heat transfer characteristics of synthetic jet impingement cooling

International Journal of Heat and Mass Transfer 53 (2010) 1057–1069

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International Journal of Heat and Mass Transfer

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Heat transfer characteristics of synthetic jet impingement cooling

Mangesh Chaudhari, Bhalchandra Puranik, Amit Agrawal *

Mechanical Engineering Department, Indian Institute of Technology Bombay, Mumbai 400076, India

a r t i c l e i n f o

Article history:Received 5 September 2008Received in revised form 23 April 2009Accepted 18 June 2009Available online 28 November 2009

Keywords:Synthetic jetsImpingement heat transferHot-wire anemometryCavity response

0017-9310/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.ijheatmasstransfer.2009.11.005

* Corresponding author. Tel.: +91 02225767516; faE-mail address: [email protected] (A. Agrawa

a b s t r a c t

Synthetic jet is a novel flow technique which synthesizes stagnant air to form a jet, and is potentially use-ful for cooling applications. The impingement heat transfer characteristics of a synthetic jet are studied inthis work. Toward that end, the behavior of the average heat transfer coefficient of the impinged heatedsurface with variation in the axial distance between the jet and the heated surface is measured. In addi-tion, radial distribution of mean and rms velocity and static pressure are also measured. The experimentsare conducted for a wide range of input parameters: the Reynolds number (Re) is in the range of 1500–4200, the ratio of the axial distance between the heated surface and the jet to the jet orifice diameter is inthe range of 0–25, and the length of the orifice plate to the orifice diameter varies between 8 and 22 inthis study. The maximum heat transfer coefficient with the synthetic jet is found to be upto 11 timesmore than the heat transfer coefficient for natural convection. The behavior of average Nusselt numberis found to be similar to that obtained for a continuous jet. The exponent of maximum Nusselt numberwith Re varies between 0.6 and 1.4 in the present experiments, depending on the size of the enclosure. Adirect comparison with a continuous jet is also made and their performances are found to be comparableunder similar set of conditions. Such detailed heat transfer results with a synthetic jet have not beenreported earlier and are expected to be useful for cooling of electronics and other devices.

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1. Introduction

In the fast growing technology, due to faster operation of eachtransistor and an increase in their density on integrated circuits,a large amount of heat needs to be dissipated. Thermal overstress-ing is one of the major causes of failure of electronic components.This underscores the requirement for proper thermal managementwhich is perhaps the most crucial part of the electronic system de-sign. Effective cooling systems are therefore required which alsomeet the space and other design constraints. Heat sinks with airas the working fluid, and different fin geometry and fan arrays havebeen traditionally used for heat removal from electronic systems.However, these traditional forced air cooled heat sinks are facingserious challenges for the cooling of the next generation of elec-tronics owing to the additional space constraints and still highercooling requirements. Due to low cost, availability and reliability,air will continue to be used as the working fluid. In the presentwork, synthetic jet impingement cooling which can potentiallybe used for cooling of hot-spots is investigated.

A synthetic jet is synthesized directly from the fluid in the sys-tem in which it is embedded. A synthetic jet is commonly formedwhen the fluid is alternately sucked into and ejected from a smallcavity by the motion of a diaphragm bounding the cavity, so that

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there is no net mass addition to the system [1]. This feature obvi-ates the need for input piping or complex fluidic packaging andmakes synthetic jets ideally suited for low-cost batch fabricationusing micro-machining techniques. The synthetic jet is a new en-trant into the means available to engineers to manipulate flow toachieve the desired result. Besides cooling, the synthetic jets havea number of other potential engineering applications, such asboundary-layer separation control, jet vectoring, better mixing offuel in the engine combustion chamber, creation of local turbu-lence, and vehicle propulsion [2–7].

A brief discussion on cooling with impinging continuous, pulsedand synthetic jet is presented next. San and Shiao [8] studied theheat transfer characteristics of a confined continuous circular airjet impinging on a flat plate for different Reynolds numbers, platespacing, jet plate width and length. The stagnation Nusselt numberwas found to be proportional to the 0.638 power of the Reynoldsnumber, and inversely proportional to the 0.3 power of the platespacing to jet diameter ratio. The stagnation Nusselt number wasalso found to vary as exp½�0:044ðW=dÞ � 0:011ðL=dÞ�, where Wand L are the width and length of the plate respectively. Colucciand Viskanta [9] performed experiments using thermochromaticliquid crystal technique and discussed the effects of nozzle geom-etries on the local heat transfer coefficient for confined impingingair jet. Katti and Prabhu [10] studied the local heat transfer charac-teristics of a circular straight pipe nozzle jet impinging on a flatplate, using infrared thermal imaging technique. The experiments

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Nomenclature

A area ðm2Þ, amplitude of vibration (m)Cp specific heat (J/kgK)d orifice diameter (m)f excitation frequency (Hz)h average heat transfer coefficient ðW=m2 KÞH cavity depth (m)I current (A)k thermal conductivity (W/mK)l length of copper block (m)L length of orifice plate (m)Lo stroke length (m)Nu average Nusselt number ðhd=kÞ (–)P pressure ðN=m2ÞPr Prandtl number ðlCp=kÞ (–)qconv net heat flux convected to the impinging jet ðW=m2Þqjoule imposed ohmic heat flux (VI/A) ðW=m2Þqloss total heat loss ðW=m2Þr radial distance (m)R half length of heated copper plate (m)Re Reynolds number ðqvd=lÞ (–)t length of the orifice (m)Ts surface temperature (�C)

T inf ambient temperature (�C)uðtÞ instantaneous velocity (m/s)Umean mean velocity (m/s)Uo average centerline orifice velocity (m/s)V voltage (V)v characteristics velocity scale (m/s)y coordinate normal to plate (m)z axial distance (m)zmax; ðz=dÞmax axial distance corresponding to hmax; Numax

respectively (mm, –)

Greek symbolsl dynamic viscosity of jet fluid (kg/ms)m kinematic viscosity of jet fluid ðm2=sÞq density of fluid ðkg=m3Þs time (s)

Subscriptsavg averagemax maximumrms root mean square

1058 M. Chaudhari et al. / International Journal of Heat and Mass Transfer 53 (2010) 1057–1069

were conducted for jet to plate spacing of 0.5 and 8 times the noz-zle diameter, in the Reynolds number range of 12,000–28,000. Thefollowing three regions are identified on the impingement surfacebased on the flow characteristics of the impinging jet: stagnationregion ð0 6 r=d 6 1:0Þ, transition region ð1:0 6 r=d 6 2:5Þ and walljet region ðr=d P 2:5Þ. They also proposed a semi-empirical corre-lation for the local heat transfer coefficient in the wall jet region,based on the assumption of flow over a constant heat flux flatplate. Gulati et al. [11] studied the effect of different shapes of noz-zle for an equivalent diameter of 20 mm on the local heat transferdistribution on a flat surface, using infrared thermal imaging tech-nique. Both local and average Nusselt numbers on the impingedsurface are presented, for Reynolds number between 5000 and15,000 and jet-to-plate spacing from 0.5 to 12 nozzle diameters.

Kataoka et al. [12] have explored the mechanism for theenhancement of stagnation point heat transfer using a pulsed jet.The large-scale turbulent structures of an impinging round jetwere analyzed by employing conditional sampling. It was foundthat the large-scale eddies impinging on the heat transfer surfacesproduce a turbulent surface renewal effect which enhances theheat transfer from the impinging surface. Eibeck et al. [13] describea technique for convective heat transfer enhancement which in-volves the use of a pulse combustor to generate a transient jet thatimpinges on a flat plate. Enhancement upto 2.5 times the steadyimpinging jet value has been reported. Zumbrunnen and Aziz[14] also show heat transfer enhancement by a factor of 2 withpulsed water jet. Sailor et al. [15] in the heat transfer enhancementstudy have investigated one additional flow variable, the duty cycle(representing the ratio of pulse cycle on-time to total cycle time)along with other parameters such as the Reynolds number, jet toplate spacing and pulse frequency. The maximum heat transferenhancement occurs for the highest flow rates, which correspondsto 65% enhancement over a steady jet. Hwang and Cho [16] usedtwo different acoustic excitation methods (jet excitation and shearlayer excitation) on an impinging jet for studying the ensuing heattransfer. The excitation frequency and the excitation level arefound to be important factors for heat transfer enhancements.

Compared to continuous and pulsed jets, fewer studies onimpinging synthetic jet have been performed. Pavlova and Amitay

[17] experimentally investigated the efficiency and mechanism ofcooling a constant heat flux surface, and compared the perfor-mance of synthetic jet against that of a continuous jet. In theirmeasurements, high frequency (1200 Hz) jets are found moreeffective at smaller axial distances and low frequency (420 Hz) jetsare found more effective at larger axial distances. Also, it was foundthat synthetic jet cools the heated surface better than the continu-ous jet at the same Reynolds numbers. Garg et al. [18] have de-signed a meso-scale synthetic jet from a 0.85 mm hydraulicdiameter rectangular orifice and a maximum velocity of 90 m/s.Microscopic infrared thermal imaging technique was used for tem-perature measurements on a foil heater. A maximum heat transferenhancement of approximately 10 times the natural convectionwas measured for V rms ¼ 90 V. Mahalingam and Glezer [7] havediscussed the design and thermal performance of synthetic air-jet based heat sink for high power dissipation electronics. Approx-imately 40% more heat dissipation occurred with the synthetic jetbased heat sinks as compared to the configuration of steady flowfrom a ducted fan blowing air through the heat sink. The averageheat transfer coefficient in the channel flow between the finswas 2.5 times that for steady flow in the duct at the same Reynoldsnumber.

From the literature it is noticed that there are relatively fewstudies on impingement cooling involving synthetic jet. In particu-lar, the heat transfer measurements by systematically varyingparameters such as orifice diameter, length of orifice plate, cavitydepth and excitation frequency have not been reported. The depthand diameter of the cavity along with the orifice length and diam-eter are the geometric parameters, while frequency and amplitudeof actuation are the control parameters pertinent in the study ofheat transfer enhancement with synthetic jet. In this work, wehave measured the average heat transfer coefficient by varyingthe different geometric and flow parameters as a function of theaxial distance between the synthetic jet and a heated copper block,while the effect of varying the orifice shape has been studied byChaudhari et al. [19]. Dimensional analysis is performed to identifythe governing non-dimensional parameters. The effect of thesenon-dimensional parameters on the Nusselt number is investi-gated in the present work. A correlation of Reynolds number

M. Chaudhari et al. / International Journal of Heat and Mass Transfer 53 (2010) 1057–1069 1059

dependency on Nusselt number is given for different configura-tions from the measured data. Also, velocity and pressure resultsare discussed, and the performance of the synthetic jet is comparedwith that of a continuous jet for the same set of boundary condi-tions and Reynolds number.

2. Experimental set-up and measurement procedure

Fig. 1 shows the schematic of the set-up used for the presentexperiments. The experiments are conducted for different configu-rations of synthetic jet impinging on a heated surface. The syn-thetic jet assembly is attached to a 2-d traverse stand so that theaxial distance between the jet orifice and the heated surface canbe controlled easily using a fine pitch traversing mechanism. Theheater block is constructed from a copper plate, and has finaldimensions 40� 40� 5 mm3. The block is heated by a nichrome

Copper Plate Heater

Speaker with cavity

2-d

Perpex

(a)

L

D

(b)

R

t

Fig. 1. (a) Schematic of heat transfer experimental set-up a

foil heater of the same size attached underneath of the block.The heater is supported by a bakelite plate to provide proper ther-mal contact between the heater and the copper block. The copperblock is insulated by glass-wool (size 180� 180� 40 mm3) tominimize the heat loss through the sides and bottom.

The heater surface provides a constant heat flux, as the drivingpower input is constant, and the flexible heater is specifically de-signed to provide a constant heat flux output. The surface temper-ature is measured with two pre-calibrated K-type thermocouples,which are placed at two sides of the copper block 4 mm from thelateral surface, thus providing a spatially averaged temperatureover the exposed surface of the copper block. An identical thermo-couple is used away from the heated surface for ambient air tem-perature measurement. The power supplied to the heater ismeasured with a multi-meter and is controlled by a rheostat. Asynthetic jet is synthesized at the edge of an orifice by a periodic

Bakellite

Glass-wool

Traverse Stand

z

d

nd (b) dimensional parameters relevant for the study.

Table 2


motion of a diaphragm mounted on one side of a sealed cavity. Airis the working fluid in the present experiments.

From the literature it is noticed that a number of researchersuse a piezo-actuated membrane as the oscillating diaphragm forthe creation of a synthetic jet. A piezoelectric actuator requires rel-atively high voltage ðV rms � 90 VÞ as compared to that required foran electromagnetic actuator. Furthermore, a piezo-actuator oper-ates at certain discrete input frequencies. For these reasons,piezo-actuators have not been used here. In the present study, anelectromagnetic actuator (acoustic speaker) of diameter 50 mmand operating at an input voltage ðV rmsÞ of 4 V is employed. Theexperiments are conducted for different orifice diameters, lengthof orifices, and cavity depths (see Table 1). The input voltage tothe actuator is maintained constant and the frequency of excitationis controlled by a signal generator and monitored by an oscillo-scope (Tektronix, TDS 2022B). The jet issuing from the orifice im-pinges normally onto the plate at a distance of z from the orifice(Fig. 1(b)). The distance between the orifice surface and the copperplate is varied with the help of a traverse stand. The effects of thesynthetic jet impingement cooling are investigated by measuringthe surface and ambient temperatures for different operating fre-quencies and other geometric parameters for a known power sup-plied to the heater. The results are presented in terms of theaverage Nusselt number as a function of normalized axial distancez=d.

The heat loss is calculated by supplying different input powersto the heater, and measuring the surface temperature of the heatedcopper block along with the ambient temperature, while insulatingthe top surface of the heated block. The losses are taken in to ac-count for calculation of heat transfer coefficient as per Eq. 6. Thelosses from the sides and the bottom of the test section are foundto be typically 22% of the input power. Due to low temperatures in-volved in this experiments, the heat loss from the surface due toradiation transfer is neglected, as it is calculated to be less than1% of the power input. The temperature difference between thecopper surface and the ambient is maintained above 15 �C for allthe experimental results.

3. Data reduction

The Reynolds number is calculated using the procedure givenby Smith and Glezer [1]

Re ¼ U0dm

ð1Þ

where d is the orifice diameter, m is the kinematic viscosity, and Uo

is the average orifice velocity during the ejection part of the cycle atthe exit and centerline of the orifice. This last parameter is calcu-lated as

Uo ¼ Lof ð2Þ

where f is the excitation frequency (or inverse of time period s) andLo is the stroke length calculated over the ejection part of the totalcycle as

Table 1Parameters varied in the present study. See Fig. 1(b) for definition of the variousparameters.

Parameter Value Dimension

d 5, 8, 14 mmt 1.6, 2.4, 5 mmL 110, 192.5 mmR 20 mmH 6.3, 8.7 mmRe 1150–4180 –

Lo ¼Z s=2

0uðtÞdt: ð3Þ

The average velocity is between 3.1 and 8.5 m/s and the maximuminstantaneous velocity ranges between 10 and 25 m/s for the pres-ent set of experiments. The Reynolds number (calculated from Eq.(1)) varies between 1150 and 4200 for the present experiments.

The procedure for calculation of the average Nusselt number forthe heated block is as follows:

Nuavg ¼havgd

k; ð4Þ

where

havg ¼qconv

ðTs � T infÞ; ð5Þ

ðTs � T infÞ is the temperature difference between the surface ðTsÞand the ambient ðT infÞ, and qconv is the net heat flux supplied. Thenet heat flux is the difference in the supplied heat flux ðqjouleÞ andheat lost ðqlossÞ, i.e.,

qconv ¼ qjoule � qloss ð6Þ

where

qjoule ¼VIA

ð7Þ

As already noted, the heat loss is estimated as approximately 22% ofthe heat supplied.

The uncertainty in measurement of the average Nusselt numberis approximately 7.5%. See Table 2 for uncertainty in the otherparameters.

4. Heat transfer with synthetic jet impingement

This section presents the results of an impinging synthetic jetissuing from a circular orifice on to a heated copper block. The var-iation in the heat transfer coefficient as a function of axial distance,for a large range of parameters is presented in this section. The val-idation of the setup and repeatability of the results are also pre-sented in this section.

4.1. Validation and repeatability

Due to paucity of results on synthetic jet with impingement,validation of the experimental setup is done by employing a con-tinuous axisymmetric jet under an otherwise identical set of con-ditions. Lytle and Webb [20] have presented local heat transferdata for different nozzle to plate spacings ðz=dÞ and different Rey-nolds numbers for a continuous axisymmetric unconfined jet. Thepresent experimental set-up is validated by comparing for theaverage Nu obtained upon suitable integration. The comparisonin Fig. 2 is for a Reynolds number of 12,000 at three nozzle to plate

Maximum uncertainty in measurements of different parameters.

Parameter Error in measurement

L 1 mmd, t 0.25 mmR, H 0.5 mmz 0.5 mmDT 0.5 �CV 0.001 VI 0.01 AUo ±3%havg 4%Nuavg 7.5%

z/d

Nu av

g

2 4 6 8 1060

70

80

90

100

110

Present resultsLytle and Webb

Fig. 2. Average Nusselt number as a function of z=d for continuous jet atRe ¼ 12; 000 and comparison with Lytle and Webb [20].


spacings. The difference between the two sets of measurements iswithin ±3%, which is well within the uncertainty of themeasurements.

The synthetic jet assembly has been benchmarked in our earlierwork [21,22]. There the centerline velocity decay of the syntheticjet has been compared against experimental results in the litera-ture and the similarity analysis of Agrawal and Verma [23]. Therepeatability of the results has been systematically checked andis found to be within ±1.7% as shown in Fig. 3. Therefore, the entiresetup can be considered to have been validated and the results tobe repeatable.

4.2. Effect of various parameters (dimensional results)

The effect of various parameters on the overall heat transfercoefficient is discussed in this section. The experiments are donewith the aim of identifying the important parameters which affectthe transfer of heat from a hot surface. The non-dimensional re-

z/d

Nu

0 5 10 15 20 25 300

10

20

30

40

50

60

First setSecond set

Fig. 3. Nusselt number versus z=d at Re = 4180, L=d ¼ 13:75;R=d ¼ 2:5 showingrepeatability of the results.

sults are presented later in Section 6. In order to clearly bring aboutthe physics of the problem, we present results in their dimensionalform in the present section.

4.2.1. Variation of havg with diaphragm frequencyFig. 4 shows the behavior of the average heat transfer coeffi-

cient with the axial distance between the orifice plate and heatedcopper block. These experiments have been conducted for differentexcitation frequencies (100–350 Hz) by keeping the same orificeplate dimensions and cavity depth. It is observed that the averageheat transfer coefficient (h) increases rapidly upto some axial dis-tance ðzmax ¼ 48—50 mmÞ and then decreases gradually with an in-crease in the axial distance, for all frequencies. Also, it is observedthat the average heat transfer coefficient increases with an in-crease in frequency upto 250 Hz, beyond which it reduces. The heattransfer coefficient is found to be maximum at the resonance fre-quency of the cavity (250 Hz) [21,22]. The maximum value of heattransfer coefficient is found to be 143 W=m2 K at 250 Hz, which islarger than most known values of heat transfer coefficient withsynthetic jet. For comparison, Pavlova and Amitay [17] foundhmax ¼ 26:7 ; W=m2 K at the first resonance frequency (420 Hz),hmax in the channels measured by Mahalingam and Glezer [7] is60 W=m2 K for frequency around 200 Hz, while Garg et al. [18] givehmax of 236 W=m2 K at high heat flux for frequency around 4400Hz.

This shows the potential of using synthetic jet for high heat re-moval; in particular, as demonstrated below, synthetic jet seems tobe very competitive with respect to continuous jet for coolingapplications.

4.2.2. Variation of havg with orifice diameterFig. 5 shows the variation of average heat transfer coefficient

with axial distance, for three different orifice diameters (5 mm,8 mm, 14 mm). The same trend as in the previous section has beenobserved for the average heat transfer coefficient along the axialdistance, i.e., h increases till a certain distance and decreases be-yond it. The other observations are:

z (mm)

h avg

(W/m

2 K)

0 50 100 150 200 250 3000

20

40

60

80

100

120

140

160100 Hz150 Hz200 Hz250 Hz350 Hz

Fig. 4. Variation of average heat transfer coefficient with axial distance for differentexcitation frequency, and for the same orifice diameter, length of orifice and lengthof orifice plate, and cavity depth (d = 8 mm, t = 2.4 mm, L = 110 mm, H = 6.3 mm).

z (mm)

h avg

(W/m

2 K)

0 50 100 150 200 250 3000

20

40

60

80

100

120

140

16014 mm8 mm5 mm

Fig. 5. Variation of average heat transfer coefficient with axial distance for differentorifice diameters, and for the same excitation frequency, length of orifice and lengthof orifice plate, and cavity depth (t = 2.4 mm, L = 110 mm, H = 110 mm, f = 250 Hz).


1. The maximum value of average heat transfer coefficient is143 W=m2 K for 8 mm orifice diameter at an axial distance of48 mm.

2. The location and the maximum value of average heat transfercoefficient changes with the orifice diameter. For example, thelocation of hmax is zmax ¼ 60; 50 and 30 mm for 5, 8 and14 mm orifice diameter, respectively.

3. The location of hmax varies monotonically with the orifice diam-eter, but not the value of hmax.

The maximum value and the variation of average heat transfercoefficient for different orifice diameters depend on the flow veloc-ity and size of the enclosure. These effects will be discussed furtherin a later section.

z (mm)

h avg

(W/m

2 K)

0 50 100 150 200 250 3000

20

40

60

80

100

120

140

160

H = 6.3mmH = 8.7mm

Fig. 6. Variation of average heat transfer coefficient with axial distance for differentcavity depth, and for the same orifice diameter, length of orifice and length of orificeplate, and excitation frequency (d=8 mm, t = 2.4 mm, L = 110 mm, f = 250 Hz).

4.2.3. Variation of havg with cavity depthFig. 6 shows the variation of average heat transfer coefficient

with axial distance, for different cavity depths (6.3 mm and8.7 mm) and keeping the value of all other parameters the same.It is noticed that the cavity depth does not have a significant effecton the average heat transfer coefficient.

As presented in our earlier work [22], the exit velocity remainsapproximately the same over a sufficiently large range of cavitydepths. Those results are therefore consistent with the presentobservation of a negligibly small effect of cavity depth on the aver-age heat transfer coefficient. Because of availability of the earlierresults, the present set of experiments are conducted for onlytwo values of cavity depths.

4.2.4. Variation of havg with thickness of orifice plateFig. 7 shows the variation of average heat transfer coefficient

with axial distance between orifice plate and copper block, for dif-ferent thickness of orifice plates (1.6 mm, 2.4 mm, 5 mm) whilekeeping the value of all other parameters the same. The thicknessof the orifice plate strongly affects the average heat transfer coeffi-cient along the axial distance; the average heat transfer coefficientincreases with a decrease in thickness of the orifice plate. The max-imum value of heat transfer coefficient is found to be 155 W=m2 Kat 40 mm axial distance for 1.6 mm thickness of orifice plate. How-ever, the average heat transfer coefficients drops precipitously fordistances smaller than zmax for the 1.6 mm thickness case. Notethat the location of the maximum heat transfer coefficient changessomewhat with orifice plate thickness; the location of maxima var-ies between 30 and 40 mm.

4.2.5. Variation of havg with length of orifice plateFig. 8 shows the effect of enclosure on the average heat transfer

coefficient as a function of axial distance. These experiments areconducted for two different lengths of orifice plate (110 mm and192.5 mm) by keeping all the other parameters the same. Thelength of the orifice plate significantly affects the average heattransfer coefficient. The average heat transfer coefficient increaseswith a decrease in length of the orifice plate. The maximum valueof average heat transfer coefficient is found to be 89 W=m2 K at28 mm of axial distance for 110 mm length of orifice. It is however

z (mm)

h avg

(W/m

2 K)

0 40 80 120 160 200 240 2800

20

40

60

80

100

120

140

160

1.6 mm thick2.4 mm thick5 mm thick

Fig. 7. Variation of average heat transfer coefficient with axial distance for differentlength of orifice and for same excitation frequency, orifice diameter, length oforifice plate, and cavity depth (d = 14 mm, L = 110 mm, H = 6.3 mm, f = 250 Hz).

z (mm)

h avg

(W/m

2 K)

0 60 120 180 2400

20

40

60

80

100

length = 110mmlength = 192.5mm

Fig. 8. Variation of average heat transfer coefficient with axial distance for differentlength of orifice plate, and for the same excitation frequency, length of orifice andorifice diameter, and cavity depth (d = 14 mm, t = 5 mm, H = 6.3 mm, f = 250 Hz).


observed that the maximum value of heat transfer coefficient is atthe same axial distance for both the cases.

4.2.6. Summary of parametric studyIn the present section, the effects of control parameters such as

excitation frequency and geometric parameters such as orificediameter, length of orifice, orifice plate length, cavity depth onthe heat transfer coefficient have been investigated. The amplitudeof excitation is kept constant ðinput voltage to speaker ¼ 4V rmsÞfor all the above measurements. It is found that the excitation fre-quency, orifice diameter, length of orifice, and length of orificeplate affect the heat transfer coefficient strongly, whereas the cav-ity depth has little or no effect. It will be argued in a later sectionthat the excitation frequency, orifice diameter, and length of orificeaffect the flow velocity, while the length of orifice plate governs theamount of recirculation. The effect of excitation frequency and ori-fice diameter on the heat transfer coefficient is non-monotonic,while that of length of orifice and length of orifice plate is mono-tonic. Therefore choosing the right excitation frequency and orificediameter for an application becomes crucial. The values of theseparameters are however expected to be set by other considerations(e.g. resonance for excitation frequency, space for orifice diameter).Note that the experiments have been repeated for other sets ofparameters and the same qualitative behavior as presented aboveis observed. These results should help in choosing the value of dif-ferent parameters.

5. Dimensional analysis

The average heat transfer coefficient is some function of the ori-fice diameter d, diameter of actuator D, cavity depth H, thickness oforifice plate t, amplitude of vibration A, length of orifice plate L, thedistance between the orifice plate and copper plate z, the halflength of copper plate R, the thermal conductivity of fluid k, theexcitation frequency f, the specific heat of fluid Cp, the density offluid q, and the dynamic viscosity of fluid l (see Fig. 1(b)). In otherwords,

h ¼ f ðd;D;H; t;A; L;R; z; k; f ; Cp;q;lÞ: ð8Þ

These 14 dimensional parameters can be condensed into the follow-ing 10 non-dimensional parameters:

hdk¼ f

qfd2

l;lCp

k;Dd;Hd;

td;Ad;Ld;Rd;zd

!: ð9Þ

The absence of Re from the above list is noteworthy, and is due tothe absence of velocity in Eq. (8). To incorporate the effect of Rey-nolds number (dependence of Nu on Re is expected in forced con-vection problems), the flow velocity v is considered.

Now v should depend on the orifice diameter d, the diameter ofactuator D, the cavity depth H, the thickness of orifice plate t, theamplitude of vibration A, the excitation frequency f, the densityof fluid q, and the dynamic viscosity of fluid l, i.e.,

v ¼ f ðd;D;H; t;A; f ;q;lÞ: ð10Þ

Upon applying the non-dimensionalization procedure to Eq. (10),the following non-dimensional parameters are obtained:

qvdl¼ f

Dd;Hd;

td;Ad;qfd2

l

!: ð11Þ

Note that all five non-dimensional parameters on the right handside of Eq. (11) are common between Eqs. (9) and (11). In otherwords, the effect of parameters D=d; H=d; t=d; A=d and fd2

=l is pri-marily to change the Reynolds number. Therefore, these fivenon-dimensional parameters can be replaced by a single parameter– the Reynolds number, and Eq. (9) reduces to:

hdk¼ f

qvdl ;

lCp

k;Ld;Rd;zd

� �: ð12Þ

The present problem is therefore governed by the followingnon-dimensional groups:

Nu ¼ f Re; Pr;Ld;Rd;zd

� �ð13Þ

where z=d is the non-dimensional axial distance, L=d contains theenclosure effect, while R=d is due to the fact that the average heattransfer coefficient is being measured. The heat transfer coefficientis a strong function of radial position (at least in continuous jet; seefor example Katti and Prabhu [10]) and therefore the value of aver-age heat transfer coefficient will depend upon the size of the heatedblock employed in the experiments. Note that R=d will not be aparameter if local h is being measured. For a continuous axisym-metric jet, some enclosure effect is expected. Due to the presenceof a plate to cover the cavity, the enclosure effect is always presentin the case of a synthetic jet.

The set of non-dimensional parameters (Eq. (13)) are thereforethe same for both synthetic and continuous jets. The primary diffi-culty with synthetic jet is in the calculation of Reynolds number,which is rather straight forward with continuous jet.

6. Non-dimensional results

The following section discusses the variation of average Nusseltnumber with respect to the various non-dimensional governingparameters. The dependence of Nusselt number on Reynolds num-ber, and a direct comparison of synthetic and continuous jets isalso provided towards the end of this section.

6.1. Effect of Reynolds number

The variation of average Nusselt number with the normalizedaxial distance for different Reynolds number is shown in Fig. 9.Note that these results are for L=d ¼ 13:75; R=d ¼ 2:5 andPr ¼ 0:7. It is observed that the average Nusselt number rapidly in-creases upto z=d � 6, and then gradually decreases with an in-crease in z=d. Also it is observed that the average Nusselt numberincreases with an increase in Reynolds numbers for any given

z/d

Nu av

g

0 5 10 15 20 250

20

40

60Re = 1150Re = 2280Re = 3250Re = 3580Re = 4180

Fig. 9. Variation of average Nusselt number with the normalized axial distance fordifferent Reynolds number (L=d ¼ 13:75 and R=d ¼ 2:5).


z=d, as expected. The maximum Nusselt number is at the samelocation (z=d = 6) for all Reynolds numbers. The maximum valueof average Nusselt number is 44 at a Reynolds number of 4180.

The variation of maximum Nusselt number Numax with differentReynolds numbers plotted on a log-log scale gives the slope of theline-of-best-fit as 1.25 (not shown). This suggests that the Nusseltnumber increases rapidly with an increase in Reynolds number.For comparison, the corresponding slope for continuous jet isabout 0.5. However, this result is for a specific value of L=d andR=d; a subsequent result will show that the slope is dependenton the value of both the other two parameters.

6.2. Effect of enclosure ðL=dÞ

Fig. 10 shows the effect of L=d on the average Nusselt numberfor different z=d. These results are for Re ¼ 3700 and R=d ¼ 1:5.The location of Numax is at z=d ¼ 2. It is noticed that there is sub-

z/d

Nu

avg

0 3 6 9 12 150

10

20

30

40

50

60

L/d = 7.86L/d = 13.75

Fig. 10. Variation of average Nusselt number with the normalized axial distance fordifferent L=dðR=d ¼ 1:5, Re = 3710).

stantial (108%) increase in maximum Nusselt number with a de-crease in L=d from 7.86 to 13.75. This difference suggests astrong enclosure effect on the heat transfer ability of synthetic jets.The confinement effect reduces with an increase in the axialdistance.

The recirculation of the fluid between orifice plate and the cop-per plate causes a significant reduction in the heat transfer coeffi-cient. The amount of air being recirculated changes with the lengthof the orifice plate. For a larger length more air gets recirculated ascompared to the case with smaller length orifice. This implies ahigher average temperature of air near the heated plate in the for-mer case, and leads to a reduction in the amount of heat transfercoefficient.

6.3. Effect of the heater size ðR=dÞ

Fig. 11 shows the variation of average Nusselt number with nor-malized half length of copper block. These findings are for the sameL=d and approximately the same Reynolds number. It is noticedthat the average Nusselt number increases with an increase inR=d, over all normalized axial distances. The increase in averageNusselt number with R=d is due to the effective utilization ofimpinging jet for heat removal. The location ððz=dÞmaxÞ for maxi-mum value of average Nusselt number increases with an increasein R=d. It is observed that there is a monotonic increase in the aver-age Nusselt number with respect to R=d and z=d. The maximum va-lue of average Nusselt number is found to be 40 and 23 for R=d of2.5 and 1.5 respectively.

6.4. Dependency on Reynolds number

As mentioned earlier, the average Nusselt number is a functionof Re, z=d; L=d and R=d besides Pr. Several correlations for Nusseltnumber with continuous axisymmetric jet impinging on a flat sur-face are available in the literature [10,24–26]. These correlationsexpress the Nusselt number as a function of Rea, where the expo-nent a is in the range of 0.45–0.8. We look for a similar variationof Nusselt number as a function of Reynolds number in the presentwork with axisymmetric synthetic jet.

z/d

Nu av

g

0 5 10 15 20 25 300

5

10

15

20

25

30

35

40

45

R/d = 2.5, Re = 3580R/d = 1.5, Re = 3710

Fig. 11. Variation of average Nusselt number with the normalized axial distanceðL=d ¼ 13:75Þ.

z/d

Nu av

g

0 5 10 15 20 25 300

10

20

30

40

50

Continuous Jet Re = 4000Synthetic Jet Re = 4180

(a)

Fig. 12. Variation of average Nusselt number with the normalized axial distance forsynthetic jet and continuous jet under the same set of boundary conditions(L=d ¼ 13:75 and R=d ¼ 2:5).


In the present work, the exponent of Reynolds number is foundto be 1.25 for the Reynolds number range of 1550–4180 and forL=d ¼ 13:75; R=d ¼ 2:5 as already noted. The data for Nuavg=Re1:25

when plotted for different Reynolds numbers collapse on to a sin-gle curve, with a maximum scatter of ±3% around the mean value,for this particular value of a. The value of the exponent for otherconfigurations is similarly determined from the available data;the value for a for other L=d and R=d cases are given in Table 3. Itis seen that, for the higher L=d and R=d the value of exponent a ishigh as compared to the lower values of L=d and R=d. Note a largervalue of the exponent for synthetic jet as compared to continuousjet.

6.5. Comparison with continuous jet

A direct comparison between the continuous axisymmetric jetand the synthetic jet for the same set of conditions has also beenperformed. It is observed from Fig. 12 that the continuous jet givesa higher value of Nusselt number at small spacings ðz=d 6 4Þ. How-ever, both the jets give comparable performance at larger spacingsðz=d P 5Þ. The maximum Nusselt number is at about z=d ¼ 4 forthe continuous jet and at z=d ¼ 6 for the synthetic jet. It is also no-ticed that the maximum Nusselt number is about 10% higher forthe continuous jet as compared to synthetic jet, at Re � 4000.

The synthetic jet is at a disadvantage at small spacings due to itsinherent suction and ejection processes. This leads to a recircula-tion of the same fluid; consequently, the fluid temperature is high-er and the ability of the fluid to remove heat from the hot surfacereduces. This is however not the case for continuous jet, wherefresh fluid is continuously supplied.

Whereas a direct comparison with continuous jet has beenmade at only one Reynolds number, our preliminary measure-ments suggest that the continuous jet out-performs the syntheticjet at smaller Reynolds numbers ðRe < 4000Þ. However, due to alarger increment in Nusselt number with an increase in Reynoldsnumber for the case of synthetic jet as seen in Section 6.4, the syn-thetic jet catches up with continuous jet. In fact, the heat transferability of synthetic jet is expected to be better than continuous jetfor large Reynolds numbers ðRe > 4000Þ. Due to limitation of ourexperimental facility, larger Reynolds number could not beachieved and this exciting result could not be confirmed. It isworth emphasizing that Re ¼ 4000 is a special case (crossing point)where the two jets give comparable performance.

7. Velocity and pressure measurements

Some velocity and pressure measurements are also made so asto obtain some idea of the radial variation of these quantities.These measurements also help in a better understanding of syn-thetic jets, and enable further better comparison with continuousjets.

7.1. Velocity measurements

The radial velocities (both mean and fluctuations) on theimpinging surface are measured with a constant temperature

Table 3Exponent of Reynolds number obtained for different configurations and peak value ofnormalized axial distance for Eq. (18).

L=d R=d Value of exponent (a) ðz=dÞmax

7.86 1.5 0.64 313.75 2.5 1.25 622 4 1.4 10

hot-wire anemometry system (TSI, IFA-300). A tungsten–platinumcoated single wire probe (Model 1210-T1.5 with temperature coef-ficient of resistance of 0.0042/�C, diameter of wire ¼ 3:8lm,length of sensing element = 1.27 mm) is used for the measure-ments. The hot-wire probe is mounted on a two-dimensional tra-versing stand. During calibration of hot-wire probe, the referencevelocity was measured with a pitot tube connected to a differentialpressure transducer (Furness Control, FCO332, leastcount = 0.01 mm water, full range = 20 mm water). The measure-ment points are fitted with King’s law curve, with a maximumuncertainty of 3%.

The velocity measurements are done along different radial posi-tions in the jet, at a fixed distance of 2:5 mm ðy=d ¼ 0:312 where yis the coordinate normal to the plate) from the copper block. Thevalues of the other parameters are maintained fixed for theseexperiments are Re = 3300, L=d ¼ 13:75.

7.1.1. Mean velocityFig. 13(a) shows the variation of normalized mean velocity

ðUmean=UoÞ along the normalized radial distance. A substantialchange in velocity distribution is noted with an increase in dis-tance between the jet and plate. At z=d ¼ 1, the velocity is maxi-mum at the centerline and exhibits a secondary peak atr=d ¼ 1:4. The strength of the secondary peak becomes larger thanthe centerline velocity with an increase in z=d. The secondary peakalso shifts to a larger radial location with an increase in z=d. Forz=d > 8, the velocity distribution is rather flat.

In order to make a direct comparison of velocity measurementwith the heat transfer results, spatially averaged velocity is calcu-lated as follows:

Umean; spatially averaged ¼R R

0 2prUmeandrR R0 2pr dr

: ð14Þ

The integration has been performed over the heater block (i.e.,R ¼ 2:5d). The spatially averaged mean velocity as a function ofthe axial distance is shown in Fig. 13(b). The spatially averagedmean velocity is found to increase up to z=d ¼ 6 and then reducesalong the axial distance. Therefore, the spatially averaged meanvelocity is correlated to the heat transfer coefficient (see Fig. 9).

r/d

Um

ean

/Uex

it

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5z/d = 1z/d = 3z/d = 6z/d = 8z/d = 12

(a)

(b)

z/d

(Um

ean)

avg

/Uex

it

0 2 4 6 8 10 12 140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Fig. 13. (a) Variation of normalized mean velocity with normalized radial distance(L=d ¼ 13:75, Re = 3300) and (b) variation of spatially averaged mean velocity withnormalized axial distance.

r/d

Urm

s/U

exit

(%)

0 0.5 1 1.5 2 2.5 30

20

40

60

80

100

z/d = 1z/d = 2z/d = 3z/d = 4z/d = 6z/d = 8z/d = 12

(a)

(b)

z/d

(Urm

s)av

g/U

exit

0 2 4 6 8 10 12 140

0.1

0.2

0.3

0.4

0.5

Fig. 14. (a) Variation of normalized rms velocity with normalized radial distance(L=d ¼ 13:75, Re = 3300) and (b) variation of spatially averaged rms velocity withnormalized axial distance.


7.1.2. Rms velocityFig. 14(a) shows the radial distribution of the normalized rms

velocity, for different normalized axial distances between the jetand plate. The normalization has been done by the mean velocityat the centerline of the orifice. Note that the normalized rms valuesare rather large and that these values reduce with an increase inthe axial distance. In contrast to the mean velocity, the rms veloc-ity distribution may exhibit two off-axis peaks. The two peaks areobserved for z=d 6 6; both these peaks shift away from the center-line with an increase in the axial distance. Beyond this distance, thenormalized rms is nearly constant (with a value of approximately30% and 20% for z=d ¼ 8 and 12, respectively). The present mea-surements show a maximum level of turbulence of 84% atz=d ¼ 1 and r=d ¼ 0:2, which is significantly higher as comparedto continuous jet (for example, 17.8 % at r=d ¼ 2 and z=d ¼ 0:1[24]).

The radially averaged normalized rms velocity has been calcu-lated in an analogous manner to Eq. (14). This quantity has been

plotted as a function of the axial distance in Fig. 14(b). It is ob-served that the spatially averaged rms increases up to z=d ¼ 4and then decreases along the axial distance. The maximum valueof spatially averaged rms is found to be 2.23 at z=d ¼ 4. The spa-tially averaged root mean square velocity therefore appears to bepoorly correlated to the average heat transfer coefficient in Fig. 9.

7.2. Pressure measurements

The radial pressure distribution on the impinging surface ismeasured for different z=d and Reynolds numbers, as shown inFig. 15. The measurements are accomplished by drilling a smallhole (1 mm) into the impingement surface and measuring thepressure with a digital pressure transducer (Furness Control,FCO332, least count = 0.01 mm water, full range = 20 mm water).The pressure difference ðDPÞ reported here represents the differ-ence between the pressure at the impingement surface with re-spect to the atmospheric pressure. This gauge pressure is

r/d

ΔP

/((1

/2)ρ

Uo2)

0 1 2 3 4 5-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

z/d =0.125z/d =0.25z/d =0.5z/d =0.75

r/d

ΔP

/((1

/2)ρ

Uo2)

0 0.5 1 1.5 2 2.5 3-0.5

0

0.5

1

1.5

2

2.5

z/d =0.07z/d =0.14z/d =0.21

(a)

(b)

Fig. 15. Variation of pressure coefficient with the normalized radial distance forapproximately same Reynolds number but different size of enclosure ((a)L=d ¼ 13:75, Re = 4180 and (b) L=d ¼ 7:86 Re = 4100).


normalized with the dynamic pressure qU2o=2, where q is the den-

sity of air and Uo is the jet exit velocity at the centerline of theorifice.

It is observed that the pressure coefficient decreases almostmonotonically with an increase in r=d (Fig. 15). The maximum va-lue of pressure coefficient is 2.15 at z=d ¼ 0:07 and close to the jetcenterline (Fig. 15(b)). Also, it is noticed that at lower z=d and forr=d approximately between 1.25 and 3, the pressure is slightlysub-atmospheric. (Such sub-atmospheric pressures have also beenreported by some researchers with respect to continuous jets; seeexample Colucci and Viskanta [9].) The value at jet centerline de-creases monotonically with an increase in the normalized axial dis-tance ðz=dÞ. Note that the gauge pressure drops rapidly with axialdistance making measurements difficult at large distances; there-fore measurements are confined to relatively small distances fromthe orifice exit.

The effect of enclosure on the pressure distribution is also mea-sured. For this, the Reynolds number is maintained constant at

approximately 4100 while L=d is reduced from 13.75 (Fig. 15(a))to 7.86 (Fig. 15(b)). With the 43% decrease in L=d, the value at cen-ter increases by 23%. Also the magnitude and radial extent of subatmospheric pressure increases with an increase in the enclosuresize. These results further underscore the benefit in employing asmaller size orifice plate, to reduce the effect of enclosure.

8. Discussion

The Reynolds number of the impinging synthetic jet changeswith change in excitation frequency, orifice diameter, cavity depth,thickness of the orifice plate, diameter of actuator, and amplitudeof excitation. The Nusselt number is further affected by the lengthof the orifice plate, besides properties of the fluid. Both orificediameter and orifice thickness play a significant role in affectingthe heat transfer from the heated surface.

Our results suggest that there is an optimum orifice diameterfor heat transfer enhancement. The distance corresponding to themaximum heat transfer coefficient also changes with the orificediameter. A reduction in thickness of the orifice plate decreasesfrictional resistance to the flow of jet; therefore, the flow velocityand heat transfer coefficient increase. Unlike orifice diameter, theheat transfer coefficient changes monotonically with the thicknessof the orifice plate. The cavity depth, however, has a negligible ef-fect on the heat transfer coefficient. This is because the averageflow velocity remains approximately the same for different cavitydepths [22].

These results suggest that for optimal performance, the orificediameter needs to be carefully chosen, minimum possible orificeplate thickness should be chosen, while the cavity depth can bechosen as per the constraint of available space. The entire assemblyshould be excited at the resonance frequency, preferably the dia-phragm frequency, at the maximum amplitude possible. UnlikeHelmoltz frequency, the diaphragm frequency is invariant of thegeometric parameters of the cavity [21]. Furthermore, at least inthe present study, the velocity corresponding to the diaphragm fre-quency is larger than that at the Helmoltz frequency, thereby mak-ing it the obvious choice.

The length of the orifice plate affects the heat transfer coeffi-cient due to the confinement effects. An increase in the length ofthe orifice plate increases the amount of recirculation of the fluidnear the heated plate, thereby reducing the heat transfer coeffi-cient at small axial distances. It is noted that the confinement ef-fect is much stronger with synthetic jet as compared tocontinuous jet, owing to the inherent suction and ejection pro-cesses in the former jet. This is clearly evident by a poor perfor-mance of synthetic jet with respect to continuous jet at smallspacings, and comparable performance at larger spacings.

From the results it is noticed that the average heat transfer coef-ficient are high for synthetic jet and are comparable to continuousjet. However, the Nusselt number increases by a larger amountwith change in Reynolds number for synthetic jets as comparedto continuous jet. Therefore, synthetic jets are expected to performbetter than the latter at high Reynolds numbers. The axial and ra-dial variation of various quantities measured here are qualitativelysimilar to those reported with respect to continuous jet in the lit-erature. The radial variation in heat transfer coefficient and thereason for it (in the context of continuous jet) is as follows [27]:In the region near the stagnation point, there is a rapid decreasein axial velocity and a corresponding rise in static pressure. Dueto the shear between the wall jet and the ambient air, fluctuationsare created which lead to an increase in the heat transfer coeffi-cient. However, as the axial distance between the jet and plate in-creases, due to entrainment of the ambient fluid into the jet, theimpinging velocity decreases leading to a reduction in the radial

Nuexp

Nu c

0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

80

+20%

-20%

45o


velocity; the spreading of the jet further reduces the radial velocity.This reduces the heat transfer coefficient with an increase in theaxial distance for all configurations. The above agreement is ex-pected to apply with respect to synthetic jet also, as indicated bythe radial distribution of velocity in Figs. 13 and 14.

Two local maxima have been observed close to the stagnationpoint in the radial variation of turbulence intensity close to theplate. The first maximum is probably due to induced velocity bythe vortex shedding from the orifice plate. The other one is dueto transition of the boundary layer from laminar to turbulent[10]. The peaks are shifting slightly away from the center withan increase in z=d, which is due to the spreading of jet along theaxial distance. The maximum value with the synthetic at the stag-nation is at lower axial distance ðz=d ¼ 1Þ which is in contrast withthe continuous jet at z=d ¼ 6 [9] which may be due to suction andejection process in synthetic jet. Also it is noticed that for the con-tinuous jet the second peak disappears at low Reynolds number,which is not the case with synthetic jet. The axial variation in areaaveraged mean velocities seems to be correlated to the averageheat transfer coefficient, but the velocity rms is poorly correlatedto the average heat transfer coefficient.

Fig. 16. Nuexp vs Nuc at higher z=d (z=d greater than approximately 3).

8.1. Correlation for synthetic jet

Correlations are developed from the experimental data usingmultiple regression analysis, for different cases. The followingequation can describe the variation in average Nusselt number asa function of both Re and z=d (for L=d ¼ 7:86 and R=d ¼ 1:5)

Nuavg ¼ 0:12ðReÞ0:64 10:073 z

d

� �� 1

1�0:75 zdð Þ

2

264

375 ð15Þ

Similarly, we have

Nuavg ¼ 0:00011ðReÞ1:25 10:0084 z

d

� �� 1

1�0:75 zdð Þ

2

264

375 ð16Þ

for L=d ¼ 13:75 and R=d ¼ 2:5, and

Nuavg ¼ 0:00003ðReÞ1:4 10:0055 z

d

� �� 1

1�0:36 zdð Þ

2

264

375 ð17Þ

for L=d ¼ 22 and R=d ¼ 4. The values obtained from the above cor-relation fit the experimental data within ± 15%.

An attempt to obtain a single correlation is also made, and thefollowing correlation is proposed based on 86 data points:

Nuavg

Pr0:333 ¼ 7:624ðReÞ0:792 Ld

� ��2:186 Rd

� �2:258 zd

� ��0:632ð18Þ

The above correlation is valid for the following range of parameters:L/d = 7.86–22, R/d = 1.5–4, and Re = 1150–4180. Also, the above cor-relation is valid only in the region where Nu reduces with an in-crease in z=d (i.e. at higher axial distances, i.e. z=d greater thanapproximately 3; see also Table 3). The above correlation incorpo-rates all non-dimensional parameters given in Eq. (12). As expectedthe correlation suggests a reduction in Nu with an increase in L=dand an increase in Nu with an increase in R=d. Note that Prandtlnumber has not been varied and the same exponent of Pr as in con-tinuous jet has been employed here. The estimated values compareto the experimental values within ± 20%, with 90% of the data pointslying between this range (Fig. 16).

9. Conclusion

The average heat transfer coefficient as a function of variousgeometric parameters has been measured and presented in thiswork. An experimental setup has been carefully designed, fabri-cated and validated towards this end. It is noticed that the averageheat transfer coefficient is affected by the orifice diameter, and in-creases with a decrease in the thickness of the orifice plate. Thecavity depth has a negligibly small effect on the average heat trans-fer coefficient. The maximum average heat transfer coefficient oc-curs at the resonance frequency of the cavity. The heat transfer firstincreases and then decreases with an increase in axial distance.The location of the maximum heat transfer coefficient dependson the above geometric parameters.

Both dimensional and non-dimensional results are presentedhere. It is noticed that the Nusselt number is a function of fivenon-dimensional numbers ðRe; Pr; z=d; L=d; R=dÞ. The averageNusselt number increases with Reynolds number and the halflength of heated copper plate to diameter ðR=dÞ, but decreases withthe length of orifice plate to orifice diameter ðL=dÞ. A strong effectof enclosure is noted; the average Nusselt number increases by108% with decreasing the L=d by 42%. It is observed that the peakof the average Nusselt number shifts towards lower z=d for the de-crease in R=d. The average Nusselt number is correlated into a sim-ple equation using the experimental data for the different casesand also a general correlation has been given for decreasing valuesof Nusselt number. The average Nusselt number is a function of the0.792 power of the Re. The radial pressure distribution has beenpresented for different z=d and Re. The pressure coefficient is foundto be higher at the lower r=d. The mean velocities are found to bewell correlated with the heat transfer coefficient. The synthetic jetperformance is found to be comparable with the continuous axi-symmetric jet at low Reynolds number (upto 4000) for the sameboundary conditions and expected to be better at high Reynoldsnumber. These results are significant in the point of view of coolingof electronic devices.

Acknowledgements

We are grateful to Professor S.V. Prabhu for help throughout thecourse of this work. The first author is thankful to Vishwakarma


Institute of Technology, Pune for sponsoring him during the courseof this work. This project is funded by the Department of Informa-tion Technology, New Delhi.

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heat transfer characteristics of synthetic jet impingement cooling

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