An innovative multiple-vibrating fan cooling system was developed by using both the piezoelectric force and the magnetic force. The system can be placed directly into a heat sink without occupying extra space. The effects of the vibrating frequency, the operating voltage, the geometries of the fans, the distance between the fans and the heat sink, and the power consumption have been analyzed to assess the performance of the cooling system. Further, a method for evaluating the performance of a single piezoelectric fan cooling system also has been presented. The method can be used to assess the performance of the multiple-vibrating fan cooling system. The major conclusions of this study are summarized below:
(1) Using a three-dimensional, transitional model to account for the flow field induced by the piezoelectric fan, the maximum velocity was found to usually occur at the position 20 mm before the fan tip; the results show sufficient agreement between the temperature drop and the flow field.
(2) The orientation of the piezoelectric fan strongly affects the M . The M of the system, which operates at a frequency of 30 Hz and an amplitude of 18 mm, reaches 2.3 (X /L =0.5, λ=5 mm, θ=0°).
(3) Although the operating frequency does not affect the M as much as the amplitude does in this cooling system, it still regulates the power consumption of the PZT fan. The use of a 6 Hz fan frequency, which is 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 of ( X /L =0.5, λ=5 mm, θ=0°), the Nu almost linearly increases with an increasing Re . According to this correlation, the Nu can be derived from the amplitude and the operating frequency that determine the Re .
Nu J 2.9297 V 0.0387Re when Re × 700
(5) The M can be correlated with the dimensionless ratio of the natural convection to the forced convection (Ri) and then generalized as the following equations:
M J 1.389 X 0.2762 ln Ri Ri × 1 M J 1.268 X 0.05663 ln Ri Ri Ú 10
The major findings of the multiple-vibrating fan cooling system are given as follows:
(6) The fan geometries have a large influence on the resonant frequency of the magnetic fan. The resonant frequency can be decreased from 36.4 Hz to 21.8 Hz by reducing the thickness of the magnetic fan from 0.3 mm to 0.2 mm. However, the additional stiffness gained by the addition of the magnet only affects the resonant frequency of the magnetic fan slightly when the value of the distance between the two magnets (x) is larger than 15 mm. For example, the resonant frequency of the magnetic fan (case 1) decreased from 33.8 Hz to 30.4 Hz when X was increased from 13.7 mm to 25.1 mm.
(7) In the same operating conditions, the multiple-vibrating fan system does not consume more power than a single PZT fan does. However, the total amplitude of the multiple-vibrating fan system reaches 56 mm, whereas the amplitude of the single PZT fan is 14 mm under an operating voltage of 80 V.
(8) The results show that the magnetic stiffness of the multiple-vibrating fan system is positive for a repulsive force. Additionally, the equation below can be used to analyze not only the resonant frequency of a magnetic fan affected by one magnet but also the resonant frequency of a magnetic fan affected by two magnets.
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ω"++ J q \]^…Q%.WZt†† s
(9) With the advantages of using both the PZT effect and the magnetic force, the multiple-vibrating fan cooling system exhibits lower power consumption and high thermal performance. When the system is used to cool the heat sink heated by a 15 W dummy heater, the average temperature decreases from 67 ℃ to 50
℃ under the operating condition of 36.4 Hz and 50 V. The temperature drop of the heat sink reaches 17 ℃ at a power consumption of 0.03 W.
(10) A double-sided magnetic fan has been developed. This vibrating fan is able to generate air flow at the fan tip and the fan bottom simultaneously. Thus, the convective ability of a vibrating fan can be further improved by using this design.
(11) By using a frequency modulator, the resonant frequency can be directly adjusted.
According to the experiments, the difference between the resonant frequencies of each magnetic fan is usually less than 2 Hz, such that this modulator is precisely able to modulate the resonant frequencies of the magnetic fans to a uniform value.
A resonant modulator weighing 0.325 g was used for the purpose. Using this resonant modulator, the resonant frequency of the magnetic fan can be adjusted between 35.4 Hz and 32.1 Hz. These results indicate that a small and light modulator is sufficient for adjusting the resonant frequency of magnetic fans.
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Fig.1-1 A finned heat sink.
Fig.1-2 The combination of a rotary fan and a finned heat sink.
Fig.1-3 Properties of piezoelectric material[8].
Fig.1-4 A water circulation cooling system by using a piezoelectric micropump[9].
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Fig.1-5 A piezoelectric fan used for a cooling application[13].
Fig.1-6 A piezoelectric actuator used for a cooling applications[14].
Fig.1-7 A piezoelectric fan mounted to a constant heat flux surface[18].
Fig.1-8 Influences of the dimensions and the material on a vibrating[24].
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Fig.1-9 A cooling system combines two piezoelectric fans with a heat sink[27].
Fig.1-10 A simulation model of a vibrating fin system[28].
Fig.1-11 Two vibrating sheets are inserted between the three fins.
Fig.1-12 Air flow generated by a piezoelectric fan primarily influences on the area of its fan tip[19].
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Fig.1-13 Air flow generated by a piezoelectric fan is in a small area[29].
Fig.1-14 An innovative design of a small finned heat sink (50mm x 50mm x 35mm) with a raked piezoelectric fan[31].
Fig.1-15 A multiple piezoelectric fans cooling system using three piezoelectric fans[32].
Fig.1-16 A multiple piezoelectric fans cooling system using four piezoelectric fans for cooling CPU[33].
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Fig.1-17 A heat sink with special configuration was used in order to place two piezoelectric fans inside it[27].
Fig.1-18 A finned heat sink with nine piezoelectric fans.
Fig.2-1 Thickness of a piezoelectric plate can be decreased to maintain the electric field at a lower voltage[34, 35].
Fig.2-2 Power consumption of a piezoelectric plate operated at 60Hz.
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Fig.2-3 Power consumption of a piezoelectric plate operated at 60V.
Fig.2-4 Power consumption of piezoelectric plates with different volume at fixed input voltage.
Fig.2-5 Schematic view of the piezoelectric fan in this research.
Fig.2-6 Schematic view of a magnetic fan.
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Fig.2-7 Schematic view of the multiple-vibrating fan system
Fig.2-8 A magnetic fan is fixed on a clamp end that can be moved along the moving direction
Fig.2-9 Repulsive forces between vibrating fans.
Fig.2-10 Repulsive force between two cylindrical magnets.
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Fig.2-11 Four effective magnetic forces existed in this system.
Fig.2-12 A magnetic fan with its end fixed is bent by a concentrated load applies at a point.
Fig.2-13 Fixed end and non-fixed end cantilever beams.
Fig.2-14 The piezoelectric fan made by Yoo et al[24].
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Fig.2-15 The system with uniform resonant frequency and without uniform resonant frequency.
Fig.2-16 The frequency modulator is added to a magnetic fan.
Fig.3-1 The arrangement of thermocouples in the heat sink.
Fig.3-2 Simulation model of the single piezoelectric fan cooling system
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Fig.3-3 The pressure field of the downstream domain with different thicknesses.
Fig.3.4 The orientations of the magnetic fans are the same.
Fig.4-1 A thermal meter used in this research (Agilent 34970A).
Fig. 4-2 A signal generator (GW Instek SFG-2004 4MHz)
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Fig.4-3 A high Voltage Amplifier (A. A. Lab-Systems A-303).
Fig.4-4 The geometries of the finned heat sink.
Fig.4-5 Thermocouples are pasted on the center of the rectangular sections.
Fig.4-6 A screenshot from the movie recorded by high-speed mode.
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Fig.4-7 A screenshot from the movie recorded by normal mode.
Fig.4-8 The piezoelectric fan is fixed by two screws.
Fig.4-9 The piezoelectric fan is connected with an adjustable basement.
Fig.4-10 The experimental devices.
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Fig.4-11 A schematic view of the multiple-vibrating fan cooling system.
Fig.5-1 The orientations of the single piezoelectric fan cooling system.
Fig.5-2 Temperature drop on the bottom and side fin surfaces. ( X /L =0.5, θ=0°, frequency=30 Hz, Amplitude=18 mm)
Fig.5-3 M versus the horizontal orientation. (λ=5 mm, θ=0°, frequency=30 Hz, Amplitude=18 mm)
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Fig.5-4 Flow field near the bottom and the side surfaces. (X /L =0.5, λ= 5 mm, θ=0°)
Fig.5-5 Power consumption of the piezoelectric fan. (X /L =0.5, λ= 5 mm, θ=0°, amplitude=10 mm)
Fig.5-6 Influence of the fan amplitude on M .
Fig.5-7 Correlation between Re and Nu of the cooling system.
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Fig.5-8 Relationship between M and Ri. (X ⁄L =0.5, λ= 5 mm, θ = 0°)
Fig.5-9 The amplitude of the magnetic fans (case 1) under different frequencies and a voltage of 50 V.
Fig.5-10 The amplitude of the magnetic fans (case 2) under different frequencies and a voltage of 50 V.
Fig.5-11 The amplitude of the magnetic fans (case 3) under different frequencies and a voltage of 50 V.
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Fig.5-12 The magnetic fan is affected by (a) one magnet, (b) a double magnet.
Fig. 5-13 Variation of the resonant frequency of the magnetic fan affected by one magnet.
Fig.5-14 Variation of the resonant frequency (case 3) of the magnetic fan is affected by one magnet and a double magnet.
Fig.5-15 The amplitude of a single PZT fan and the multiple-vibrating fan system (case 4) under different voltages.
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Fig.5-16 Power consumption of a single PZT fan and the multiple-vibrating fan system under different voltages. (both at resonant frequency)
Fig.5-17 The cooling ability of the system is demonstrated by the temperature dropped of the thermal couples.
Fig.5-18 The average surface temperature at the heat sink base under different values of λ.
Fig.5-19 A magnetic fan with a frequency modulator.
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Fig.5-20 The relationship between the graduation of the resonant frequency and the resonant frequency of the magnetic fan.
Fig.5-21 A double-side fan
Fig.5-22 The screenshot of the vibration of a double-side fan.
Fig.5-23 Two double-side fans are actuated by a piezoelectric fan.
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Fig.5-24 A rotary fan occupies a lot of space.
Fig.5-25 The schematic view of a plate which can be used to fix different vibrating fans.
Fig.5-26 A multiple-vibrating fan cooling system module.
Fig.5-27 A multiple-vibrating fan cooling system module embedded in a motherboard for cooling CPU.
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Table 1 Power consumption of rotary fans[1, 2, 3, 4].
COOLERMASTER 120X120X25 (mm) 12 V 0.16 A 1.92 W 58.4 CFM
THERMALTAKE 120X120X25 (mm) 12 V 0.2 A 2.88 W 45.5 CFM
SUNON 120X120X25 (mm) 12 V 0.16 A 1.92 W 55 CFM
SCYTHE 120X120X25 (mm) 12 V 0.12A 1.44 W 45.9 CFM
Table 2 Power consumption of piezoelectric fans[5, 6].
Piezo system 56.7X12.7X1(mm) 12 V 60Hz 2.2mA 26 mW
MIDE 70X15.4X0.8 (mm) 115V 60Hz No data 30 mW
Table 3 Power consumption of single-layer and multilayer piezoelectric fans[31].
Table 4 Power consumption of piezoelectric plates with different geometries[6].
Specification Length
Table 5 Lifetime of the piggyback piezoelectric actuator[37, 38].
Temperature(K) Driving
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Table 6 Geometries of the vibrating fans used in this research.
Fan geometry(mm) Magnet geometry(mm) Material
Table 7 Resonant frequencies of the piezoelectric fans made by Yoo et al[24].
L(mm) W(mm) H(mm) Measured
Table 8 Resonant frequencies of the piezoelectric fans in this research.
L(mm) W(mm) H(mm) Measured
Table 9 The specification of the piezoelectric plate used in this research.
Standard Stripe Actuator TM 40140
Length 40 mm Free Length 33 mm
Width 20 mm Total Deflection > 1.0 mm
Thickness 0.6 mm Blocking Force > 0.40 N
Capacitance 115,000 pF Resonant Frequency 175 Hz
Table 10 The specification of INTEL CPUs[46].