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TECHNICAL PAPERS: Heat Transfer Enhancement

# Local Heat Transfer Coefficients Induced by Piezoelectrically Actuated Vibrating Cantilevers

[+] Author and Article Information
Mark Kimber, Arvind Raman

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

1

Corresponding author.

J. Heat Transfer 129(9), 1168-1176 (Jan 17, 2007) (9 pages) doi:10.1115/1.2740655 History: Received October 17, 2006; Revised January 17, 2007

## Abstract

Piezoelectric fans have been shown to provide substantial enhancements in heat transfer over natural convection while consuming very little power. These devices consist of a piezoelectric material attached to a flexible cantilever beam. When driven at resonance, large oscillations at the cantilever tip cause fluid motion, which in turn results in improved heat transfer rates. In this study, the local heat transfer coefficients induced by piezoelectric fans are determined experimentally for a fan vibrating close to an electrically heated stainless steel foil, and the entire temperature field is observed by means of an infrared camera. Four vibration amplitudes ranging from $6.35to10mm$ are considered, with the distance from the heat source to the fan tip chosen to vary from 0.01 to 2.0 times the amplitude. The two-dimensional contours of the local heat transfer coefficient transition from a lobed shape at small gaps to an almost circular shape at intermediate gaps. At larger gaps, the heat transfer coefficient distribution becomes elliptical in shape. Correlations developed with appropriate Reynolds and Nusselt number definitions describe the area-averaged thermal performance with a maximum error of less than 12%.

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## Figures

Figure 9

Normalized area-averaged Nusselt numbers for four different Reynolds numbers (Repz=3550, 2810, 2370, and 1860 corresponding to A=10, 8.5, 7.5, and 6.35mm, respectively) with (a) G∕A=0.01 and (b) G∕A=2.0

Figure 10

Stagnation Nusselt number (Nu0) behavior versus nondimensional gap (G∕A) for three separate Reynolds numbers (Repz) corresponding to vibration amplitude of 10mm(Repz=3550), 8.5mm(Repz=2810), and 7.5mm(Repz=2370)

Figure 11

Correlations with experimental data for (a) stagnation Nusselt number (Eq. 15) with average and maximum deviations of 2.1% and 5.8%, respectively, and (b) area-averaged Nusselt number (Eq. 15 substituted in Eq. 13) with average and maximum deviations of 3.3% and 11.4%, respectively

Figure 1

Schematic diagram of constant heat flux surface

Figure 2

Flux balance on foil (neglecting lateral conduction)

Figure 3

Geometric parameters of fan: length (L) and width (w). Also shown are the parameters varied throughout experiments: vibration amplitude (A) and gap distance from heat source (G).

Figure 4

Natural convection temperature distribution

Figure 5

Natural convection temperature profile in the vertical direction at the heat source center, x=0mm

Figure 6

Experimental convection coefficient (hpz) for A=10mm (top row), A=8.5mm (second row), A=7.5mm (third row), and A=6.35mm (bottom row). Each column represents a different gap corresponding to G∕A=0.01, 0.5, and 2.0. The heater size shown is 101.6mm×152.4mm.

Figure 7

Convection coefficient (hpz) along horizontal direction (y=0) over range of nondimensional gaps (G∕A=0.01,0.25,0.5,1.0,2.0) for: (a) A=10mm, (b) A=8.5mm, (c) A=7.5mm, and (d) A=6.35mm. For comparison, the natural convection profile is also shown.

Figure 8

Area-averaged Nusselt number (Nu¯) versus nondimensional diameter of circular heater (Deq∕A) for Repz=3550(A=10mm) over range of nondimensional gaps (G∕A=0.01–2.0)

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