Research Papers: Electronic Cooling

Cooling Performance of Arrays of Vibrating Cantilevers

[+] Author and Article Information
Mark Kimber

NSF Cooling Technologies Research Center, School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907-2088

Suresh V. Garimella1

NSF Cooling Technologies Research Center, School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907-2088sureshg@purdue.edu


Corresponding author.

J. Heat Transfer 131(11), 111401 (Aug 19, 2009) (8 pages) doi:10.1115/1.3153579 History: Received February 15, 2008; Revised April 21, 2009; Published August 19, 2009

Piezoelectric fans are vibrating cantilevers actuated by a piezoelectric material and can provide heat transfer enhancement while consuming little power. Past research has focused on feasibility and performance characterization of a single fan, while arrays of such fans, which have important practical applications, have not been widely studied. This paper investigates the heat transfer achieved using arrays of cantilevers vibrating in their first resonant mode. This is accomplished by determining the local convection coefficients due to the two piezoelectric fans mounted near a constant heat flux surface using infrared thermal imaging. The heat transfer performance is quantified over a wide range of operating conditions, including vibration amplitude (7.5–10 mm), distance from heat source (0.01–2 times the fan amplitude), and pitch between fans (0.5–4 times the amplitude). The convection patterns observed are strongly dependent on the fan pitch, with the behavior resembling a single fan for small fan pitch and two isolated fans at a large pitch. The area-averaged thermal performance of the fan array is superior to that of a single fan, and correlations are developed to describe this enhancement in terms of the governing parameters. The best thermal performance is obtained when the fan pitch is 1.5 times its vibration amplitude.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Experimental parameters: vibration amplitude (A), gap from heat source (G), and fan pitch (P). Also shown is the piezoelectric fan length (L) and width (w).

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Figure 2

Experimental convection coefficient contours (hpz) for A=10 mm and G/A=0.01 (first column), G/A=0.50 (second column), and G/A=2.0 (last column). The first row illustrates single-fan performance at the same gaps, while the remaining rows are the results from array experiments with each row representing a different pitch corresponding to P/A=0.5,1.25,4.0. The heater size shown is 101.6×152.5 mm2. Vibration envelopes are superimposed to show location of fans with solid and dashed lines depicting the first and second fans, respectively.

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Figure 3

Convection coefficients (hpz) along the horizontal centerline of the heat source (y=0) over a range of nondimensional gaps (G/A=0.01,0.1,0.25,0.5,1.0,2.0) for (a) P/A=0.5, (b) P/A=1.0, (c) P/A=1.25, and (d) P/A=4.0. For comparison, the single-fan (G/A=0.01) and natural convection profiles are also shown. The solid and dashed vertical lines represent the vibration envelopes of the first and second fans, respectively.

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Figure 4

Stagnation Nusselt number for fan arrays at Repz=3640, 2920, and 2430 corresponding to A=10, 8.5, and 7.5 mm. These are compared with the single fan correlation in Eq. 9.

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Figure 5

Map of Nu¯/Nu0 (values in boxes) for a single fan from the correlation in Eq. 10. Also illustrated are polar coordinates (r, θ) as defined in Eq. 11.

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Figure 6

Illustration of unit cell area used in computing Nu¯. The horizontal dimension is always equal to half the pitch (x=P/2), while the vertical dimension can vary depending on the size of the heat source.

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Figure 7

Profiles of Nu¯/Nu0 at different x/A locations: (a) single-fan correlation results from Fig. 5 and (b) experimental array data at the largest amplitude (Repz=3640). In the case of fan arrays, 2x is better represented as P so that the two sets of data correspond to the same area on the heat source.

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Figure 8

Experimental enhancement observed with arrays at the largest amplitude (Repz=3640) over the full range of pitches considered. The horizontal dimension of the targeted heat source is x=P/2, while the vertical dimension varies with y/w (values of 3.0, 2.0, 1.0, and 0.5 are shown).

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Figure 9

Expression for array enhancement over single-fan performance (Eq. 13) at three amplitudes (Repz=3640, 2920, and 2430) and two values for y/w (3.0 and 0.5)




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