International Journal of Heat and Mass Transfer 55 (2012) 5514–5525

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Optimum tip gap and orientation of multi-piezofan for heat transfer enhancementof finned heat sink in microelectronic cooling

M.K. Abdullah a,⇑, N.C. Ismail b, M. Abdul Mujeebu c, M.Z. Abdullah b, K.A. Ahmad d, Muhamad Husaini b,M.N.A. Hamid a

a Mechanical Section, Universiti Kuala Lumpur, Malaysian Spanish Institute, 09000 Kulim Hi-Tech Park, Kedah, Malaysiab Aerodynamic and Advanced Cooling Laboratory, School of Mechanical and Aerospace Engineering, Engineering Campus, Universiti Sains Malaysia, 14300 Nibong Tebal,Penang, Malaysiac Department of Mechanical Engineering, Anjuman Institute of Technology and Management (Visvesvaraya Technological University, Belgaum), 58320 Bhatkal, Karnataka, Indiad Department of Aerospace Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

a r t i c l e i n f o a b s t r a c t

Article history:Received 28 September 2011Received in revised form 6 May 2012Accepted 6 May 2012Available online 19 June 2012

Keywords:Finned heat sinkMulti-piezofanTip gapOptimizationTemperature dropHeat transfer coefficient

0017-9310/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.05

⇑ Corresponding author.E-mail address: mkhalil@eng.usm.my (M.K. Abdul

Piezoelectric fans can be manipulated to generate airflow for cooling microelectronic devices. Their out-standing features include noise-free operation, low power consumption and suitability for confinedspaces. This paper presents experimental optimization of tip gap and orientation angle of three piezoelec-tric fans (multi-piezofan) to maximize the heat removal performance of finned heat sink for microelec-tronic cooling. Design of experiments (DOE) approach is used for the optimization, and a threedimensional simulation using FLUENT 6.3.2 is carried out to better understand the flow induced by themulti-piezofan and the resulting heat transfer from the heat sink surface. For the optimization, the Cen-tral Composite Design (CCD) of response surface methodology (RSM) is exploited from the Design Expertsoftware. In the numerical model, the flow induced by the piezofan is treated as incompressible and tur-bulent; the turbulence is taken care by the shear stress transport (SST) k–x model. The experimentalresults are found to be in good agreement with the predictions. Out of 13 experimental trials determinedby CCD, the optimum tip gap and fan orientation are found to be d = 0.17 and 90� respectively. At thiscondition, an enhancement in convective heat transfer coefficient exceeding 88% is achieved, comparedto natural convection.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Piezoelectric fan (named henceforth as piezofan) is a cantileverbeam bonded with a piezoelectric material near its clamped end.The mechanism of alternate expansion and contraction generatesshear forces within the beam, whenever an alternative input signalis applied to the piezoelectric material. These forces produce oscil-lations at the free end of the cantilever beam which creates motionin the surrounding fluid. As piezofans facilitate noise-free opera-tion with low power consumption, and require less space, theycan be adapted to operate at frequencies which are too quiet tothe human ear and can be built and modified to meet various geo-metric constraints for many applications. Owing to the excellentthermal management capability, recently piezofans gained signifi-cant attention for electronic cooling applications [1].

Piezofan was first emerged in the early seventies, and was rein-troduced by Toda [2,3] who found that the piezofans were able tocool either side of a power transistor panel of a television receiver,

ll rights reserved..024

lah).

with a temperature drop of 17 �C. Ihara and Watanabe [4] investi-gated the flow around the ends of oscillating flexible cantilevers.The experimental flow profiles were matched with the simulationflow fields developed by discrete vortex method. Acıkalın et al. [5]compared analytical, computational and experimental flow pro-files for the baffled fan, and obtained a close match among them.Advanced flow measurements were carried out by Abdullah et al.[6,7] at different piezofan heights by using particle image veloci-metry (PIV) system.

Schmidt [8] focused on the local and average transfer coeffi-cients on a vertical surface by using two piezofans in out-of-phase,and showed that the transfer coefficients were affected by the tipgap, and the fan spacing. In a similar study using single piezofan,Acikalin et al. [9] obtained significant localized cooling and morethan 100% enhancement in convective heat transfer coefficient rel-ative to natural convection. In their extension work [10], it wasshown that for a given power consumption piezofans were signif-icantly better than axial fans, and compared to natural convectionheat sink the piezofans used lesser volume. Yoo et al. [11]attempted the possibility of replacing rotary fan by piezofan.Different vibrating metal plates were analyzed theoretically and

List of symbols

A movement area (m2)Af frequency dependent amplitudeDx cross-diffusion termF external body force (N)G gap between piezofan and heat sink (mm)eGk generation of turbulence kinetic energyeGx generation of xg gravitational acceleration (m/s2)Hf fin height (mm)hhs heat convection coefficient (W/m2 K)kt turbulent kinetic energy (m2/s2)lp length of piezofan (mm)lu length of un-patch piezofan (mm)P static pressure (N/m2)_qh heater heat generation (W/m3)R2 correlation coefficientS source termSD standard deviationT temperature (K)Tj junction temperature (K)Tn=1,2.. temperature at a n-point (K)Ts-exp experiment heat sink surface temperature (K)T1 ambient temperature (K)t time (s)th heater thickness (mm)

tp piezofan thickness (mm)~u velocity vectoru velocity (m/s)ug grid velocityV control volumew beam position (mm)_w beam velocity (rad/s)

wp width of piezofan (mm)x, y, z space coordinatesY dissipation coefficient

Greek symbolsa angleb eigen valued normalized tip gape turbulent kinetic energy dissipation rate (m2/s3)q fluid density (kg/m3)s viscous stress tensor (N/m2)C diffusion coefficientU general scalar for transport equationx ratio of e to k (s�1)xb beam angular velocity (rad/s)

M.K. Abdullah et al. / International Journal of Heat and Mass Transfer 55 (2012) 5514–5525 5515

showed that piezofans were capable of generating jet flow for cool-ing purpose. Hosaka and Itao [12] and Basak and Raman [13] re-ported that the vibration characteristics of a vibrating cantileverwere altered by the presence of a second oscillating beam depend-ing on the vibration amplitude as well as the pitch, and the phasedifference between the neighboring cantilevers. These findingswere also confirmed experimentally by Kimber and co-workers[14,15] who studied the fluidic coupling between piezofans.

While most of the researchers focused on the use of singlepiezofan, only few works [4,8,12–16] were reported on multi-piezofan which has important practical applications. Few research-ers were interested in the combination of piezofan and finned heatsink [17–19], which was proved to be relatively excellent. Howeverthe combination of multi-piezofan with finned heat sink is yet tobe explored. Moreover, a three dimensional (3D) numerical analy-sis on the heat transfer performance of piezofans is also lacking.Accordingly, the present study is focused on experimental analysisand optimization, and 3D modeling of multi-piezofan arranged inconjunction with finned heat sink. The coupled effect of tip gap(d) and fan orientation angle (a) on the heat transfer performanceof the heat sink is studied. As an excellent tool for experimental de-sign and optimization, the design of experiment (DOE) approach isemployed for the estimation of the number of experimental trials,and subsequent optimization of d and a with the objective of min-imizing the temperature (maximize the temperature drop) of theheat sink surface; the procedure was similar to that of Elnaggaret al. [20]. Based on the best and worst cases of d and a, 3D simu-lations are performed by using FLUENT 6.3.2, and the results arecompared with the experimental findings.

Fig. 1. The experimental setup to study the temperature.

2. Experimental setup and procedure

Fig. 1 shows the experimental apparatus for the temperaturemeasurement. The test section of size 800 mm � 120 mm �250 mm is made from clear glass. The electronic package ismimicked as a heater (size 30 mm � 30 mm � 3 mm) into which

a constant heat flux of 9166.7 W/m2 is applied. One side of the hea-ter is embedded on a wood platform which also serves as thermalinsulator, while the other side is pasted to the heat sink bottom sur-face, by using RS� heat sink compound which has high thermal con-ductivity. The target being cooled is an aluminum heat sink(Fig. 2(a)), which has base plate of size 80 mm � 60 mm � 1 mm,and is provided with four fins of 1 mm thickness and 30 mm height(total footprint of the heat sink is 80 mm � 60 mm � 31 mm). EightK-type thermocouples are used to monitor temperatures at criticallocations as shown in Fig. 2(b) and (c). An additional thermocoupleis used to monitor the ambient air temperature in the enclosure.The temperatures are displayed and recorded by the computer bymeans of data logger, for each minute during the experiment.

The multi-piezofan consists of three piezofans that can be ori-ented at angles (a) of 0� to 90�; Table 1 shows the specifications

Fig. 2. Schematic of the heat sink and thermocouple locations. Red area representsthe heat flux imposed (all dimensions in mm and not to scale). (For interpretation ofthe references to colour in this figure legend, the reader is referred to the webversion of this article.)

Fig. 3. (a) Fan height and (b) Piezofan gap height and orientation angle, and finheight.

Table 1Specifications of the piezoelectric fan.

Specification Value

Material Stainless steelFan size (mm) 47 (lP) � 12 (wP) � 0.4 (tP)Resonant frequency (Hz) 111Power consumption of fan and circuit (mW) 42Fan weight (gm) 2.0

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of the piezofan (PiezoSystem Inc, USA). The length of the un-patchpiezofan (lu) is 23 mm. The oscillating drive signal to match theresonant frequency of the beam was provided by means of an in-verter circuit. In the rest of this article a normalized tip gap (d) will

be used, which is defined as the ratio of gap height (G) to the finheight (Hf); a, Hf and G are illustrated in Fig. 3.

A laser displacement system (KEYENCE LK-G152) was used tomeasure the deflection produced by the piezofan; Fig. 4 showsthe experimental setup. The laser beam is pointed on the tip ofthe vertically mounted piezofan. When the piezofan swings leftand right, the IMC DAQ system records the displacement and itsfrequency from peak-to-peak position to the initial position, andstores in the computer. The heat sink-piezofan assembly is per-fectly isolated from external disturbances by means of a largetransparent housing fixed on a rigid platform. For the best perfor-mance, the piezofans are excited at the resonance frequency(111 Hz) and 16.5 V. The maximum deflection of each piezofan is5.01 mm which is symmetric in both directions.

In this study, Central Composite Design (CCD), the most widelyused approach of Response Surface Methodology (RSM), is em-ployed to optimize d and a with the objective of maximizing tem-perature drop (DT); the entire DOE procedure is facilitated by the‘Design Expert 6’ software, similar to the published work [20].

3. Modeling

3.1. Computational domain

The 3D model used in this simulation consisted of a heater, sim-ple heat sink and three piezofans. Fig. 5 shows the multi-piezofanmounted in vertical (Fig. 5(a)) and horizontal (Fig. 5(b)) positions.The heat flux employed for numerical simulation was same as thatused in the experiment (9166.7 W/m2).

The size of the computational domain is 120 mm � 100 mm �46.1 mm, which includes heater, heat sink and multi-fans; theclamp of the piezofan is neglected. The fan boundary is modeledas a moving adiabatic wall whose location in time is set by aUDF in FLUENT. The fan is modeled as infinitesimally thin wallwith no thermal conduction through it. No-slip boundary condi-tions are applied to the walls such as platform and heat sink. Other

Fig. 4. Experimental setup to study piezofan deflection.

Fig. 5. Multi-piezofan orientations used in simulation. Fig. 6. The meshed models.

Fig. 7. Mesh generation regions.

M.K. Abdullah et al. / International Journal of Heat and Mass Transfer 55 (2012) 5514–5525 5517

boundaries are treated as pressure boundaries, permitting the airflow in inward or outward direction. A combination of tetrahedraland quad literal elements (about half million) is used for meshing(see Fig. 6).

The fluid domain is divided into two regions namely region ‘a’and region ‘b’ as shown in Fig. 7. The boundary of these two regionswas imposed as a fluid interface. The purpose of fluid interface is toavoid damaged fluid cells since region ‘a’ of the fluid domain in-cludes the deforming beam (piezoelectric fan). The fluid cells canbe greatly skewed due to its movement. This technique can over-come the problem by flagging the cells from one side of the interface

Fig. 8. Temperature variation over time.

5518 M.K. Abdullah et al. / International Journal of Heat and Mass Transfer 55 (2012) 5514–5525

as deforming cells. In addition, only single cell spacing is includedfrom the tip of the beam to the fluid interface to avoid stretching,which may lead to failure of the fluid cells. Region ‘b’ is distinguishedby stationary fluid cells that interact with region ‘a’ through the fluidinterface. The ‘smoothing’ and ‘remeshing’ functions of FLUENT [21]are exploited in the present dynamic meshing.

3.2. Mathematical model

The flow is assumed incompressible and turbulent. The govern-ing equations employed in FLUENT, for describing the transientfluid flow are as follows:

Continuity:@q@tþ @

@xiðquiÞ ¼ 0 ð1Þ

Momentum (non-accelerating reference frame):

@

@tðquiÞ þ

@

@xjðquiujÞ ¼ �

@P@xjþ @sij

@xjþ qgi þ Fi ð2Þ

where q is the fluid density, P is the pressure in the fluid, sij is theviscous stress tensor and gi and Fi are the gravitational accelerationand external body force in the i-direction, respectively.

However, FLUENT allows the user to simulate moving anddeforming domains through the use of user defined function(UDF). Dynamic meshes can be used to model flow where theshape of the domain is changing with time due to motion of thedomain boundaries. The integral form of the transport equationfor a general scalar (U), on an arbitrary control volume (V), on amoving mesh is written as:

ddt

ZVqUdVþ

ZdV

qUð~u�~ugÞdA ¼Z

dVCrUdAþ

ZV

SUdV ð3Þ

where~u is the flow velocity vector and~ug is the grid velocity of themoving meshes. The first and second terms on the left are the timederivative and convective terms respectively. The terms on the rightare the diffusive and the source terms. C is the diffusion coefficientand SU is the source term of U. oV represents the boundary of thecontrol volume V and dA is the area movement.

Energy:

@

@tðqcpTÞ þ @

@xjðquicpTÞ ¼ k

@2T@x2

j

ð4Þ

where cp is specific heat of air, and k is thermal conductivity.The shear stress transport (SST) k–x model as expressed in Eqs.

(5) and (6) is used to describe the flow induced by the piezofan,which has local turbulence.

@

@tðqktÞ þ

@

@xiðqktuiÞ ¼

@

@xjþ ðCk

@kt

@xjÞ þ eGk � Yk þ Sk ð5Þ

@

@tðqxÞ þ @

@xiðqxuiÞ ¼

@

@xjþ ðCx

@x@xjÞ þ eGx � Yx þ Dx þ Sx ð6Þ

where eGk represents the generation of turbulence kinetic energydue to mean velocity gradients, Gx denotes the generation of x,and Ck and Cx are the effective diffusivity of kt and x, respectively.Yk and Yx are terms for the dissipations of k and x respectively, dueto turbulence. Dx is the cross-diffusion term, and Sk and Sx areuser-defined source terms.

In present study, the mode shape of a piezoelectric fan isapproximated by that of a clamped-free beam [22]. Assuming asinusoidal driving, position of the beam is given by:

wðx; tÞ ¼ Af �ðsinðbluÞ� sinhðbluÞÞðsinðbxÞ� sinhðbxÞÞþðcosðbluÞ� coshðbluÞÞðcosðbxÞ� coshðbxÞÞ

� �� sinðxbtÞ

ð7Þ

Differentiating this equation with respect to time gives the velocityof the beam,

_wðx; tÞ ¼ Af �ðsinðbluÞ� sinhðbluÞÞðsinðbxÞ� sinhðbxÞÞþðcosðbluÞ� coshðbluÞÞðcosðbxÞ� coshðbxÞÞ

� ��xb cosðxbtÞ

ð8Þ

where b values can be calculated from the frequency equation asfollows:

cosðbluÞ � coshðbluÞ ¼ �1 ð9Þ

This must be solved numerically and yields infinity solutions of b.The b value corresponding to the first mode shape is:

b ¼ 1:875lu

ð10Þ

3.3. Simulation

The first-order upwind discretization scheme is used both formomentum and energy equations, with the SIMPLE scheme forpressure-velocity coupling. For the treatment of the turbulentflow at the near-wall region (heat sink surface), the y+ value isset as 1.The beam is assumed to vibrate at a frequencyof 100 Hz; this round off (compared to the experimental valueof 111 Hz) is made for numerical stability. Time-step size of0.0001 s is chosen for all the cases, with 100 time steps percycle of fan vibration. This value is arrived after three attemptsto check the trend and proximity with the profiles investigated;for instance, the trials are done by increasing the meshelements (0.34 � 106 � 0.6 � 106) and decreasing the time steps(2.5 � 10�4 � 5.0 � 10�5). With reference to the finest mesh size,the discrepancy in the temperature of the selected mesh is 0.4%.The total duration of the simulation is selected such that thetemperature reaches steady state during this period. It took5000 iterations, which corresponds to approximately three daysof computation time per each case on a Pentium DualCore proces-sor (each 2.8 GHz) computer with 2.0 GB of memory. Fig. 8 showsthe temperature variation over time once the piezofan is actuated.It can be observed that the temperature increases rapidly up to0.1 s and then slightly increases before attaining steady state at0.2 s. Thus, the quasi-steady temperature can be considered from0.2 s onwards. However, in the current set up these readings aretaken at 0.5 s, as additional precaution.

Fig. 9. Effect of multi-piezofan on the heat sink temperature.

Table 2Response values for different experimental conditions.

Run no. Factor A: a Factor B: d Response 1: DT (�C)

1 45.00 0.33 16.602 45.00 0.33 15.963 90.00 0.33 16.294 45.00 0.33 15.945 45.00 0.5 15.766 45.00 0.33 16.077 90.00 0.50 15.538 0.00 0.17 17.319 45.00 0.17 17.7910 45.00 0.33 15.6711 90.00 0.17 18.0812 0.00 0.50 16.2413 0.00 0.33 15.53

Table 3Summary of ANOVA of the quadratic model for DT.

Source Sum ofsquares

Degree offreedom

Meansquare

F-value Prob > F

Model 10.24 5 2.05 20.56 0.0005a 1.01 1 1.01 10.14 0.0154d 7.99 1 7.99 80.18 <0.0001a2 0.31 1 0.31 3.11 0.1212d2 0.38 1 0.38 3.78 0.0930ad 0.14 1 0.14 1.37 0.2797Residual 0.7 7 0.1Lack of fit 0.36 3 0.12 1.42 0.611Pure error 0.34 4 0.084SD = 0.32 R2 = 0.9363 R2

adj ¼ 0:8907 Adeq. Precision = 15.099

Fig. 10. Normal probability plot of the studentized residual for heat removal.

M.K. Abdullah et al. / International Journal of Heat and Mass Transfer 55 (2012) 5514–5525 5519

4. Results and discussion

4.1. Experimental results

4.1.1. Effect of multi-piezofan on temperatureThe transient temperature distributions at different locations of

the heat sink, with and without piezofans, are shown in Fig. 9. Firstof all, keeping the fans off, the heater is turned on (time t = 0), andthe temperature is monitored; the steady state is reached ataround t = 80 min. At this condition, the piezofans are turned onand a new steady state is reached at around 100 min. The multi-piezofan is seen to cause a maximum of 22% reduction in temper-ature relative to natural convection.

4.1.2. Results of DOE analysisA total of 13 runs obtained from the CCD, and the corresponding

responses are shown in Table 2. It is observed that, the tempera-ture drop (DT) due to the presence of multi-piezofan varies be-tween 15.53 �C and 18.08 �C. Table 3 shows the analysis ofvariance (ANOVA) of regression parameters of the predicted re-sponse surface quadratic model for DT. The value of correlationcoefficient obtained for DT is R2 = 0.9363.

The final regression model, in terms of their coded factors, is ex-pressed by the following second-order polynomial equation (Eq.(11)).

DT ¼ 15:79þ 0:41a� 1:15dþ 0:33a2 þ 0:37d2 � 0:18ad ð11Þ

In order to ensure that the selected model adequately representsthe real system, the diagnostic plots such as normal probabilityplots of the studentized residuals, as well as the predicted versusactual value plots, are plotted as shown in Figs. 10 and 11 respec-tively. It can be observed that the data is almost normally distrib-uted even though there is some scattering which is acceptable.The predicted and experimental values of DT are in good agreementas shown in Fig. 10. The 3D response surface and contour plots ofthe quadratic model as shown in Fig. 12, demonstrate the interac-tive relationship between d and a on DT. The maximum DT ob-served is 18.2337 �C at d = 0.17 and a = 90�, while the minimumDT (15.5908 �C) is obtained at d = 0.50 and a = 0�. Thus the optimumvalues of d and a are 0.17 and 90� respectively, which are furtherverified by exploiting the optimization facility of Design Expert 6.

4.1.3. Heat transfer coefficientThe experimental convective heat transfer coefficient (hhs) in

each case (without and with the fans) is calculated by using an en-ergy balance on a control volume between the power input and theheat removed from the surface of the heat sink by convection, asproposed by Incropera and Dewitt [23]:

hhs ¼_qhth

Ts�exp � T1ð12Þ

where _qh is the uniform heat generation (W/m3) from the heater, th

is the heater thickness, and Ts and T1 are the temperatures of theheat sink surface and the ambient respectively. Accordingly, hhs

Fig. 11. Comparison of actual and predicted DT.

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for three cases namely, best (d = 0.17 and a = 90�), mediocre(d = 0.33 and a = 45�) and worst (d = 0.50 and a = 0�) are comparedwith that of natural convection, as shown in Fig. 13. It is apparentthat, compared to the natural convection case, the multi-piezofanwith vertical orientation and minimum tip gap contributes for88.5% enhancement in heat transfer coefficient while the mediocreand worst cases produce 68.8% and 65% respectively. The experi-mental uncertainties for the parameters (temperature and heattransfer coefficient) are ±1.72 and 1.88 respectively, which are esti-mated from 5 sets of readings, by the statistical procedure proposedby Taylor [24].

Fig. 12. (a) Response surface and (b) contour plots for DT as functions of d and a.

4.2. Numerical results

4.2.1. Validation of the structural modelIn the present study, the piezofan is approximated as a

clamped-free beam, and Eqs. (7)–(10) are used to define the beamlocation during vibration. In order to ensure that this mode shapematches the desired amplitude, these equations are programmedin MATLAB software. Fig. 14 demonstrates the successful peak-to-peak deflection of the beam (piezofan) with respect to the phaseangle (product of angular velocity and time). The mode equationsare then employed into the UDF.

Fig. 13. Enhancement in heat transfer coefficient for three different cases.

4.2.2. Flow visualizationThe transient thermal analysis from FLUENT 6.3.2 is performed

to study the flow field and temperature distribution, for the bestand the worst cases. Fig. 15(a) shows the streamlines, velocity vec-tors and temperature contours for the best case at t = 0.5 s. Thepiezofan produces air streams mainly in the longitudinal andtransverse directions (with respect to the piezofan). The first direc-tion is generated by the impinged jet, while the second is gener-ated by the normal force due to the vibration of the beam [25].So there is fresh cooling air being entrained into the air flow whilethe vortices are being formed. As the piezofan vibrates, two regionsof circulation are formed on both sides, forcing the fluid to displacemore rapidly. High velocity regions are found at the front of themoving beam, which then strikes the heat sink surface and flowsin the outward direction. Fig. 15(b) shows the correspondingimages for the worst case. Unlike the previous case, the velocitydistribution is asymmetric since the states of air on either sidesof the vibrating piezofan are different to each other. With respect

Fig. 14. Piezofan deflection with respect to phase angle.

Fig. 15. (a) Predicted streamlines, velocity vectors and temperatures for best case at t = 0.5 s. (b) Predicted streamlines, velocity vectors and temperatures for worst case att = 0.5 s.

M.K. Abdullah et al. / International Journal of Heat and Mass Transfer 55 (2012) 5514–5525 5521

to the piezofan orientation, the air below the beam is more con-fined and hotter compared to the other side.

Fig. 16 shows the top views of streamlines and vortices att = 0.5 s. In the best case (Fig. 16(a)), three vortices are observed ex-actly at the center of the heat sink surface, while the other case(Fig. 16(b)) shows five vortices located away from the center. As

the heater is situated at the bottom center of the heat sink base,the central portion of the heat sink gets hotter, and thus the vorti-ces generated and concentrated centrally in the first case enablesefficient heat removal, compared to the second case. Moreover, itis observed that the magnitude of vorticity for the best case is200% greater than that of the other case.

Fig. 16. (a) Streamlines and vorticity vectors for best case at t = 0.5 s. (b)Streamlines and vorticity vectors for worst case at t = 0.5 s.

Fig. 17. (a) Temperature contours and (b) labels for best case at t = 0.5 s.

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4.2.3. Temperature contoursThe temperature contours of the heat sink base, for the best and

worst cases are shown in Figs. 17 and 18 respectively. For the bestcase, a rounded rectangular pattern is observed at the heat sinkcenter (due to the middle fan) and this behavior transforms intoa lobed pattern towards the locations of side fans. A symmetricgrowth of the temperature pattern can be observed in all direc-tions. However, a distinctly different distribution of temperatureis observed in the worst case where the temperature distributionis non-uniform. These observations are consistent with the profilesshown in Figs. 15 and 16 respectively.

Figs. 19 and 20 show the corresponding temperature contourson the fins, at t = 0.5 s. For the first case, a droplet cooling zone isobserved at the centre of the fins and these droplets appear to besymmetric in the direction of piezofan vibration. The droplet zoneswiden laterally due to the induced swirling flow on both sides ofthe fan. However, for the other case, asymmetric cooling zone isobserved at one end of the heat sink surface, as the induced flowfreely goes outward. Both profiles agree that this droplet coolingzone is prominent at the central fins compared to the side fins; thisis attributed to the enhanced cooling of the central fins due to thepresence of piezofans on both sides.

Fig. 21 illustrates the comparison of temperature distributionsfor the best and worst cases, along the centre line (parallel to thex-direction referring to Fig. 2) of the heat sink surface. The signifi-cant difference between the curves indicates the critical influence

of d and a on the cooling performance. The temperatures at theleading edge (lhs/lh = 2.76) are almost the same because at this loca-tion, the induced flows have similar influences for both the cases.However, temperatures at the center and at the trailing edge aretremendously different (the best case shows lower temperatures);this behavior is expected according to the respective flow and vor-tex profiles.

4.3. Heat transfer coefficient

Fig. 22 shows the heat transfer coefficient (hhs) for the best andworst cases. In each case, the heat transfer coefficient decreases asit moves to the heat sink’s center which is the hottest zone. The in-crease in hhs of the best case compared to the worst case is around1% at the leading edge, increases dramatically to 16% at the centreand then decreases to 10% at the trailing edge. This trend demon-strates the crucial roles of a and d on the heat removalperformance.

4.4. Comparison of simulation and experimental results

The predicted and measured temperatures at the locationsshown in Fig. 2(b) are compared for the best and worst cases assummarized in Tables 4 and 5 respectively. It can be observed thatthere is good agreement between simulation and experiment, witha maximum discrepancy of only 1%. Similarly, Fig. 23 shows thecomparison of convective heat transfer coefficients at the locationlhslh¼ 0 of the heat sink. A maximum of 5% under-prediction is ob-

served in the simulation, which is attributed to the omission ofradiation effect in the numerical model; this presumption isconfirmed by deducting the experimentally determined radiative

Fig. 18. (a) Temperature contours and (b) labels for worst case at t = 0.5 s.

Fig. 19. Temperature contours of the fins for the best case at t = 0.5 s.

Fig. 20. Temperature contours of the fins for the worst case at t = 0.5 s.

Fig. 21. Temperature plots on the reference line for the comparison of best andworst cases.

Fig. 22. Heat transfer coefficient plots on the reference line for the comparison ofbest and worst cases.

M.K. Abdullah et al. / International Journal of Heat and Mass Transfer 55 (2012) 5514–5525 5523

contribution, from the predicted value. Also, the thickness of thethermal compound in the simulation is treated as uniform in allthe cases; the real thickness was not necessarily so, as the com-pound was manually applied. Furthermore, the ambient tempera-ture in the experiments is measured with a single thermocouple,whereas the average fluid temperature inside the domain is usedin the simulation. In addition, the lack of match between the exper-imental and predicted frequencies might contribute to the incon-sistency which leads to difference in performance.

Table 4Comparison of experimental and simulation temperatures (best case).

Temperature points Ts 1 2 3 4 5 6 7

Exp. (K) 317.48 312.34 310.64 312.06 306.46 306.98 306.83 306.33a = 90 (K) 317.80 312.82 311.66 312.44 310.76 311.55 311.29 309.39DTexp–sim (K) 0.32 0.48 1.02 0.38 4.3 4.57 4.46 3.06%DTexp–sim 0.1 0.15 0.33 0.12 1.4 1.49 1.45 1.0% Average DTexp–sim 0.76

Table 5Comparison of experimental and simulation temperatures (worst case).

Temperature points Ts 1 2 3 4 5 6 7

Exp. (K) 320.39 312.76 312.82 311.89 306.08 310.64 305.31 308.06a = 0 (K) 321.52 314.44 313.94 314.02 311.94 313.01 310.79 313.09DTexp–sim (K) 1.13 1.68 1.12 2.13 5.86 2.37 5.48 5.03%DTexp–sim 0.35 0.54 0.36 0.68 1.91 0.76 1.79 1.63% Average DTexp–sim 1.0

5524 M.K. Abdullah et al. / International Journal of Heat and Mass Transfer 55 (2012) 5514–5525

Fig. 23. Comparison of predicted and experimental heat transfer coefficients forbest and worst cases.

5. Conclusions

Optimization of tip gap and orientation of piezofans is per-formed by using the DOE approach, to maximize the heat removalperformance of finned heat sink. A 3D simulation using FLUENT6.3.2 is carried out to better understand the induced flow andthe resulting heat transfer. The turbulence was incorporated bythe shear stress transport (SST) k–x model. The experimental re-sults are well matched with the predictions. By the use of DOE, sig-nificant savings in effort and time are achieved to conduct therequired experiments and analyze the coupled influence of tipgap and piezofan orientation. It is observed that multi-piezofanwith vertical orientation and a tip gap d = 0.17 yields 88% enhance-ment in the convective heat transfer coefficient compared to natu-ral convection. The present finding would be a valuable input inthe application of finned heat sink with multi-peizofan in micro-electronic cooling. This study may be extended for lesser tip gaps,and with various piezofan-heat sink configurations.

Acknowledgements

This work is supported by the Fundamental Research GrantScheme (FRGS) under contract 1001/PMEKANIK/811076. Theauthors would like to acknowledge S.F. Shaker, T.Y. Chong, and

W. Amri for their contributions in fabrication of the test apparatusand in conducting the noise and vibration experiments. Specialthanks also dedicated to M. Hashim for helping in conducting thecontrol and instrumentation experiments.

References

[1] T. Acikalin, S.V. Garimella, Analysis and prediction of the thermal performanceof piezoelectrically actuated fans, Heat Transfer Eng. 30 (6) (2009) 487–498.

[2] M. Toda, Theory of air flow generation by a resonant type PVF2 bimorphcantilever vibrator, Ferroelectrics 22 (1979) 911–918.

[3] M. Toda, Voltage-induced large amplitude bending device-PVF2 Bimorph—itsproperties and applications, Ferroelectrics 32 (1981) 127–133.

[4] A. Ihara, H. Watanabe, On the flow around flexible plates, oscillating with largeamplitude, J. Fluids Struct. 8 (1994) 601–619.

[5] T. Acıkalın, A. Raman, S.V. Garimella, Two-dimensional streaming flowsinduced by resonating thin beams, J. Acoust. Soc. Am. 114 (No. 4-Pt. 1)(2003) 1785–1795.

[6] M.K. Abdullah, M.Z. Abdullah, M.V. Ramana, C.Y. Khor, K.A. Ahmad, M.A.Mujeebu, Y. Ooi, Z. Mohd Ripin, Numerical and experimental investigations oneffect of fan height on the performance of piezoelectric fan in microelectroniccooling, Int. Commun. Heat Mass Transfer 36 (2009) 51–58.

[7] M.K. Abdullah, M.Z. Abdullah, M.V. Ramana, C.Y. Khor, K.A. Ahmad, M.A.Mujeebu, Y. Ooi, Z. Mohd Ripin, Effect of piezoelectric fan height on flow andheat transfer for electronics cooling applications, in: Proceedings of the EMAP2008 Conference, Taipei, Taiwan, 2008, pp. 165–170.

[8] R.R. Schmidt, Local and average transfer coefficients on a vertical surface dueto convection from a piezoelectric fan, in: Proceedings of the I-THERM IVConference, Washington, 1994, pp. 41–49.

[9] T. Acıkalın, S.M. Wait, S.V. Garimella, A. Raman, Experimental investigation ofthe thermal performance of piezoelectric fans, Heat Transfer Eng. 25 (1) (2004)4–14.

[10] T. Acıkalın, I. Sauciuc, S.V. Garimella, Piezoelectric actuators for low-formfactor electronics cooling, in: Proceedings of the IPACK2005-ASME InterPACKConference, San Fransisco, CA, 2005, pp. 939–943.

[11] J.H. Yoo, J.I. Hong, W. Cao, Piezoelectric ceramic bimorph coupled to thin metalplate as cooling fan for electronic devices, Sensors Actuat. 79 (2000) 8–12.

[12] H. Hosaka, K. Itao, Coupled vibration of microcantilever array induced byairflow force, ASME J. Vib. Acoust. 124 (2002) 26–32.

[13] S. Basak, A. Raman, Hydrodynamic coupling between micromechanical beamsoscillating in viscous fluids, Phys. Fluids 19 (1017105) (2007) 1–13.

[14] M. Kimber, R. Lonergan, S.V. Garimella, Experimental study of aerodynamicdamping in arrays of vibrating cantilevers, J. Fluids Struct. 25 (2009) 1334–1347.

[15] M. Kimber, S.V. Garimella, Cooling performance of arrays of vibratingcantilevers, J. Heat Transfer 131 (2009) 1–8.

[16] M.K. Abdullah, N.C. Ismail, M.Z. Abdullah, K.A. Ahmad, M.A. Mujeebu, F. Husin,Z. Mohd Ripin, Heat transfer enhancement using piezoelectric fan in electroniccooling-experimental and numerical observations, ISI Bilimi ve TeknigiDergisi-journal of thermal science and technology 32 (2012) 1.

[17] T. Acikalin, S.V. Garimella, A. Raman, J. Petroski, Characterization andoptimization of the thermal performance of miniature piezoelectric fans, Int.J. Heat Fluid Flow 28 (2007) 806–820.

[18] J. Petroski, M. Arik, M. Gursoy, Optimization of piezoelectric oscillating fan-cooled heat sinks for electronics cooling, IEEE Trans. Comp. Pack. Technol. 33(1) (2010) 25–31.

[19] M.K. Abdullah, N.C. Ismail, M.Z. Abdullah, M. Abdul Mujeebu, K.A. Ahmad, Z.Mohd Ripin, Effects of tip gap and amplitude of piezoelectric fans on the

M.K. Abdullah et al. / International Journal of Heat and Mass Transfer 55 (2012) 5514–5525 5525

performance of heat sinks in microelectronic cooling, Heat Mass Transfer(2012), http://dx.doi.org/10.1007/s00231-011-0944-z.

[20] H.A. Mohamed, M.Z. Elnaggar, M. Abdullah, Abdul Mujeebu, Experimentalinvestigation and optimization of heat input and coolant velocity of finnedtwin U-shaped heat pipe for CPU cooling. Experimental Techniques, http://dx.doi.org/10.1111/j.1747-1567.2011.00757.x.

[21] Modeling Flows Using Sliding and Deforming Meshes, FLUENT 6.3.26, FLUENTInc. Lebanon, New Hampshire, 2006, Chapter 11.3.

[22] L. Meirovitch, Principle and Techniques of Vibration, Prentice Hall, EnglewoodCliffs, Singapore, 1997.

[23] F.P. Incropera, D.P. Dewitt, Fundamentals of Heat and Mass Transfer, fourthed., John Wiley & Sons, Singapore, 1996. pp. 103–105.

[24] J.R. Taylor, An Introduction to Error Analysis: The Study of Uncertainties inPhysical Measurements, second ed., vol. 94965, University Science Books,Sausalito, CA, 1997.

[25] S.F. Liu, R.T. Huang, W.J. Sheu, C.C. Wang, Heat transfer by a piezoelectric fanon a flat surface subject to the influence of horizontal/vertical arrangement,International Journal of Heat and Mass Transfer 52 (2009) 2565–2570.