dimensions of each part and its mesh density play important roles in the accuracy of the simulation results. The suitable mesh densities prevent truncation errors and rounding errors. In order to build a good model, a mesh independence study has been performed. 4.1. Dimension of the model The dimensions of the air domain may affect the simulation results because the heat sink is surrounded by air. Therefore, it was necessary to check its influence. The air domain was separated into three parts — the upstream domain, the downstream domain, and the side domain. Fig. 2 shows the schematic view of the simulation model. Fig. 3 shows the pressure field of the downstream domain with different thicknesses. When the thickness is more than 30 mm, the pressure fields are almost the same. However, when the thickness is 10 mm or 20 mm, the pressure fields are obviously affected by the boundary
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H.K. Ma et al. / International Communications in Heat and Mass Transfer 39 (2012) 603–609
5. Results and discussion In order to choose the best arrangement of the piezoelectric fan, different orientations for the piezoelectric fan were investigated. The simulation model was also used to examine the correlation between the flow field induced by the piezoelectric fan and the temperature drop on the inner fin surface. In addition, the piezoelectric fan's power consumption was investigated and the important dimensionless parameters were used to analyze the experimental data in a more efficient way. 5.1. The arrangement of the piezoelectric fan
Fig. 2. Schematic view of the simulation model.
conditions. Thus, the thickness of 40 mm was chosen for the downstream domain. The pressure fields of the upstream domain with different thicknesses and the side domain with different thicknesses have also been done. In order to prevent unusual pressure fields, 20 mm was chosen as the thickness of the upstream domain and 30 mm was chosen as the thickness of the side domain.
4.2. Mesh density of the model After confirming the dimensions of the simulation model, the mesh independence test has been performed. The mesh independence test of the model was established based on the heat flux of the heated surface. The results were considered to be mesh independent when the variance in heat flux was less than 0.01%. According to the result of the gap air domain test, the variance was only 0.005% when the mesh density was 15 cell/per 4.5 mm. Eight mesh independence tests have been done to decide the suitable mesh density of the simulation model, including upstream domain, downstream domain, side domain, gap air domain, fin height, fin length, fin thickness, and piezoelectric fan thickness.
The arrangement of the piezoelectric fan may influence the generated flow field and the performance of the cooling system. In order to find the best arrangement of the piezoelectric fan, the vertical orientation—y, the horizontal orientation —XPZT/LFIN, and the inclined angle of the cooling system θ were considered when investigating the cooling system. According to previous studies, the gap between the fan and the heated surface strongly affected the performance of the cooling system. In this study, three different vertical orientations, y (5 mm, 10 mm, and 15 mm), were tested under the condition of XPZT/ LFIN = 0.5 and θ = 0°. As shown in Fig. 4, the results indicated that the temperature drop on both the bottom and the side fin surfaces obviously increased when the piezoelectric fan approached the bottom fin surface. Thus, y = 5 mm was chosen as the vertical orientation. Tests of the inclined angle θ (at 0°, 15°, 30°, 45°, 60°, 75°, and 90°) were completed under the conditions of XPZT/LFIN = 0.5, y = 5 mm. The performance of the cooling system with θ = 0° was superior to those with other inclined angles. Fig. 5 shows the dimensionless PZT-convection number(Mp) versus the horizontal orientation XPZT/LFIN under the condition of y = 5 mm, θ = 0°. The experimental data demonstrates that the heat dissipation rate reaches its peak value between XPZT/LFIN = 0.5 and XPZT/LFIN = 0.6. 5.2. The flow field of the cooling system A three-dimensional model was built to investigate the flow field of the cooling system. Fig. 6 shows that the maximum velocity near the bottom surface and the side surface both occur at XPZT/LFIN = 0.3–0.5. Theoretically, the high velocity leads to a larger temperature drop. Fig. 4 shows good agreement with this anticipated phenomenon. The
Fig. 3. Pressure fields of the downstream domain with different thicknesses.
H.K. Ma et al. / International Communications in Heat and Mass Transfer 39 (2012) 603–609
607
maximum temperature drop occurs at the position where the maximum velocity occurs. The three-dimensional simulation model may help to decide the position of the heat source and the arrangement of the piezoelectric fan. 5.3. The power consumption of the piezoelectric fan
Fig. 4. Temperature drop on the bottom and side fin surfaces (XPZT/LFIN = 0.5, θ = 0°, frequency = 30 Hz, amplitude = 18 mm).
In the fan cooling system, the power consumption of the PZT fan is also an important issue. Fig. 7 shows the power consumption and theMp when the piezoelectric fan vibrates at different frequency. The power consumption was 0.511 W andMp was 1.4 under the operating frequency of 24 Hz. However, the power consumption decreased to 0.022 W and theMp changed to 1.53 at the operating frequency of 30 Hz because 30 Hz is the resonant frequency that allows the PZT fan to vibrate at its maximum amplitude. According to this result, power consumption should be considered, rather thanMp when selecting an operating frequency. An inappropriate operating frequency will increase the power consumption by twenty times. 5.4. The amplitude of the piezoelectric fan The fan amplitude plays an important role in the fan's cooling ability. Mp depending on the amplitude at different operating frequencies is demonstrated in Fig. 8. Mp increased as the amplitude and the operating frequency increased. According to the figure, the influence of the amplitude on Mp is obviously larger than that of the operating frequency. Mp can be increased from 1.05 to 1.3 at 25 Hz, with a 5 mm amplitude increased (4 mm to 9 mm). However, the influence of the operating frequency onMp is not significant, especially at low amplitudes. 5.5. The correlation between RePZT and NuPZT of the cooling system
Fig. 5. Mp versus the horizontal orientation (y = 5 mm, θ = 0°, frequency = 30 Hz, amplitude = 18 mm).
Flow field nearbottom surface
According to Eq. (8), the frequency and the fan amplitude are directly proportional to RePZT. The two parameters can be easily observed. They also play important roles in enhancing NuPZT. However, the NuPZT cannot be calculated directly from the frequency and the amplitude, so the correlation between RePZT and NuPZT may help us to estimate the NuPZT conveniently. Fig. 9 shows the NuPZT and the RePZT of the experimental data at different amplitudes and
Flow field nearside surface
T=0
XPZT/LFIN
0.5
0
XPZT/LFIN
0.5
0 M/S 1.2
T=1/4
1.0 0.8
T=1/2
0.6 0.4 0.2
T=3/4 0
T=1
Fig. 6. Flow field near the bottom and the side surfaces (XPZT/LFIN = 0.5, y = 5 mm, θ = 0°).
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H.K. Ma et al. / International Communications in Heat and Mass Transfer 39 (2012) 603–609
frequencies. When the RePZT is below 700, the NuPZT number increases almost linearly with the increasing RePZT number. 5.6. The relationship between Mp and Ri 2 ), repreThe dimensionless parameter is defined as Ri (Gr/Repzt senting the importance of natural convection relative to the forced convection. When Ri b 1, natural convection is negligible. However, when Ri > 10, forced convection is negligible [18]. Fig. 10 shows the dimensionless analysis of the experimental data at different frequencies and amplitudes. In Fig. 10, two fitting curves are drawn according to the experimental data. The Mp can be correlated with the Ri and then generalized as the following equations. The equations may be used to analyze and assess the performance of the piezoelectric fan cooling system more conveniently.
Fig. 7. Power consumption of the piezoelectric fan (XPZT/LFIN = 0.5, y = 5 mm, θ = 0°, amplitude = 10 mm).
Mp ¼ 1:268−0:05663 lnRi Mp ¼ 1:389−0:2762 lnRi
Ri > 10 Rib1
ð16Þ ð17Þ
6. Conclusions This study evaluated the performance of a piezoelectric fan cooling system using experiments, simulation, and non-dimensional analysis. The major findings are as follows:
Fig. 8. Influence of the fan amplitude onMp.
Fig. 9. Correlation between RePZT and Nupzt of the cooling system.
(1) Using a three-dimensional, transitional model to account for the flow field induced by the piezoelectric fan, maximum velocity usually occurs at the position 20 mm before the fan tip; the results show good agreement between the temperature drop and the flow field. (2) The orientations of the piezoelectric fan strongly affect theMp. The Mp of the system which operates with a frequency of 30 Hz and an amplitude of 18 mm reaches 2.3 ( XPZT/LFIN =0.5, y=5 mm, θ=0°) (3) Although the operating frequency does not affectMp as much as amplitude does in this cooling system, it regulates the power consumption of the PZT fan. A 6 Hz fan frequency, offset from the resonant frequency, increases the power consumption by twenty times. Thus, the resonant frequency should be chosen for all conditions. (4) In the case (XPZT/LFIN = 0.5, y = 5 mm, θ = 0°), the Nupzt almost linearly increases with an increasing Repzt. According to this
Fig. 10. Relationship between Mp and Ri (XPZT/LFIN = 0.5, y = 5 mm, θ = 0°).
H.K. Ma et al. / International Communications in Heat and Mass Transfer 39 (2012) 603–609
correlation, the Nupzt can be derived from the amplitude and the operating frequency that determines Repzt. Nupzt ¼ 2:9297 þ 0:0387Repzt whenRepzt b700 (5) TheMp can be correlated with the dimensionless ratio of natural convection to forced convection (Ri) and generalized as the following equations: Mp ¼ 1:268−0:05663 lnRi Mp ¼ 1:389−0:2762 lnRi
Ri > 10 Rib1
The equations can be used to analyze the performance of the piezoelectric fan cooling system conveniently. Acknowledgment This research was funded by the National Science Council of the Republic of China (NSC100-3113-E-002-013). References [1] N. Narendran, Y. Gu, Life of LED-based white light sources, Journal of Display Technology 1 (1) (2005) 167–170. [2] H.K. Ma, B.R. Hou, C.Y. Lin, J.J. Gao, The improved performance of one-side actuating diaphragm micropump for a liquid cooling system, International Communications in Heat and Mass Transfer 35 (2008) 957–966. [3] H.K. Ma, B.R. Chen, C.Y. Lin, J.J. Gao, Development of an OAPCP-micropump liquid cooling system in a laptop, International Communications in Heat and Mass Transfer 36 (2009) 225–232.
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[4] B.G. Loh, S. Hyun, P.I. Ro, C. Kleinstreuer, Acoustic streaming induced by ultrasonic flexural vibrations and associated enhancement of convective heat transfer, Acoustical Society of America 111 (2) (2002) 875–883. [5] T. Acikalin, S.V. Garimella, J. Petroski, A. Raman, Optimal design of miniature piezoelectric fans for cooling light emitting diodes, The Ninth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, Las Vegas, 2004, pp. 663–671. [6] M. Toda, Theory of air flow generation by a resonant type PVF2 bimorph cantilever vibrator, Ferroelectrics 22 (1979) 911–918. [7] M. Toda, Voltage-induced large amplitude bending device-PVF2 bimorph-its properties and applications, Ferroelectrics 32 (1981) 127–133. [8] I. Sauciuc, et al., Key challenges for the piezo technology with applications to low form factor thermal solutions, ITHERM 2006, 2006, pp. 781–785, San Diego. [9] K. Yao, K. Uchino, Analysis on a composite cantilever beam coupling a piezoelectric bimorph to an elastic blade, Sensors and Actuators 89 (2001) 215–221. [10] T. Acikalin, S.M. Wait, S.V. Garimella, A. Raman, Experimental investigation of thermal performance of piezoelectric fans, Heat Transfer Engineering 25 (1) (2004) 4–14. [11] T. Acikalin, S.V. Garimella, A. Raman, J. Petroski, Characterization and optimization of the thermal performance of miniature piezoelectric fans, International Journal of Heat and Fluid Flow 28 (2007) 806–820. [12] M. Kimber, K. Suzuki, N. Kitsunai, K. Seki, S.V. Garimella, Quantification of piezoelectric fan flow rate performance and experimental identification of installation effects, Proceedings of ITHERM 2008, 2008, pp. 471–479, Florida. [13] J.H. Yoo, J.I. Hong, W. Cao, Piezoelectric ceramic bimorph coupled to thin metal plate as cooling fan for electronic devices, Sensors and Actuators 79 (2000) 8–12. [14] J. Petroski, M. Arik, M. Gursoy, Optimization of piezoelectric oscillating fan-cooled heat sinks for electronics cooling, IEEE Transactions on Components and Packaging Technology 33 (2010) 25–31. [15] H.K. Ma, B.R. Chen, H.W. Lan, K.T. Lin, C.Y. Chao, Study of an LED device with vibrating piezoelectric fins, IEEE Semi-Therm 2008, 2008, San Jose. [16] M. Kimber, Suresh V. Garimella, Measurement and prediction of the cooling characteristics of a generalized vibrating piezoelectric fan, International Journal of Heat and Mass Transfer 52 (2009) 4470–4478. [17] M. Kimber, S.V. Garimella, A. Raman, Local heat transfer coefficients induced by piezoelectrically actuated vibrating cantilevers, Journal of Heat Transfer 123 (2007) 1168–1176. [18] Y.A. Cengel, Heat Transfer, MacGraw-Hill, New York, 2004, pp. 460–466.
Contents lists available at SciVerse ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Investigation of a piezoelectric fan embedded in a heat sink☆ H.K. Ma ⁎, H.C. Su, C.L. Liu, W.H. Ho Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan
a r t i c l e
i n f o
Available online 29 March 2012 Keywords: Piezoelectric fan Cooling Heat sink Force convection
a b s t r a c t Previous studies show that the performance of a piezoelectric (PZT) fan is strongly affected by length, vibrating frequency, and fan amplitude. This study examines a cooling system, which is composed of a heat sink made of aluminum and a piezoelectric fan. An oscillating airflow can be generated and induced by the fan deformation. The piezoelectric fan between two fins may break the thermal boundary layer and enhance the heat dissipation rate of the cooling system with forced convection. In order to estimate the optimum design of the cooling system, 2 the effects of operating frequency, fan amplitude, fan arrangement, Ri (Gr/Repzt ), and power consumption are analyzed. Moreover, the relationship between the dimensionless PZT-convection number (Mp) and Ri has been investigated to analyze the performance of the cooling system. A three-dimensional, transitional model has been built to account for the flow field of the cooling system. The optimum cooling system shows the Mp reaches 2.3. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction LEDs (light-emitting diodes) have become a popular lighting source due to its advantages of low power consumption, small size, and long life. However, the operating temperature has an extreme effect on the performance of the LEDs. The brightness and the lifetime may decay rapidly under high operating temperatures [1]. In general, the heat dissipation problem of LEDs is solved by natural convection. However, natural convection is insufficient for the high-power LED lighting equipment of today. Although rotary fans can improve heat convection by forced convection, it requires high-power input and produces loud noise. A number of studies on the piezoelectric actuators used for cooling applications are presented recently, including liquid cooling [2,3] and air cooling [4,5]. Toda and Osaka [6,7] proposed the concept of piezoelectric fans for cooling systems because of their small size, lower power consumption, and long life [8]. A piezoelectric fan is manufactured by attaching a cantilever beam to a piezoelectric plate. An alternating current is applied at the resonant frequency of the piezoelectric fan. Thus, the piezoelectric fan can operate at a high ratio of fan tip deflection to power consumption [9]. The vibrating cantilever beam can operate with enough air-moving capability to cool electronic equipment as small fans. The theoretical vibration model of a piezoelectric bimorph with a thin elastic plate was derived from a lumped-mass system [10], which indicated that the damping effect could not be ignored on the mechanical wobbling of the attached elastic plate.
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (H.K. Ma). 0735-1933/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2012.03.003
Acikalin et al. [11] presented a piezoelectric fan mounted to a constant heat flux surface. Several experimental parameters, including configuration, fan amplitude, fan length, and frequency, as well as the distance between the fan and the heat source, were explored to assess the cooling ability of the piezoelectric fan. The results showed that the fan frequency offset from resonance and fan amplitude were the crucial parameters of the design. Kimber et al. [12] presented experimental methods of pressure and flow rate measurements for piezoelectric fans and the Reynolds number was also defined to evaluate their performance. Yoo et al. [13] researched the influences of the dimensions and the material on a vibrating fan. Their study indicated that phosphor bronze and aluminum were also good choices for a vibrating fan. Before 2010, most of studies were concerning a piezoelectric fan used to cool a heated surface. In 2010, Petroski et al. [14] proposed a cooling system combining two piezoelectric fans with a heat sink. This cooling system has a five times heat transfer rate than that of a typical naturalconvection. Ma et al. [15] examined an innovative design of a vibrating fins cooling system. A three-dimensional simulated model for the cooling system was built to investigate its performance. Simulated results showed that the performance of the vibrating fins cooling system was strongly affected by dimensions, operating frequency, pitch, and amplitude of the fins. In this study, the piezoelectric fan is placed inside the heat sink, thus allowing it to cool the inner surfaces of the heat sink. The effects of operating frequency, fan amplitude, fan arrangement, the importance of natural convection relative to the 2 forced convection (Ri (Gr/Repzt ), and power consumption of the fan are analyzed to assess the performance of the cooling system. Moreover, the relationship between the dimensionless PZT-convection number (Mp) and the importance of natural convection relative to the forced convection (Ri) are also investigated. A three-dimensional, transitional
604
T1:1
Nomenclature
T1:2 T1:3 T1:4 T1:5 T1:6 T1:7 T1:8 T1:9 T1:10 T1:11 T1:12 T1:13 T1:14 T1:15 T1:16 T1:17 T1:18 T1:19 T1:20 T1:21 T1:22 T1:23 T1:24 T1:25 T1:26 T1:27 T1:28 T1:29 T1:30 T1:31 T1:32 T1:33
Ri
H.K. Ma et al. / International Communications in Heat and Mass Transfer 39 (2012) 603–609
Importance of natural convection relative to the forced convection. Gr Grashof number of the PZT fan cooling system. Repzt Reynolds number of the PZT fan cooling system. Nupzt Nusselt number of the PZT fan cooling system. Lpzt Characteristic length of the PZT fan cooling system y Vertical orientation. XPZT Length of the fan inside the heat sink. LFIN Length of the heat sink. XPZT/LFIN Horizontal orientation. θ Inclined angle of the cooling system. ω Vibrating frequency. α Fan tip amplitude. QH Input heat from the heat source. QFIN, Total Total dissipated heat from the fin surface by convection. QFIN, i Dissipated heat from each section. AFIN Total area of the inner fin surface. T s Average temperature of the inner surface. T∞ Ambient air temperature. h PZT Forced convection coefficient with the PZT fan h 0 Natural convection coefficient Tbase, i Temperature of each section at the bottom fin surface. Tside, i Temperature of each section at the side fin surface. Abase, i Area of each section at the side bottom surface. Aside, i Area of each section at the side fin surface. y Vertical orientation. k Conductivity of air. ν Dynamic viscosity w Width of the piezoelectric fan. Mp Dimensionless PZT-convection number
model has been successfully built to account for the flow field of the cooling system. This study provides a comprehensive technique to analyze the piezoelectric fan cooling system. By taking advantage of this technique, the performance of a cooling system can be assessed conveniently.
2. Design and experimental set-up The schematic view of the experimental set-up is shown in Fig. 1(a). The dimensions of the fin base were 100 × 30 × 1 (mm) and the dimensions of the extruded fin were 100 × 20 × 1 (mm). Fifteen thermocouples were pasted on the inner surfaces of the heat sink. A heat source device, which could dissipate 1 W–3 W power was attached to the outer surface of the heat sink. The outer surfaces of the heat sink were covered by insulation block. The piezoelectric fan was driven in the range between 60 V–100 V by an AC power supply. The system was placed in an acrylic box to prevent perturbation from external convective currents. A thermal meter was used to record the temperature data. The fan amplitude could be observed by a high-speed camera (JVC-HM550). Thus, the power consumption, the operating frequency, and the fan amplitude could be recorded to analyze the performance of the cooling system. The piezoelectric fan, composed of a rectangular piezoelectric plate and a polyvinyl chloride (PVC) sheet, was placed inside the heat sink. As shown in Fig. 1(b), the parameters included the vertical orientation y, the horizontal orientation XPZT/LFIN, the inclined angle of the cooling system θ, the vibrating frequency ω, and the fan amplitude α.
Fig. 1. Arrangement of (a) experimental devices, (b) piezoelectric fan, and (c) thermocouples.
3. Theoretical analysis In order to calculate the overall convection heat transfer coefficient, the fin surface was divided into fifteen equal sections. The thermocouples were arranged in each section as shown in Fig. 1(c). Eq. (1) shows the energy balance of the cooling system where QH is the input heat from the heat source, QFIN, Total is the total dissipated heat from the fin surfaces by convection, and QFIN, i is the dissipated heat from each section. 15
Q H ¼ Q FIN;Total ¼ ∑i¼1 Q FIN;i
ð1Þ
Eq. (1) can be taken to be the following Eq. (2) by substituting the notations. Q FIN ¼ h AFIN T S −T∞
ð2Þ
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It is denoted that AFIN is the total area of the inner fin surface, T S is the average temperature of the inner surface, T∞ is the ambient air temperature, and h is the overall convective heat transfer coefficient. Thus, the overall convective heat transfer coefficient can be computed by Eq. (3). h ¼
Q FIN AFIN TS −T∞
ð3Þ
By dividing the bottom and the side fin surface equally into five sections, as shown in Fig. 1(c), the central temperature of a section can be assumed the average temperature of the section. Thus, the average temperature of the inner surface can be derived by using the weighting method, as shown in Eq. (4), ∑5i¼1 Tbase;i Abase;i þ 2∑5i¼1 Tside;i Aside;i T S ¼ AFIN
ð4Þ
where Tbase, i is the temperature measured by the thermocouples of each section at the bottom fin surface, and Tside, i is the temperature measured by the thermocouples of each section at the side fin surface; Abase, iis the area of each section at the bottom fin surface, and Aside, i is the area of each section at the side fin surface. According to Eq. (4), the overall convective heat transfer coefficient of the heat sink with the vibrating piezoelectric fan can be calculated as Eq. (5) and the overall heat convection coefficient of the heat sink with natural convection can be calculated as Eq. (6). h PZT ¼
¼ h 0
Q FIN AFIN T S;PZT −T∞
Q FIN AFIN T S;0 −T∞
Repzt ¼
ωαLpzt ν
ð8Þ
Nupzt ¼
L h PZT pzt k
ð9Þ
where ν is the dynamic viscosity, α is the fan tip amplitude, ω is the vibrating frequency,k is the conductivity, and Lpzt is the characteristic length. The characteristic length is chosen by employing the hydraulic diameter of the vibrating fan envelope as shown in Eq. (10) [17], 4αw 2ðα þ wÞ
Gr Re2pzt
ð11Þ
By replacing the notations of Gr and Repzt, Ri can be expressed as Ri ¼
3 gβ T S;PZT −T∞ Lc
ð12Þ
V2 Lpzt 2
In Eq. (12), the characteristic length (Lc) is defined as the height of the fin (H) for buoyancy effect and β is the expansion coefficient. For an ideal gas, the thermal expansion coefficient β is expressed as 1/T, where T is assumed as 273 K. Therefore, Ri can be rewritten as Eq. (13).
Ri ¼
gβH3 T S;PZT −T∞ ω2 α2 Lpzt 2 T
:
ð13Þ
4. Flow field simulation Using CFD-GEOM and CFD-ACE+, a three-dimensional, transitional model was built to account for the flow field of the cooling system. In order to simplify the model, the vibrating motion of the piezoelectric fan was defined as an equation of sine wave, and expressed as Eq. (14), α x2 sinð2πωtÞ; 2 L
ð14Þ
where ω is the vibrating frequency and L is the length of the piezoelectric fan. The vibration period is divided into ten equal time steps. The time step is set as Eq. (15). Δt ¼
1 10ω
ð15Þ
Other major assumptions of the model are as follows: ð7Þ
The Reynolds number and the Nusselt number are also calculated to estimate the convective ability of the cooling system. In this study, the fan amplitude is used as the length scale. The velocity terms of the Reynolds number and the Nusselt number are based on the maximum fan tip velocity. Thus, the Reynolds number and the Nusselt number can be expressed as Eqs. (8) and (9) [16],
Lpzt ¼
Ri ¼
y¼
In order to demonstrate the convection ability improved by the piezoelectric fan, the dimensionless PZT-convection number(Mp) is defined as shown in Eq. (7) to assess the convection ability. h Forced convection coefficient with the PZT fan Mp ¼ PZT ¼ Natrual convection coefficient h0
to the forced convection (Ri) is defined as Eq. (11) by the Grashof number (Gr) and the Reynolds number (Re) [18].
ð5Þ
ð6Þ
605
ð10Þ
where w is the width of the piezoelectric fan. In addition, the cooling effect of this cooling system is the combination of natural convection and forced convection. The importance of natural convection relative
(1) The stable temperature of the cooling system without a piezoelectric fan is set as the initial condition of simulation. (2) The isothermal temperature of 340 K is set as the boundary condition of the heat source. (3) The density and the viscosity of fluid are constants. (4) There is no slip condition on the wall. (5) The effect of gravity is considered. (6) The inlet and outlet pressures of control surfaces are fixed pressures. In the simulation model, the dimensions of each part and its mesh density play important roles in the accuracy of the simulation results. The suitable mesh densities prevent truncation errors and rounding errors. In order to build a good model, a mesh independence study has been performed. 4.1. Dimension of the model The dimensions of the air domain may affect the simulation results because the heat sink is surrounded by air. Therefore, it was necessary to check its influence. The air domain was separated into three parts — the upstream domain, the downstream domain, and the side domain. Fig. 2 shows the schematic view of the simulation model. Fig. 3 shows the pressure field of the downstream domain with different thicknesses. When the thickness is more than 30 mm, the pressure fields are almost the same. However, when the thickness is 10 mm or 20 mm, the pressure fields are obviously affected by the boundary
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5. Results and discussion In order to choose the best arrangement of the piezoelectric fan, different orientations for the piezoelectric fan were investigated. The simulation model was also used to examine the correlation between the flow field induced by the piezoelectric fan and the temperature drop on the inner fin surface. In addition, the piezoelectric fan's power consumption was investigated and the important dimensionless parameters were used to analyze the experimental data in a more efficient way. 5.1. The arrangement of the piezoelectric fan
Fig. 2. Schematic view of the simulation model.
conditions. Thus, the thickness of 40 mm was chosen for the downstream domain. The pressure fields of the upstream domain with different thicknesses and the side domain with different thicknesses have also been done. In order to prevent unusual pressure fields, 20 mm was chosen as the thickness of the upstream domain and 30 mm was chosen as the thickness of the side domain.
4.2. Mesh density of the model After confirming the dimensions of the simulation model, the mesh independence test has been performed. The mesh independence test of the model was established based on the heat flux of the heated surface. The results were considered to be mesh independent when the variance in heat flux was less than 0.01%. According to the result of the gap air domain test, the variance was only 0.005% when the mesh density was 15 cell/per 4.5 mm. Eight mesh independence tests have been done to decide the suitable mesh density of the simulation model, including upstream domain, downstream domain, side domain, gap air domain, fin height, fin length, fin thickness, and piezoelectric fan thickness.
The arrangement of the piezoelectric fan may influence the generated flow field and the performance of the cooling system. In order to find the best arrangement of the piezoelectric fan, the vertical orientation—y, the horizontal orientation —XPZT/LFIN, and the inclined angle of the cooling system θ were considered when investigating the cooling system. According to previous studies, the gap between the fan and the heated surface strongly affected the performance of the cooling system. In this study, three different vertical orientations, y (5 mm, 10 mm, and 15 mm), were tested under the condition of XPZT/ LFIN = 0.5 and θ = 0°. As shown in Fig. 4, the results indicated that the temperature drop on both the bottom and the side fin surfaces obviously increased when the piezoelectric fan approached the bottom fin surface. Thus, y = 5 mm was chosen as the vertical orientation. Tests of the inclined angle θ (at 0°, 15°, 30°, 45°, 60°, 75°, and 90°) were completed under the conditions of XPZT/LFIN = 0.5, y = 5 mm. The performance of the cooling system with θ = 0° was superior to those with other inclined angles. Fig. 5 shows the dimensionless PZT-convection number(Mp) versus the horizontal orientation XPZT/LFIN under the condition of y = 5 mm, θ = 0°. The experimental data demonstrates that the heat dissipation rate reaches its peak value between XPZT/LFIN = 0.5 and XPZT/LFIN = 0.6. 5.2. The flow field of the cooling system A three-dimensional model was built to investigate the flow field of the cooling system. Fig. 6 shows that the maximum velocity near the bottom surface and the side surface both occur at XPZT/LFIN = 0.3–0.5. Theoretically, the high velocity leads to a larger temperature drop. Fig. 4 shows good agreement with this anticipated phenomenon. The
Fig. 3. Pressure fields of the downstream domain with different thicknesses.
H.K. Ma et al. / International Communications in Heat and Mass Transfer 39 (2012) 603–609
607
maximum temperature drop occurs at the position where the maximum velocity occurs. The three-dimensional simulation model may help to decide the position of the heat source and the arrangement of the piezoelectric fan. 5.3. The power consumption of the piezoelectric fan
Fig. 4. Temperature drop on the bottom and side fin surfaces (XPZT/LFIN = 0.5, θ = 0°, frequency = 30 Hz, amplitude = 18 mm).
In the fan cooling system, the power consumption of the PZT fan is also an important issue. Fig. 7 shows the power consumption and theMp when the piezoelectric fan vibrates at different frequency. The power consumption was 0.511 W andMp was 1.4 under the operating frequency of 24 Hz. However, the power consumption decreased to 0.022 W and theMp changed to 1.53 at the operating frequency of 30 Hz because 30 Hz is the resonant frequency that allows the PZT fan to vibrate at its maximum amplitude. According to this result, power consumption should be considered, rather thanMp when selecting an operating frequency. An inappropriate operating frequency will increase the power consumption by twenty times. 5.4. The amplitude of the piezoelectric fan The fan amplitude plays an important role in the fan's cooling ability. Mp depending on the amplitude at different operating frequencies is demonstrated in Fig. 8. Mp increased as the amplitude and the operating frequency increased. According to the figure, the influence of the amplitude on Mp is obviously larger than that of the operating frequency. Mp can be increased from 1.05 to 1.3 at 25 Hz, with a 5 mm amplitude increased (4 mm to 9 mm). However, the influence of the operating frequency onMp is not significant, especially at low amplitudes. 5.5. The correlation between RePZT and NuPZT of the cooling system
Fig. 5. Mp versus the horizontal orientation (y = 5 mm, θ = 0°, frequency = 30 Hz, amplitude = 18 mm).
Flow field nearbottom surface
According to Eq. (8), the frequency and the fan amplitude are directly proportional to RePZT. The two parameters can be easily observed. They also play important roles in enhancing NuPZT. However, the NuPZT cannot be calculated directly from the frequency and the amplitude, so the correlation between RePZT and NuPZT may help us to estimate the NuPZT conveniently. Fig. 9 shows the NuPZT and the RePZT of the experimental data at different amplitudes and
Flow field nearside surface
T=0
XPZT/LFIN
0.5
0
XPZT/LFIN
0.5
0 M/S 1.2
T=1/4
1.0 0.8
T=1/2
0.6 0.4 0.2
T=3/4 0
T=1
Fig. 6. Flow field near the bottom and the side surfaces (XPZT/LFIN = 0.5, y = 5 mm, θ = 0°).
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frequencies. When the RePZT is below 700, the NuPZT number increases almost linearly with the increasing RePZT number. 5.6. The relationship between Mp and Ri 2 ), repreThe dimensionless parameter is defined as Ri (Gr/Repzt senting the importance of natural convection relative to the forced convection. When Ri b 1, natural convection is negligible. However, when Ri > 10, forced convection is negligible [18]. Fig. 10 shows the dimensionless analysis of the experimental data at different frequencies and amplitudes. In Fig. 10, two fitting curves are drawn according to the experimental data. The Mp can be correlated with the Ri and then generalized as the following equations. The equations may be used to analyze and assess the performance of the piezoelectric fan cooling system more conveniently.
Fig. 7. Power consumption of the piezoelectric fan (XPZT/LFIN = 0.5, y = 5 mm, θ = 0°, amplitude = 10 mm).
Mp ¼ 1:268−0:05663 lnRi Mp ¼ 1:389−0:2762 lnRi
Ri > 10 Rib1
ð16Þ ð17Þ
6. Conclusions This study evaluated the performance of a piezoelectric fan cooling system using experiments, simulation, and non-dimensional analysis. The major findings are as follows:
Fig. 8. Influence of the fan amplitude onMp.
Fig. 9. Correlation between RePZT and Nupzt of the cooling system.
(1) Using a three-dimensional, transitional model to account for the flow field induced by the piezoelectric fan, maximum velocity usually occurs at the position 20 mm before the fan tip; the results show good agreement between the temperature drop and the flow field. (2) The orientations of the piezoelectric fan strongly affect theMp. The Mp of the system which operates with a frequency of 30 Hz and an amplitude of 18 mm reaches 2.3 ( XPZT/LFIN =0.5, y=5 mm, θ=0°) (3) Although the operating frequency does not affectMp as much as amplitude does in this cooling system, it regulates the power consumption of the PZT fan. A 6 Hz fan frequency, offset from the resonant frequency, increases the power consumption by twenty times. Thus, the resonant frequency should be chosen for all conditions. (4) In the case (XPZT/LFIN = 0.5, y = 5 mm, θ = 0°), the Nupzt almost linearly increases with an increasing Repzt. According to this
Fig. 10. Relationship between Mp and Ri (XPZT/LFIN = 0.5, y = 5 mm, θ = 0°).
H.K. Ma et al. / International Communications in Heat and Mass Transfer 39 (2012) 603–609
correlation, the Nupzt can be derived from the amplitude and the operating frequency that determines Repzt. Nupzt ¼ 2:9297 þ 0:0387Repzt whenRepzt b700 (5) TheMp can be correlated with the dimensionless ratio of natural convection to forced convection (Ri) and generalized as the following equations: Mp ¼ 1:268−0:05663 lnRi Mp ¼ 1:389−0:2762 lnRi
Ri > 10 Rib1
The equations can be used to analyze the performance of the piezoelectric fan cooling system conveniently. Acknowledgment This research was funded by the National Science Council of the Republic of China (NSC100-3113-E-002-013). References [1] N. Narendran, Y. Gu, Life of LED-based white light sources, Journal of Display Technology 1 (1) (2005) 167–170. [2] H.K. Ma, B.R. Hou, C.Y. Lin, J.J. Gao, The improved performance of one-side actuating diaphragm micropump for a liquid cooling system, International Communications in Heat and Mass Transfer 35 (2008) 957–966. [3] H.K. Ma, B.R. Chen, C.Y. Lin, J.J. Gao, Development of an OAPCP-micropump liquid cooling system in a laptop, International Communications in Heat and Mass Transfer 36 (2009) 225–232.
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