Heat transfer characteristics of synthetic jet impingement cooling

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

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

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 2008 Received in revised form 23 April 2009 Accepted 18 June 2009 Available online 28 November 2009 Keywords: Synthetic jets Impingement heat transfer Hot-wire anemometry Cavity response

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 useful for cooling applications. The impingement heat transfer characteristics of a synthetic jet are studied in this work. Toward that end, the behavior of the average heat transfer coefficient of the impinged heated surface with variation in the axial distance between the jet and the heated surface is measured. In addition, radial distribution of mean and rms velocity and static pressure are also measured. The experiments are 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 in the range of 0–25, and the length of the orifice plate to the orifice diameter varies between 8 and 22 in this study. The maximum heat transfer coefficient with the synthetic jet is found to be upto 11 times more than the heat transfer coefficient for natural convection. The behavior of average Nusselt number is found to be similar to that obtained for a continuous jet. The exponent of maximum Nusselt number with Re varies between 0.6 and 1.4 in the present experiments, depending on the size of the enclosure. A direct comparison with a continuous jet is also made and their performances are found to be comparable under similar set of conditions. Such detailed heat transfer results with a synthetic jet have not been reported earlier and are expected to be useful for cooling of electronics and other devices. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction In the fast growing technology, due to faster operation of each transistor and an increase in their density on integrated circuits, a large amount of heat needs to be dissipated. Thermal overstressing is one of the major causes of failure of electronic components. This underscores the requirement for proper thermal management which is perhaps the most crucial part of the electronic system design. Effective cooling systems are therefore required which also meet the space and other design constraints. Heat sinks with air as the working fluid, and different fin geometry and fan arrays have been traditionally used for heat removal from electronic systems. However, these traditional forced air cooled heat sinks are facing serious challenges for the cooling of the next generation of electronics owing to the additional space constraints and still higher cooling requirements. Due to low cost, availability and reliability, air will continue to be used as the working fluid. In the present work, synthetic jet impingement cooling which can potentially be used for cooling of hot-spots is investigated. A synthetic jet is synthesized directly from the fluid in the system in which it is embedded. A synthetic jet is commonly formed when the fluid is alternately sucked into and ejected from a small cavity by the motion of a diaphragm bounding the cavity, so that * Corresponding author. Tel.: +91 02225767516; fax: +91 02225726875. E-mail address: [email protected] (A. Agrawal). 0017-9310/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2009.11.005

there is no net mass addition to the system [1]. This feature obviates the need for input piping or complex fluidic packaging and makes synthetic jets ideally suited for low-cost batch fabrication using micro-machining techniques. The synthetic jet is a new entrant into the means available to engineers to manipulate flow to achieve the desired result. Besides cooling, the synthetic jets have a number of other potential engineering applications, such as boundary-layer separation control, jet vectoring, better mixing of fuel in the engine combustion chamber, creation of local turbulence, and vehicle propulsion [2–7]. A brief discussion on cooling with impinging continuous, pulsed and synthetic jet is presented next. San and Shiao [8] studied the heat transfer characteristics of a confined continuous circular air jet impinging on a flat plate for different Reynolds numbers, plate spacing, jet plate width and length. The stagnation Nusselt number was found to be proportional to the 0.638 power of the Reynolds number, and inversely proportional to the 0.3 power of the plate spacing to jet diameter ratio. The stagnation Nusselt number was also found to vary as exp½0:044ðW=dÞ  0:011ðL=dÞ, where W and L are the width and length of the plate respectively. Colucci and Viskanta [9] performed experiments using thermochromatic liquid crystal technique and discussed the effects of nozzle geometries on the local heat transfer coefficient for confined impinging air jet. Katti and Prabhu [10] studied the local heat transfer characteristics of a circular straight pipe nozzle jet impinging on a flat plate, using infrared thermal imaging technique. The experiments

1058

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

Nomenclature A Cp d f h H I k l L Lo Nu P Pr qconv qjoule qloss r R Re t Ts

area ðm2 Þ, amplitude of vibration (m) specific heat (J/kg K) orifice diameter (m) excitation frequency (Hz) average heat transfer coefficient ðW=m2 KÞ cavity depth (m) current (A) thermal conductivity (W/m K) length of copper block (m) length of orifice plate (m) stroke length (m) average Nusselt number ðhd=kÞ (–) pressure ðN=m2 Þ Prandtl number ðlC p =kÞ (–) net heat flux convected to the impinging jet ðW=m2 Þ imposed ohmic heat flux (VI/A) ðW=m2 Þ total heat loss ðW=m2 Þ radial distance (m) half length of heated copper plate (m) Reynolds number ðqv d=lÞ (–) length of the orifice (m) surface temperature (°C)

were conducted for jet to plate spacing of 0.5 and 8 times the nozzle diameter, in the Reynolds number range of 12,000–28,000. The following three regions are identified on the impingement surface based on the flow characteristics of the impinging jet: stagnation region ð0 6 r=d 6 1:0Þ, transition region ð1:0 6 r=d 6 2:5Þ and wall jet region ðr=d P 2:5Þ. They also proposed a semi-empirical correlation for the local heat transfer coefficient in the wall jet region, based on the assumption of flow over a constant heat flux flat plate. Gulati et al. [11] studied the effect of different shapes of nozzle for an equivalent diameter of 20 mm on the local heat transfer distribution on a flat surface, using infrared thermal imaging technique. Both local and average Nusselt numbers on the impinged surface are presented, for Reynolds number between 5000 and 15,000 and jet-to-plate spacing from 0.5 to 12 nozzle diameters. Kataoka et al. [12] have explored the mechanism for the enhancement of stagnation point heat transfer using a pulsed jet. The large-scale turbulent structures of an impinging round jet were analyzed by employing conditional sampling. It was found that the large-scale eddies impinging on the heat transfer surfaces produce a turbulent surface renewal effect which enhances the heat transfer from the impinging surface. Eibeck et al. [13] describe a technique for convective heat transfer enhancement which involves the use of a pulse combustor to generate a transient jet that impinges on a flat plate. Enhancement upto 2.5 times the steady impinging jet value has been reported. Zumbrunnen and Aziz [14] also show heat transfer enhancement by a factor of 2 with pulsed water jet. Sailor et al. [15] in the heat transfer enhancement study 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 to plate spacing and pulse frequency. The maximum heat transfer enhancement occurs for the highest flow rates, which corresponds to 65% enhancement over a steady jet. Hwang and Cho [16] used two different acoustic excitation methods (jet excitation and shear layer excitation) on an impinging jet for studying the ensuing heat transfer. The excitation frequency and the excitation level are found to be important factors for heat transfer enhancements. Compared to continuous and pulsed jets, fewer studies on impinging synthetic jet have been performed. Pavlova and Amitay

ambient temperature (°C) T inf uðtÞ instantaneous velocity (m/s) mean velocity (m/s) U mean average centerline orifice velocity (m/s) Uo 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 symbols dynamic viscosity of jet fluid (kg/m s) kinematic viscosity of jet fluid ðm2 =sÞ density of fluid ðkg=m3 Þ time (s)

l m q s

Subscripts avg average max maximum rms root mean square

[17] experimentally investigated the efficiency and mechanism of cooling a constant heat flux surface, and compared the performance of synthetic jet against that of a continuous jet. In their measurements, high frequency (1200 Hz) jets are found more effective at smaller axial distances and low frequency (420 Hz) jets are found more effective at larger axial distances. Also, it was found that synthetic jet cools the heated surface better than the continuous jet at the same Reynolds numbers. Garg et al. [18] have designed a meso-scale synthetic jet from a 0.85 mm hydraulic diameter rectangular orifice and a maximum velocity of 90 m/s. Microscopic infrared thermal imaging technique was used for temperature measurements on a foil heater. A maximum heat transfer enhancement of approximately 10 times the natural convection was measured for V rms ¼ 90 V. Mahalingam and Glezer [7] have discussed the design and thermal performance of synthetic airjet based heat sink for high power dissipation electronics. Approximately 40% more heat dissipation occurred with the synthetic jet based heat sinks as compared to the configuration of steady flow from a ducted fan blowing air through the heat sink. The average heat transfer coefficient in the channel flow between the fins was 2.5 times that for steady flow in the duct at the same Reynolds number. From the literature it is noticed that there are relatively few studies on impingement cooling involving synthetic jet. In particular, the heat transfer measurements by systematically varying parameters such as orifice diameter, length of orifice plate, cavity depth and excitation frequency have not been reported. The depth and diameter of the cavity along with the orifice length and diameter are the geometric parameters, while frequency and amplitude of actuation are the control parameters pertinent in the study of heat transfer enhancement with synthetic jet. In this work, we have measured the average heat transfer coefficient by varying the different geometric and flow parameters as a function of the axial distance between the synthetic jet and a heated copper block, while the effect of varying the orifice shape has been studied by Chaudhari et al. [19]. Dimensional analysis is performed to identify the governing non-dimensional parameters. The effect of these non-dimensional parameters on the Nusselt number is investigated in the present work. A correlation of Reynolds number

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

dependency on Nusselt number is given for different configurations from the measured data. Also, velocity and pressure results are discussed, and the performance of the synthetic jet is compared with that of a continuous jet for the same set of boundary conditions and Reynolds number. 2. Experimental set-up and measurement procedure Fig. 1 shows the schematic of the set-up used for the present experiments. The experiments are conducted for different configurations of synthetic jet impinging on a heated surface. The synthetic jet assembly is attached to a 2-d traverse stand so that the axial distance between the jet orifice and the heated surface can be controlled easily using a fine pitch traversing mechanism. The heater block is constructed from a copper plate, and has final dimensions 40  40  5 mm3 . The block is heated by a nichrome

foil heater of the same size attached underneath of the block. The heater is supported by a bakelite plate to provide proper thermal contact between the heater and the copper block. The copper block is insulated by glass-wool (size 180  180  40 mm3 ) to minimize the heat loss through the sides and bottom. The heater surface provides a constant heat flux, as the driving power input is constant, and the flexible heater is specifically designed to provide a constant heat flux output. The surface temperature is measured with two pre-calibrated K-type thermocouples, which are placed at two sides of the copper block 4 mm from the lateral surface, thus providing a spatially averaged temperature over the exposed surface of the copper block. An identical thermocouple is used away from the heated surface for ambient air temperature measurement. The power supplied to the heater is measured with a multi-meter and is controlled by a rheostat. A synthetic jet is synthesized at the edge of an orifice by a periodic

(a)

Speaker with cavity

2-d Traverse Stand

Copper Plate

Heater

Perpex Bakellite Glass-wool

(b)

L D

d

t

1059

z

R

Fig. 1. (a) Schematic of heat transfer experimental set-up and (b) dimensional parameters relevant for the study.

1060

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

motion of a diaphragm mounted on one side of a sealed cavity. Air is the working fluid in the present experiments. From the literature it is noticed that a number of researchers use a piezo-actuated membrane as the oscillating diaphragm for the creation of a synthetic jet. A piezoelectric actuator requires relatively high voltage ðV rms  90 VÞ as compared to that required for an electromagnetic actuator. Furthermore, a piezo-actuator operates at certain discrete input frequencies. For these reasons, piezo-actuators have not been used here. In the present study, an electromagnetic actuator (acoustic speaker) of diameter 50 mm and operating at an input voltage ðV rms Þ of 4 V is employed. The experiments are conducted for different orifice diameters, length of orifices, and cavity depths (see Table 1). The input voltage to the actuator is maintained constant and the frequency of excitation is controlled by a signal generator and monitored by an oscilloscope (Tektronix, TDS 2022B). The jet issuing from the orifice impinges normally onto the plate at a distance of z from the orifice (Fig. 1(b)). The distance between the orifice surface and the copper plate is varied with the help of a traverse stand. The effects of the synthetic jet impingement cooling are investigated by measuring the surface and ambient temperatures for different operating frequencies and other geometric parameters for a known power supplied to the heater. The results are presented in terms of the average Nusselt number as a function of normalized axial distance z=d. The heat loss is calculated by supplying different input powers to the heater, and measuring the surface temperature of the heated copper block along with the ambient temperature, while insulating the top surface of the heated block. The losses are taken in to account for calculation of heat transfer coefficient as per Eq. 6. The losses from the sides and the bottom of the test section are found to be typically 22% of the input power. Due to low temperatures involved in this experiments, the heat loss from the surface due to radiation transfer is neglected, as it is calculated to be less than 1% of the power input. The temperature difference between the copper surface and the ambient is maintained above 15 °C for all the experimental results. 3. Data reduction The Reynolds number is calculated using the procedure given by Smith and Glezer [1]

Re ¼

U0 d

ð1Þ

m

where d is the orifice diameter, m is the kinematic viscosity, and U o is the average orifice velocity during the ejection part of the cycle at the exit and centerline of the orifice. This last parameter is calculated as

U o ¼ Lo f

ð2Þ

where f is the excitation frequency (or inverse of time period s) and Lo is the stroke length calculated over the ejection part of the total cycle as

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

Value

Dimension

d t L R H Re

5, 8, 14 1.6, 2.4, 5 110, 192.5 20 6.3, 8.7 1150–4180

mm mm mm mm mm –

Lo ¼

Z s=2

uðtÞ dt:

ð3Þ

0

The average velocity is between 3.1 and 8.5 m/s and the maximum instantaneous velocity ranges between 10 and 25 m/s for the present 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 for the heated block is as follows:

Nuavg ¼

havg d ; k

ð4Þ

where

havg ¼

qconv ; ðT s  T inf Þ

ð5Þ

ðT s  T inf Þ is the temperature difference between the surface ðT s Þ and the ambient ðT inf Þ, and qconv is the net heat flux supplied. The net heat flux is the difference in the supplied heat flux ðqjoule Þ and heat lost ðqloss Þ, i.e.,

qconv ¼ qjoule  qloss

ð6Þ

where

qjoule ¼

VI A

ð7Þ

As already noted, the heat loss is estimated as approximately 22% of the heat supplied. The uncertainty in measurement of the average Nusselt number is approximately 7.5%. See Table 2 for uncertainty in the other parameters. 4. Heat transfer with synthetic jet impingement This section presents the results of an impinging synthetic jet issuing from a circular orifice on to a heated copper block. The variation in the heat transfer coefficient as a function of axial distance, for a large range of parameters is presented in this section. The validation of the setup and repeatability of the results are also presented 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 continuous axisymmetric jet under an otherwise identical set of conditions. Lytle and Webb [20] have presented local heat transfer data for different nozzle to plate spacings ðz=dÞ and different Reynolds numbers for a continuous axisymmetric unconfined jet. The present experimental set-up is validated by comparing for the average Nu obtained upon suitable integration. The comparison in Fig. 2 is for a Reynolds number of 12,000 at three nozzle to plate

Table 2 Maximum uncertainty in measurements of different parameters. Parameter

Error in measurement

L d, t R, H z DT V I Uo havg Nuavg

1 mm 0.25 mm 0.5 mm 0.5 mm 0.5 °C 0.001 V 0.01 A ±3% 4% 7.5%

1061

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

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

110

Present results Lytle and Webb 100

Nuavg

90

80

70

60 2

4

6

8

10

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

spacings. The difference between the two sets of measurements is within ±3%, which is well within the uncertainty of the measurements. The synthetic jet assembly has been benchmarked in our earlier work [21,22]. There the centerline velocity decay of the synthetic jet has been compared against experimental results in the literature and the similarity analysis of Agrawal and Verma [23]. The repeatability of the results has been systematically checked and is found to be within ±1.7% as shown in Fig. 3. Therefore, the entire setup can be considered to have been validated and the results to be repeatable. 4.2. Effect of various parameters (dimensional results) The effect of various parameters on the overall heat transfer coefficient is discussed in this section. The experiments are done with the aim of identifying the important parameters which affect the transfer of heat from a hot surface. The non-dimensional re-

4.2.1. Variation of havg with diaphragm frequency Fig. 4 shows the behavior of the average heat transfer coefficient with the axial distance between the orifice plate and heated copper block. These experiments have been conducted for different excitation frequencies (100–350 Hz) by keeping the same orifice plate dimensions and cavity depth. It is observed that the average heat transfer coefficient (h) increases rapidly upto some axial distance ðzmax ¼ 48—50 mmÞ and then decreases gradually with an increase in the axial distance, for all frequencies. Also, it is observed that the average heat transfer coefficient increases with an increase in frequency upto 250 Hz, beyond which it reduces. The heat transfer coefficient is found to be maximum at the resonance frequency of the cavity (250 Hz) [21,22]. The maximum value of heat transfer coefficient is found to be 143 W=m2 K at 250 Hz, which is larger than most known values of heat transfer coefficient with synthetic jet. For comparison, Pavlova and Amitay [17] found hmax ¼ 26:7 ; W=m2 K at the first resonance frequency (420 Hz), hmax in the channels measured by Mahalingam and Glezer [7] is 60 W=m2 K for frequency around 200 Hz, while Garg et al. [18] give hmax of 236 W=m2 K at high heat flux for frequency around 4400 Hz. This shows the potential of using synthetic jet for high heat removal; in particular, as demonstrated below, synthetic jet seems to be very competitive with respect to continuous jet for cooling applications.

4.2.2. Variation of havg with orifice diameter Fig. 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 been observed for the average heat transfer coefficient along the axial distance, i.e., h increases till a certain distance and decreases beyond it. The other observations are:

160

60

50

100 Hz 150 Hz 200 Hz 250 Hz 350 Hz

140

First set Second set

120

havg (W/m2K)

Nu

40

30

100 80 60

20 40 20

10

0 0

0

5

10

15

20

25

30

0

50

100

150

200

250

300

z (mm)

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

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

1062

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

160

4.2.3. Variation of havg with cavity depth Fig. 6 shows the variation of average heat transfer coefficient with axial distance, for different cavity depths (6.3 mm and 8.7 mm) and keeping the value of all other parameters the same. It is noticed that the cavity depth does not have a significant effect on the average heat transfer coefficient. As presented in our earlier work [22], the exit velocity remains approximately the same over a sufficiently large range of cavity depths. Those results are therefore consistent with the present observation of a negligibly small effect of cavity depth on the average heat transfer coefficient. Because of availability of the earlier results, the present set of experiments are conducted for only two values of cavity depths.

14 mm 8 mm 5 mm

140

100

2

havg (W/m K)

120

80 60 40 20 0 0

50

100

150

200

250

300

z (mm) Fig. 5. Variation of average heat transfer coefficient with axial distance for different orifice diameters, and for the same excitation frequency, length of orifice and length of 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 is 143 W=m2 K for 8 mm orifice diameter at an axial distance of 48 mm. 2. The location and the maximum value of average heat transfer coefficient changes with the orifice diameter. For example, the location of hmax is zmax ¼ 60; 50 and 30 mm for 5, 8 and 14 mm orifice diameter, respectively. 3. The location of hmax varies monotonically with the orifice diameter, but not the value of hmax . The maximum value and the variation of average heat transfer coefficient for different orifice diameters depend on the flow velocity and size of the enclosure. These effects will be discussed further in a later section.

4.2.4. Variation of havg with thickness of orifice plate Fig. 7 shows the variation of average heat transfer coefficient with axial distance between orifice plate and copper block, for different thickness of orifice plates (1.6 mm, 2.4 mm, 5 mm) while keeping the value of all other parameters the same. The thickness of the orifice plate strongly affects the average heat transfer coefficient along the axial distance; the average heat transfer coefficient increases with a decrease in thickness of the orifice plate. The maximum value of heat transfer coefficient is found to be 155 W=m2 K at 40 mm axial distance for 1.6 mm thickness of orifice plate. However, the average heat transfer coefficients drops precipitously for distances smaller than zmax for the 1.6 mm thickness case. Note that the location of the maximum heat transfer coefficient changes somewhat with orifice plate thickness; the location of maxima varies between 30 and 40 mm. 4.2.5. Variation of havg with length of orifice plate Fig. 8 shows the effect of enclosure on the average heat transfer coefficient as a function of axial distance. These experiments are conducted for two different lengths of orifice plate (110 mm and 192.5 mm) by keeping all the other parameters the same. The length of the orifice plate significantly affects the average heat transfer coefficient. The average heat transfer coefficient increases with a decrease in length of the orifice plate. The maximum value of average heat transfer coefficient is found to be 89 W=m2 K at 28 mm of axial distance for 110 mm length of orifice. It is however

160

160

H = 6.3mm H = 8.7mm

1.6 mm thick 2.4 mm thick 5 mm thick

140

120

120

100

100

havg (W/m 2K)

havg (W/m2K)

140

80 60

80 60

40

40

20

20

0

0

0

50

100

150

200

250

300

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

0

40

80

120

160

200

240

280

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

1063

M. Chaudhari et al. / International Journal of Heat and Mass Transfer 53 (2010) 1057–1069 2

100

hd qfd lC p D H t A L R z ; ¼f ; ; ; ; ; ; ; : k l k d d d d d d d

length = 110mm length = 192.5mm

60

40

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:

20

!

2 qv d D H t A qfd : ¼f ; ; ; ; d d d d l l

0

ð9Þ

The absence of Re from the above list is noteworthy, and is due to the absence of velocity in Eq. (8). To incorporate the effect of Reynolds number (dependence of Nu on Re is expected in forced convection problems), the flow velocity v is considered. Now v should depend on the orifice diameter d, the diameter of actuator D, the cavity depth H, the thickness of orifice plate t, the amplitude of vibration A, the excitation frequency f, the density of fluid q, and the dynamic viscosity of fluid l, i.e.,

80

havg (W/m2K)

!

0

60

120

180

240

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

ð11Þ

Note that all five non-dimensional parameters on the right hand side of Eq. (11) are common between Eqs. (9) and (11). In other 2 words, the effect of parameters D=d; H=d; t=d; A=d and fd =l is primarily to change the Reynolds number. Therefore, these five non-dimensional parameters can be replaced by a single parameter – the Reynolds number, and Eq. (9) reduces to:

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

  hd qv d lC p L R z ¼f ; ; ; : ; k l k d d d

4.2.6. Summary of parametric study In the present section, the effects of control parameters such as excitation frequency and geometric parameters such as orifice diameter, length of orifice, orifice plate length, cavity depth on the heat transfer coefficient have been investigated. The amplitude of excitation is kept constant ðinput voltage to speaker ¼ 4V rms Þ for all the above measurements. It is found that the excitation frequency, orifice diameter, length of orifice, and length of orifice plate affect the heat transfer coefficient strongly, whereas the cavity depth has little or no effect. It will be argued in a later section that the excitation frequency, orifice diameter, and length of orifice affect the flow velocity, while the length of orifice plate governs the amount of recirculation. The effect of excitation frequency and orifice diameter on the heat transfer coefficient is non-monotonic, while that of length of orifice and length of orifice plate is monotonic. Therefore choosing the right excitation frequency and orifice diameter for an application becomes crucial. The values of these parameters 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 of parameters and the same qualitative behavior as presented above is observed. These results should help in choosing the value of different parameters.

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

5. Dimensional analysis The average heat transfer coefficient is some function of the orifice diameter d, diameter of actuator D, cavity depth H, thickness of orifice plate t, amplitude of vibration A, length of orifice plate L, the distance between the orifice plate and copper plate z, the half length of copper plate R, the thermal conductivity of fluid k, the excitation frequency f, the specific heat of fluid C p , the density of fluid q, and the dynamic viscosity of fluid l (see Fig. 1(b)). In other words,

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 following 10 non-dimensional parameters:

  L R z Nu ¼ f Re; Pr; ; ; d d d

ð12Þ

ð13Þ

where z=d is the non-dimensional axial distance, L=d contains the enclosure effect, while R=d is due to the fact that the average heat transfer coefficient is being measured. The heat transfer coefficient is a strong function of radial position (at least in continuous jet; see for example Katti and Prabhu [10]) and therefore the value of average heat transfer coefficient will depend upon the size of the heated block employed in the experiments. Note that R=d will not be a parameter if local h is being measured. For a continuous axisymmetric jet, some enclosure effect is expected. Due to the presence of a plate to cover the cavity, the enclosure effect is always present in the case of a synthetic jet. The set of non-dimensional parameters (Eq. (13)) are therefore the same for both synthetic and continuous jets. The primary difficulty 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 Nusselt number with respect to the various non-dimensional governing parameters. The dependence of Nusselt number on Reynolds number, and a direct comparison of synthetic and continuous jets is also provided towards the end of this section. 6.1. Effect of Reynolds number The variation of average Nusselt number with the normalized axial 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 and Pr ¼ 0:7. It is observed that the average Nusselt number rapidly increases upto z=d  6, and then gradually decreases with an increase in z=d. Also it is observed that the average Nusselt number increases with an increase in Reynolds numbers for any given

1064

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

60

stantial (108%) increase in maximum Nusselt number with a decrease in L=d from 7.86 to 13.75. This difference suggests a strong enclosure effect on the heat transfer ability of synthetic jets. The confinement effect reduces with an increase in the axial distance. The recirculation of the fluid between orifice plate and the copper plate causes a significant reduction in the heat transfer coefficient. The amount of air being recirculated changes with the length of the orifice plate. For a larger length more air gets recirculated as compared to the case with smaller length orifice. This implies a higher average temperature of air near the heated plate in the former case, and leads to a reduction in the amount of heat transfer coefficient.

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

Nuavg

40

20

6.3. Effect of the heater size ðR=dÞ

0

0

5

10

15

20

25

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

z=d, as expected. The maximum Nusselt number is at the same location (z=d = 6) for all Reynolds numbers. The maximum value of average Nusselt number is 44 at a Reynolds number of 4180. The variation of maximum Nusselt number Numax with different Reynolds numbers plotted on a log-log scale gives the slope of the line-of-best-fit as 1.25 (not shown). This suggests that the Nusselt number increases rapidly with an increase in Reynolds number. For comparison, the corresponding slope for continuous jet is about 0.5. However, this result is for a specific value of L=d and R=d; a subsequent result will show that the slope is dependent on 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 number for 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-

Fig. 11 shows the variation of average Nusselt number with normalized half length of copper block. These findings are for the same L=d and approximately the same Reynolds number. It is noticed that the average Nusselt number increases with an increase in R=d, over all normalized axial distances. The increase in average Nusselt number with R=d is due to the effective utilization of impinging jet for heat removal. The location ððz=dÞmax Þ for maximum value of average Nusselt number increases with an increase in R=d. It is observed that there is a monotonic increase in the average Nusselt number with respect to R=d and z=d. The maximum value of average Nusselt number is found to be 40 and 23 for R=d of 2.5 and 1.5 respectively.

6.4. Dependency on Reynolds number As mentioned earlier, the average Nusselt number is a function of Re, z=d; L=d and R=d besides Pr. Several correlations for Nusselt number with continuous axisymmetric jet impinging on a flat surface are available in the literature [10,24–26]. These correlations express the Nusselt number as a function of Rea , where the exponent a is in the range of 0.45–0.8. We look for a similar variation of Nusselt number as a function of Reynolds number in the present work with axisymmetric synthetic jet.

45

60 L/d = 7.86 L/d = 13.75

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

40

50 35 30

Nuavg

Nu avg

40

30

20

25 20 15 10

10 5

0

0

0

3

6

9

12

15

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

0

5

10

15

20

25

30

z/d Fig. 11. Variation of average Nusselt number with the normalized axial distance ðL=d ¼ 13:75Þ.

1065

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

50

Continuous Jet Re = 4000 Synthetic Jet Re = 4180 40

30

Nuavg

In the present work, the exponent of Reynolds number is found to be 1.25 for the Reynolds number range of 1550–4180 and for L=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 single curve, with a maximum scatter of ±3% around the mean value, for this particular value of a. The value of the exponent for other configurations is similarly determined from the available data; the value for a for other L=d and R=d cases are given in Table 3. It is seen that, for the higher L=d and R=d the value of exponent a is high as compared to the lower values of L=d and R=d. Note a larger value of the exponent for synthetic jet as compared to continuous jet.

20

6.5. Comparison with continuous jet A direct comparison between the continuous axisymmetric jet and the synthetic jet for the same set of conditions has also been performed. It is observed from Fig. 12 that the continuous jet gives a higher value of Nusselt number at small spacings ðz=d 6 4Þ. However, both the jets give comparable performance at larger spacings ðz=d P 5Þ. The maximum Nusselt number is at about z=d ¼ 4 for the continuous jet and at z=d ¼ 6 for the synthetic jet. It is also noticed that the maximum Nusselt number is about 10% higher for the continuous jet as compared to synthetic jet, at Re  4000. The synthetic jet is at a disadvantage at small spacings due to its inherent suction and ejection processes. This leads to a recirculation of the same fluid; consequently, the fluid temperature is higher and the ability of the fluid to remove heat from the hot surface reduces. This is however not the case for continuous jet, where fresh fluid is continuously supplied. Whereas a direct comparison with continuous jet has been made at only one Reynolds number, our preliminary measurements suggest that the continuous jet out-performs the synthetic jet at smaller Reynolds numbers ðRe < 4000Þ. However, due to a larger increment in Nusselt number with an increase in Reynolds number for the case of synthetic jet as seen in Section 6.4, the synthetic jet catches up with continuous jet. In fact, the heat transfer ability of synthetic jet is expected to be better than continuous jet for large Reynolds numbers ðRe > 4000Þ. Due to limitation of our experimental facility, larger Reynolds number could not be achieved and this exciting result could not be confirmed. It is worth 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 as to obtain some idea of the radial variation of these quantities. These measurements also help in a better understanding of synthetic jets, and enable further better comparison with continuous jets. 7.1. Velocity measurements The radial velocities (both mean and fluctuations) on the impinging surface are measured with a constant temperature

10

(a)

0 0

5

L=d

R=d

Value of exponent (a)

ðz=dÞmax

7.86 13.75 22

1.5 2.5 4

0.64 1.25 1.4

3 6 10

15

20

25

30

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

hot-wire anemometry system (TSI, IFA-300). A tungsten–platinum coated single wire probe (Model 1210-T1.5 with temperature coefficient of resistance of 0.0042/°C, diameter of wire ¼ 3:8lm, length of sensing element = 1.27 mm) is used for the measurements. The hot-wire probe is mounted on a two-dimensional traversing stand. During calibration of hot-wire probe, the reference velocity was measured with a pitot tube connected to a differential pressure transducer (Furness Control, FCO332, least count = 0.01 mm water, full range = 20 mm water). The measurement points are fitted with King’s law curve, with a maximum uncertainty of 3%. The velocity measurements are done along different radial positions in the jet, at a fixed distance of 2:5 mm ðy=d ¼ 0:312 where y is the coordinate normal to the plate) from the copper block. The values of the other parameters are maintained fixed for these experiments are Re = 3300, L=d ¼ 13:75. 7.1.1. Mean velocity Fig. 13(a) shows the variation of normalized mean velocity ðU mean =U o Þ along the normalized radial distance. A substantial change in velocity distribution is noted with an increase in distance between the jet and plate. At z=d ¼ 1, the velocity is maximum at the centerline and exhibits a secondary peak at r=d ¼ 1:4. The strength of the secondary peak becomes larger than the centerline velocity with an increase in z=d. The secondary peak also shifts to a larger radial location with an increase in z=d. For z=d > 8, the velocity distribution is rather flat. In order to make a direct comparison of velocity measurement with the heat transfer results, spatially averaged velocity is calculated as follows:

RR U mean; spatially averaged ¼

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

10

0

2prU mean dr : RR 2pr dr 0

ð14Þ

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

1066

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

100

1.5

(a)

(a)

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

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

80

Umean / Uexit

Urms / Uexit (%)

1 60

40

0.5

20

0 0

0.5

1

1.5

2

2.5

0

3

0

0.5

1

1.5

2

2.5

3

r/d

r/d 0.5

0.8

(b)

(b) 0.7

0.4

0.5

(Urms)avg / Uexit

(Umean)avg / Uexit

0.6

0.4 0.3

0.3

0.2

0.2

0.1 0.1 0

0

2

4

6

8

10

12

14

0

0

2

4

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 with normalized axial distance.

7.1.2. Rms velocity Fig. 14(a) shows the radial distribution of the normalized rms velocity, for different normalized axial distances between the jet and plate. The normalization has been done by the mean velocity at the centerline of the orifice. Note that the normalized rms values are rather large and that these values reduce with an increase in the axial distance. In contrast to the mean velocity, the rms velocity distribution may exhibit two off-axis peaks. The two peaks are observed for z=d 6 6; both these peaks shift away from the centerline with an increase in the axial distance. Beyond this distance, the normalized rms is nearly constant (with a value of approximately 30% and 20% for z=d ¼ 8 and 12, respectively). The present measurements show a maximum level of turbulence of 84% at z=d ¼ 1 and r=d ¼ 0:2, which is significantly higher as compared to 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 calculated in an analogous manner to Eq. (14). This quantity has been

6

8

10

12

14

z/d

z/d

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 with normalized axial distance.

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

7.2. Pressure measurements The radial pressure distribution on the impinging surface is measured for different z=d and Reynolds numbers, as shown in Fig. 15. The measurements are accomplished by drilling a small hole (1 mm) into the impingement surface and measuring the pressure 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 difference between the pressure at the impingement surface with respect to the atmospheric pressure. This gauge pressure is

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

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 center increases by 23%. Also the magnitude and radial extent of sub atmospheric pressure increases with an increase in the enclosure size. These results further underscore the benefit in employing a smaller size orifice plate, to reduce the effect of enclosure.

1.8

(a)

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

1.6 1.4 1.2

Δ P/((1/2)ρ U2o )

1067

1

8. Discussion

0.8 0.6 0.4 0.2 0

-0.2 0

1

2

3

4

5

r/d 2.5

(b)

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

2

Δ P/((1/2)ρU2o )

1.5

1

0.5

0

-0.5 0

0.5

1

1.5

2

2.5

3

r/d Fig. 15. Variation of pressure coefficient with the normalized radial distance for approximately 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 qU 2o =2, where q is the density of air and U o is the jet exit velocity at the centerline of the orifice. It is observed that the pressure coefficient decreases almost monotonically with an increase in r=d (Fig. 15). The maximum value of pressure coefficient is 2.15 at z=d ¼ 0:07 and close to the jet centerline (Fig. 15(b)). Also, it is noticed that at lower z=d and for r=d approximately between 1.25 and 3, the pressure is slightly sub-atmospheric. (Such sub-atmospheric pressures have also been reported by some researchers with respect to continuous jets; see example Colucci and Viskanta [9].) The value at jet centerline decreases monotonically with an increase in the normalized axial distance ðz=dÞ. Note that the gauge pressure drops rapidly with axial distance making measurements difficult at large distances; therefore measurements are confined to relatively small distances from the orifice exit. The effect of enclosure on the pressure distribution is also measured. For this, the Reynolds number is maintained constant at

The Reynolds number of the impinging synthetic jet changes with change in excitation frequency, orifice diameter, cavity depth, thickness of the orifice plate, diameter of actuator, and amplitude of excitation. The Nusselt number is further affected by the length of the orifice plate, besides properties of the fluid. Both orifice diameter and orifice thickness play a significant role in affecting the heat transfer from the heated surface. Our results suggest that there is an optimum orifice diameter for heat transfer enhancement. The distance corresponding to the maximum heat transfer coefficient also changes with the orifice diameter. A reduction in thickness of the orifice plate decreases frictional resistance to the flow of jet; therefore, the flow velocity and heat transfer coefficient increase. Unlike orifice diameter, the heat transfer coefficient changes monotonically with the thickness of the orifice plate. The cavity depth, however, has a negligible effect on the heat transfer coefficient. This is because the average flow velocity remains approximately the same for different cavity depths [22]. These results suggest that for optimal performance, the orifice diameter needs to be carefully chosen, minimum possible orifice plate thickness should be chosen, while the cavity depth can be chosen as per the constraint of available space. The entire assembly should be excited at the resonance frequency, preferably the diaphragm frequency, at the maximum amplitude possible. Unlike Helmoltz frequency, the diaphragm frequency is invariant of the geometric parameters of the cavity [21]. Furthermore, at least in the present study, the velocity corresponding to the diaphragm frequency is larger than that at the Helmoltz frequency, thereby making it the obvious choice. The length of the orifice plate affects the heat transfer coefficient due to the confinement effects. An increase in the length of the orifice plate increases the amount of recirculation of the fluid near the heated plate, thereby reducing the heat transfer coefficient at small axial distances. It is noted that the confinement effect is much stronger with synthetic jet as compared to continuous jet, owing to the inherent suction and ejection processes in the former jet. This is clearly evident by a poor performance of synthetic jet with respect to continuous jet at small spacings, and comparable performance at larger spacings. From the results it is noticed that the average heat transfer coefficient are high for synthetic jet and are comparable to continuous jet. However, the Nusselt number increases by a larger amount with change in Reynolds number for synthetic jets as compared to continuous jet. Therefore, synthetic jets are expected to perform better than the latter at high Reynolds numbers. The axial and radial variation of various quantities measured here are qualitatively similar to those reported with respect to continuous jet in the literature. The radial variation in heat transfer coefficient and the reason for it (in the context of continuous jet) is as follows [27]: In the region near the stagnation point, there is a rapid decrease in axial velocity and a corresponding rise in static pressure. Due to the shear between the wall jet and the ambient air, fluctuations are created which lead to an increase in the heat transfer coefficient. However, as the axial distance between the jet and plate increases, due to entrainment of the ambient fluid into the jet, the impinging velocity decreases leading to a reduction in the radial

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

velocity; the spreading of the jet further reduces the radial velocity. This reduces the heat transfer coefficient with an increase in the axial distance for all configurations. The above agreement is expected to apply with respect to synthetic jet also, as indicated by the radial distribution of velocity in Figs. 13 and 14. Two local maxima have been observed close to the stagnation point in the radial variation of turbulence intensity close to the plate. The first maximum is probably due to induced velocity by the vortex shedding from the orifice plate. The other one is due to transition of the boundary layer from laminar to turbulent [10]. The peaks are shifting slightly away from the center with an increase in z=d, which is due to the spreading of jet along the axial distance. The maximum value with the synthetic at the stagnation is at lower axial distance ðz=d ¼ 1Þ which is in contrast with the continuous jet at z=d ¼ 6 [9] which may be due to suction and ejection process in synthetic jet. Also it is noticed that for the continuous jet the second peak disappears at low Reynolds number, which is not the case with synthetic jet. The axial variation in area averaged mean velocities seems to be correlated to the average heat transfer coefficient, but the velocity rms is poorly correlated to the average heat transfer coefficient.

80 70

o

45

+20%

60 -20%

50

Nuc

1068

40 30 20 10 0

0

10

20

30

40

50

60

70

80

Nuexp 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 using multiple regression analysis, for different cases. The following equation can describe the variation in average Nusselt number as a function of both Re and z=d (for L=d ¼ 7:86 and R=d ¼ 1:5)

2 Nuavg

3

1 6  ¼ 0:12ðReÞ0:64 4 0:073 dz 

1 10:75ð

z 2 d

7 5

ð15Þ

Þ

Similarly, we have

2 6 Nuavg ¼ 0:00011ðReÞ1:25 4

3 1  0:0084 dz 

1 10:75ð

z 2 d

7 5

ð16Þ

Þ

for L=d ¼ 13:75 and R=d ¼ 2:5, and

2 1 6  Nuavg ¼ 0:00003ðReÞ1:4 4 0:0055 dz 

3 1 z 2 d

10:36ð

7 5

ð17Þ

Þ

for L=d ¼ 22 and R=d ¼ 4. The values obtained from the above correlation fit the experimental data within ± 15%. An attempt to obtain a single correlation is also made, and the following correlation is proposed based on 86 data points:

Nuavg Pr0:333

¼ 7:624ðReÞ0:792

 2:186  2:258  0:632 L R z d d d

ð18Þ

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 correlation is valid only in the region where Nu reduces with an increase in z=d (i.e. at higher axial distances, i.e. z=d greater than approximately 3; see also Table 3). The above correlation incorporates all non-dimensional parameters given in Eq. (12). As expected the correlation suggests a reduction in Nu with an increase in L=d and an increase in Nu with an increase in R=d. Note that Prandtl number has not been varied and the same exponent of Pr as in continuous jet has been employed here. The estimated values compare to the experimental values within ± 20%, with 90% of the data points lying between this range (Fig. 16).

9. Conclusion The average heat transfer coefficient as a function of various geometric parameters has been measured and presented in this work. An experimental setup has been carefully designed, fabricated and validated towards this end. It is noticed that the average heat transfer coefficient is affected by the orifice diameter, and increases with a decrease in the thickness of the orifice plate. The cavity depth has a negligibly small effect on the average heat transfer coefficient. The maximum average heat transfer coefficient occurs at the resonance frequency of the cavity. The heat transfer first increases and then decreases with an increase in axial distance. The location of the maximum heat transfer coefficient depends on the above geometric parameters. Both dimensional and non-dimensional results are presented here. It is noticed that the Nusselt number is a function of five non-dimensional numbers ðRe; Pr; z=d; L=d; R=dÞ. The average Nusselt number increases with Reynolds number and the half length of heated copper plate to diameter ðR=dÞ, but decreases with the length of orifice plate to orifice diameter ðL=dÞ. A strong effect of enclosure is noted; the average Nusselt number increases by 108% with decreasing the L=d by 42%. It is observed that the peak of the average Nusselt number shifts towards lower z=d for the decrease in R=d. The average Nusselt number is correlated into a simple equation using the experimental data for the different cases and also a general correlation has been given for decreasing values of Nusselt number. The average Nusselt number is a function of the 0.792 power of the Re. The radial pressure distribution has been presented for different z=d and Re. The pressure coefficient is found to be higher at the lower r=d. The mean velocities are found to be well correlated with the heat transfer coefficient. The synthetic jet performance is found to be comparable with the continuous axisymmetric jet at low Reynolds number (upto 4000) for the same boundary conditions and expected to be better at high Reynolds number. These results are significant in the point of view of cooling of electronic devices. Acknowledgements We are grateful to Professor S.V. Prabhu for help throughout the course of this work. The first author is thankful to Vishwakarma

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

Institute of Technology, Pune for sponsoring him during the course of this work. This project is funded by the Department of Information Technology, New Delhi. References [1] B.L. Smith, A. Glezer, The formation and evolution of synthetic jets, Phys. Fluids 10 (1998) 2281–2297. [2] A.A. Hassan, R.D. JanakiRam, Effects of zero-mass ‘‘synthetic” jets on the aerodynamics of the NACA-0012 airfoil, J. Amer. Helicopter Soc. 43 (1998) 303–311. [3] D.C. McCormick, Boundary layer separation control with directed synthetic jets, AIAA Paper 2000-0159, 2000. [4] W. Hwang, J.K. Eaton, Creating homogeneous and isotropic turbulence without a mean flow, Exp. Fluids 36 (2004) 444–454. [5] T. Mautner, Application of the synthetic jet concept to low Reynolds number biosensor microfluidic flows for enhanced mixing: a numerical study using the lattice Boltzmann method, Biosensors Bioelectron. 19 (2004) 1409–1419. [6] D.A. Lockerby, P.W. Carpenter, C. Davies, Control of sublayer streaks using microjet actuators, AIAA J. 43 (2005) 1878–1886. [7] R. Mahalingam, A. Glezer, Design and thermal characteristics of a synthetic jet ejector heat sink, J. Electron. Packaging 127 (2005) 172–177. [8] J.Y. San, W.Z. Shiao, Effects of jet plate size and plate spacing on the stagnation Nusselt number for a confined circular air jet impinging on a flat surface, Int. J. Heat Mass Transfer 49 (2006) 3477–3486. [9] D.W. Colucci, R. Viskanta, Effect of nozzle geometry on local convective heat transfer to a confined impinging air jet, Exp. Therm. Fluid Sci. 13 (1996) 71–80. [10] V. Katti, S.V. Prabhu, Experimental study and theoretical analysis of local heat transfer distribution between smooth flat surface and impinging air jet from a circular straight pipe nozzle, Int. J. Heat Mass Transfer 51 (2008) 4480–4495. [11] P. Gulati, V. Katti, S.V. Prabhu, Influence of the shape of the nozzle on local heat transfer distribution between smooth flat surface and impinging air jet, Int. J. Therm. Sci. 48 (2009) 602–617. [12] K. Kataoka, M. Suguro, H. Degawa, K. Maruo, I. Mihata, The effect of surface renewal due to large-scale eddies on jet impingement heat transfer, Int. J. Heat Mass Transfer 30 (1987) 559–567.

1069

[13] P.A. Eibeck, J.O. Keller, T.T. Bramlette, D.J. Sailor, Pulse combustion: impinging jet heat transfer enhancement, Combust. Sci. Technol. 94 (1993) 147–165. [14] D.A. Zumbrunnen, M. Aziz, Convective heat transfer enhancement due to intermittency in an impinging, ASME J. Heat Transfer 115 (1993) 91–97. [15] D.J. Sailor, D.J. Rohli, Q. Fu, Effect of variable duty cycle flow pulsations on heat transfer enhancement for an impinging air jet, Int. J. Heat Fluid Flow 20 (1999) 574–580. [16] S.D. Hwang, H.H. Cho, Effects of acoustic excitation positions on heat transfer and flow in axisymmetric impinging jet: main jet excitation and shear layer excitation, Int. J. Heat Fluid Flow 24 (2002) 199–209. [17] A. Pavlova, M. Amitay, Electronic cooling with synthetic jet impingement, J. Heat Transfer 128 (2006) 897–907. [18] J. Garg, M. Arik, S. Weaver, T. Wetzel, S. Saddoughi, Meso scale pulsating jets for electronics cooling, J. Electron. Packaging 127 (2005) 503–511. [19] M. Chaudhari, B.P. Puranik, A. Agrawal, Effect of orifice shape in synthetic jet based impingement cooling, Exp. Therm. Fluid Sci., in press, 2009 doi: 10.1016/j.expthermflusci.2009.11.001. [20] D. Lytle, B. Webb, Air jet impingement heat transfer at low nozzle – plate spacing, Int. J. Heat Mass Transfer 37 (1994) 1687–1697. [21] M. Chaudhari, G. Verma, A. Baramade, B. Puranik, A. Agrawal, Near-field measurements and cavity design of synthetic jet, in: 38th AIAA Fluid Dynamics Conference, Seattle, Paper No. 4068-2008. [22] M. Chaudhari, G. Verma, B. Puranik, A. Agrawal, Frequency response of a synthetic jet cavity, Exp. Therm. Fluid Sci. 33 (2009) 439–448. [23] A. Agrawal, G. Verma, Similarity analysis of planar and axisymmetric turbulent synthetic jets, Int. J. Heat Mass Transfer 51 (2008) 6194–6198. [24] J.A. Fitzgerald, S.V. Garimella, A study of the flow field of a confined and submerged impinging jet, Int. J. Heat Mass Transfer 41 (1998) 1025–1034. [25] E. Sparrow, Z. Xu, L. Azevedo, Heat (mass) transfer for circular jet impingement on a confined disk with annular collection of the spent air, J. Heat Transfer 109 (1987) 329–335. [26] L. Huang, M. Genk, Heat transfer of an impinging jet on a flat surface, Int. J. Heat Mass Transfer 37 (1994) 1915–1923. [27] K. Jambunathan, E. Lai, M.A. Moss, L.B. Button, A review of heat transfer data for single circular jet impingement, Int. J. Heat Fluid Flow 13 (1992) 106–115.