Krishna KotaDepartment of Mechanical and

Aerospace Engineering,

New Mexico State University,

P. O. Box 30001/MSC 3450,

Las Cruces, NM 88003-8001

e-mail: kkota@nmsu.edu

Ludovic Burtone-mail: ludovic@gatech.edu

Yogendra Joshie-mail: yogendra.joshi@me.gatech.edu

Microelectronics and Emerging

Technologies Thermal Laboratory,

The George W. Woodruff School

of Mechanical Engineering,

Georgia Institute of Technology,

771 Ferst Drive NW,

Atlanta, GA 30332-0405

Performance of an Air-CooledHeat Sink Channel WithMicroscale Dimples UnderTransitional Flow ConditionsThe objective of this effort is to pursue artificial microscale surface roughness features inthe form of dimples, on the walls of an air-cooled heat sink channel, as a passive optionto energy-efficiently augment heat transfer in forced convection flows. High fidelity nu-merical simulations were employed for realizing an optimized dimple configuration andto comprehend the behavior of microsized dimples under high velocity (�17 m/s) transi-tional flow conditions. Fully developed flow simulations were performed, and design ofexperiments with response surface methodology was employed for the numerical optimi-zation. The results showed �30% heat transfer improvement and �15% pressuredrop increase in the fully developed region compared to a smooth-walled channel.Practicability of manufacturing 200 lm deep dimples on a 600 lm thin aluminum fin wasdemonstrated. Experiments were also carried out to assess the performance of the afore-mentioned optimized configuration in a custom built setup in the laboratory, whichshowed up to 10.5% heat transfer improvement and �12% pressure drop increase over acorresponding smooth-walled channel. The above results indicate that the performanceof dimples is allied with the flow development characteristics. In addition, experimentsperformed at Reynolds numbers other than one at which the dimples were optimizedshowed inferior performance showing that application-specific optimization of dimples iscrucial. With further exploration of shape and design parameters, dimples might have thepotential to improve thermal performance passively and form an attractive candidate torealize high-performance air-cooled heat sinks in the future. [DOI: 10.1115/1.4024598]

Keywords: passive heat transfer enhancement, air cooling, transitional flow, microscaledimples, periodic flow, design of experiments, response surface methodology, designoptimization

1 Introduction

With regard to cooling, especially for electronics in the comput-ing and telecommunication industries, the most popular choice isto integrate a fan-driven, air-cooled heat sink into the system. Aircooling offers distinct advantages in that air is ubiquitous, avail-able free of cost, environmentally safe, light in weight, and aneffective dielectric. Therefore, it would help to develop high-performance heat sinks to further the state of the art limits ofcomponent-level air cooling for heat flux applications that aretypically arduous to handle with conventional air-cooled heatsinks without directly opting for complicated liquid coolingtechniques.

Passive cooling enhancements are preferred over active meth-ods owing to their less consumption of parasitic power for/duringimplementation. A multitude of passive options for forced con-vection heat transfer enhancement exist. Some of them include ribturbulators, dimples, bumps, pins, delta wings [1], and wavy walls[2–5], and have been employed for enhancing performance ofboth air and liquid cooling. Of all the passive surface features,dimples are attractive owing to their flow noninvasive nature. Thisfeature of dimples, enables a smaller rise in the pressure drop(or even reduced pressure drop) compared to other surface

modifications depending on the flow regime and operating condi-tions with simultaneous heat transfer augmentation.

Dimples were analyzed for air cooling and optimized in manyprior efforts [6–22]. Numerous conclusions regarding their depthand spacing were also provided. While most of the prior effortsfocused on laminar or turbulent flows, limited focus has been onassessing the performance and flow behavior in dimpled channelsin the transitional regime and for microsized features. Efforts onpassive heat transfer enhancements at meso/microscale for aircooling is garnering recent attention [e.g., 23–27] owing to thedecreasing form factors of heat sinks in next generation highpower and packaging density electronics. While small sizes ofmicro-/mini-sized channels (hydraulic diameter less than 2–3 mm)in compact heat sinks theoretically could make the air flow lami-nar, practical electronic devices typically have obstructions to theflow before it enters the heat sink which might cause a prematureflow transition. Transition might also occur in high velocity flows,often occurring in centrifugal heat sinks which are recently gar-nering attention owing to their compactness and ability to gener-ate high heat transfer coefficients. In addition, it is interesting toobserve the role of dimples as vortex generators in compact heatsinks with narrow flow passages, where there might be little scopefor vortices to form and influence the bulk flow.

Therefore, this work focuses on numerically and experimentallyassessing the performance of dimples by considering demandingoperating conditions of transitional flow with a very high velocity(akin to typical flow conditions in centrifugal heat sinks) and withmicrosized surface features, which will be typical of future air-cooled heat sink designs.

Contributed by the Heat Transfer Division of ASME for publication in theJOURNAL OF HEAT TRANSFER. Manuscript received April 1, 2012; final manuscriptreceived September 28, 2012; published online September 23, 2013. Assoc. SujoyKumar Saha.

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2 Modeling Methodology

The numerical model is a useful tool for observing the interac-tion between dimples and the flow, the physics of which is noteasy to obtain from experiments. The goal of this task was toidentify an optimum passive feature (circular dimple) configura-tion on the walls of a heat sink channel that would enhancethe overall performance (i.e., for the combined increase in heattransfer performance, pressure drop and surface area) under con-stant pumping power condition. For realizing this task, a straight-ened, high aspect ratio, uniform cross-section passage (length¼ 30 mm, height¼ 27.4 mm, wall thickness¼ 0.6 mm, and chan-nel width¼ 0.8 mm) replicating a single, laterally symmetricalflow channel in a large air-cooled heat sink (specifically, a centrif-ugal type heat sink) was considered. The channel dimensions inthe heat sink were chosen based on the application-dependentspace constraints.

The key challenge of this task was to model high velocity tran-sitional air flow (with an application-specific inlet velocity of�17 m/s corresponding to a Reynolds number, Re, of 1650)through the heat sink channel. Based on the description of the gridsizes and types used in prior similar published studies [23–27], avery dense mesh (O(1� 106) for one dimple) is required to rea-sonably capture the small scale local turbulence/mixing and heattransfer (in/around the vicinity of the dimples) that will existaround the Re of interest. This leads to large mesh sizes for simu-lation of flow in the entire channel with many dimples, and is bothtime-consuming to solve and difficult to be tackled by physicalmemory in most computers including small-sized clusters. There-fore, the following simplifications were implemented to handlethe mesh size problem.

First, the flow was assumed to be fully developed so thatperiodicity of flow physics in the domain can be utilized and onlya repetitive portion of the channel along its length in the flowdirection can be modeled. Flow behavior in the developing flowregime in the presence of dimples would not be captured by thisassumption but it will significantly help in selecting an optimumdesign reasonably quickly using a realistic mesh size that fallswithin the realm of the problem sizes that a basic computing clus-ter can handle. Second, a dimpled surface was used rather than afull conjugate heat transfer surface (i.e., with fin) to isolate theeffect of fin conduction/efficiency on dimple performance. A con-stant surface temperature (303.15 K) boundary condition wasapplied to the dimpled surface, which was obtained from a differ-ent simulation of heat transfer in the fin for a condition of constantheat flux on its wall. Symmetry in the fin height direction was alsoassumed to further reduce the grid size, and the corner effects inthe channel were neglected owing to the high aspect ratio of thechannels.

In addition to finding an optimum dimple configuration, anotherobjective of this study was to obtain physical insight into themechanisms affecting dimple performance. Therefore, using thesame boundary conditions as above, a controlled comparison ofthe temperature and pressure field between a dimpled surface anda smooth surface of the fin was performed to isolate the flow fea-tures responsible for promoting heat transfer and pressure loss.

Design of experiments (DOE) with response surface methodol-ogy was employed to arrive at an optimum configuration. Thefollowing procedure was implemented.

(1) A second order quadratic model was used for the responsefunction, which is the performance factor [28], PF(Eq. (1)), with interaction terms of the considered responsevariables (xþ, yþ, zþ) defined in Eqs. (2) and (3). Theresponse variables and their ranges were defined aftera careful analysis of manufacturability constraints andresults obtained from the numerical simulations of 30exploratory runs that included various preliminary dimpleconfigurations.

(2) A three-dimensional design space with the center and axialpoints (representing experiments/cases) was formed using

central composite design (CCD) with face centered struc-ture [29]. Owing to the extensive computational nature ofthe problem at-hand, a model that generates less number ofnumerical experiments to be performed is preferable. Thechoice of CCD helped in a reduction in the number ofexperiments compared to a complete three-level factorialdesign and was implemented using the ccdesign function inMATLAB [30].

(3) The model was fitted to the data obtained using numericalsimulations to generate the coefficients (an) of the responsefunction.

PF ¼ NuD=NuS½ �= DPD=DPS½ �ð1=3Þ(1)

PF xþ; yþ; zþð Þ ¼ a0 þ a1xþ þ a2yþ þ a3zþ þ a11xþ2

þ a22yþ2 þ a33zþ2 þ a12xþyþ

þ a13xþzþ þ a23yþzþ (2)

xþ ¼ d=W range: 0:025� 0:5ð Þ;yþ ¼ sc=D range: 2:1� 4ð Þ;zþ ¼ d=D range: 0:2� 0:4ð Þ (3)

where, NuD is the Nusselt number in the channel with dimpledwalls; NuS is the Nusselt number in the channel with smoothwalls; DPD is the pressure drop in the channel with dimpled walls;DPS is the pressure drop in the channel with smooth walls; W isthe channel half-width; d is dimple depth; sc is dimple center-to-center spacing; D is dimple footprint diameter, all in SI units.

The objective function, PF, was obtained by eliminating thecommon term (which is the mass flux ratio) from the expressionsfor heat conductance ratio and frictional pumping power ratiobetween rough (here, dimpled) and smooth channels. Equation (1)shows the definition when the pumping power ratio is set to unity,i.e., a condition of constant pumping power for both the channels.Since Re (and also the hydraulic diameter) was kept constant forboth the dimpled and straight channels, and since the fluid isthe same (and hence the Prandtl number) as well for both thechannels, Nu was directly used in Eq. (1) in this paper instead ofStanton number as defined in Ref. [28]. PF was maximized andthe corresponding set of xþ, yþ and zþ were used as the optimumparameters to define the best possible dimple configuration(geometry and spacing). Based on prior studies [e.g., 16–19], astaggered arrangement of dimples was considered in this studyowing to its capability of providing better vortex interactionwithin dimples compared to an inline arrangement.

CFD modeling of low Re transitional flow was performed usingthe k-x closure for Reynolds averaged Navier–Stokes equationswith shear stress transport correction applied in the near-wallregion. Commercial computational fluid dynamics/heat transfersoftware, FLUENT [31], was used. One unit cell consisting of onehalf-dimple and two quarter-dimples was modeled assuming fullydeveloped flow conditions as described. Figure 1 shows the simu-lation domain with boundary conditions and meshing strategy.The grid independency studies revealed a mesh size of between0.8� 106 to 1� 106 nodes to be sufficient to satisfactorily resolvethe flow and temperature fields. Structured boundary layer mesh-ing was done close to the wall, while hexahedral meshing withfine elements near the wall and coarse elements far from the wallwas done in the fluid region. Very fine boundary layer mesh(�10 lm) (along with under-relaxation) also helped in dissipatingnumerical instabilities associated with this high velocity recircu-lating flow problem.

To capture the small relative changes in pressure and tempera-ture from inlet to outlet, double precision solver was used. It wasfound that the default convergence criteria imposed in the soft-ware for terminating the iterations would yield an incomplete so-lution for most periodic simulations. Therefore, to ensure fullconvergence of the periodic problem, Eqs. (4) and (5) signifying

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constant pressure drop (Pout – Pin) and wall heat transfer coeffi-cient (hwall, for a constant wall temperature boundary condition)for the simulation domain were imposed that are physically inher-ent for fully developed flows.

Pout ¼ Pin þ C1; C1 � constant <10�3 Pa� �

(4)

hwall ¼ C2; C2 � constant <10�3 W=m2 � K� �

(5)

3 Experimental Setup

To demonstrate the practicability of the proposed passivemicroscale surface features, dimple configuration obtainedthrough numerical optimization was machined at the GeorgiaInstitute of Technology on a 600 lm thin aluminum sheet(representative of material and small thickness of a practical fin ina typical heat sink). A 1.45 mm diameter ball end-mill bit wasused for this purpose. A computer numerical control (CNC) millrotating at 3000 rpm with controlled Z/vertical movement wasused to hold and guide the mill bit.

Figure 2 shows the scanning electron microscopy (SEM) imageof a milled dimple. White light interferometry technique was usedto measure the dimple geometric features. The lateral offset of thevalley point from the center of the dimple was found to be lessthan 18 lm for more than 90% of the milled dimples. The foot-print diameter of more than 85% of the dimples was found to bebetween 990 lm and 1.01 mm showing the practicability of realiz-ing the features using a low-cost conventional machining method.

Figure 2 also shows the optimized pattern of dimples machined onthe wall of a fin of a heat sink channel.

Figure 3 shows the experimental setup built for testingthe dimple and smooth-walled channels, each with thefollowing dimensions: length¼ 30 mm, height¼ 27.4 mm, wallthickness¼ 0.6 mm, and channel width¼ 0.8 mm. Air flow wasregulated using a flow control valve at the inlet of the flow meter.A rotameter type flow meter was used, which was connected tothe entrance section of a custom built wind tunnel. A thermocou-ple was placed into the tubing just before the inlet of the massflow meter to measure the inlet air temperature. Pressure wasmeasured at the inlet using a high precision digital pressure gauge(7 – 7000 Pa range; accuracy of 67 Pa), while the outlet condi-tions were maintained at the ambient. Off-the-shelf thin film heat-ers (powered using a DC power supply) were attached to the outersurfaces of the fins (over the thermocouples for measuring thewall temperatures) to supply heat. Thick wool insulation was pro-vided around the channel extending up to the wind tunnel sectionto minimize heat losses from the setup. The ambient conditions atthe channel outlet were isolated using an insulated extension sec-tion to the channel and was done after taking the pressuremeasurements.

The following conditions were maintained/observed for all theexperiments at steady state: Flow rate¼ 22.7 l/min (correspondingto an inlet velocity of �17 m/s), inlet temperature¼ 22 �C(295 K), ambient temperature¼ 22 �C, and power supplied¼ 2.9 W per fin (with an uncertainty of 60.015 W). AWG 40,t-type thermocouples were calibrated and were employed to

Fig. 1 (a) Dimple simulation domain, (b) meshing strategy and boundary conditions, and (c)structured boundary layer mesh near the wall

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measure the wall temperatures (with a maximum uncertainty of60.1 �C). A 95% confidence level was used to specify the uncer-tainty and a minimum sample size of twenty was available for anyof the measured parameters. Appropriate quotient, difference andpower formulae were used to estimate measurement uncertainties[32] wherever applicable, for example, in evaluating the errorpropagation in heat transfer coefficient, which was found to be60.87 W/m2 �K. The measurement error in the pressure dropvalues obtained was found to be 61 Pa.

Significance of thermocouple placement locally within the spanof each dimpled region (with a goal of possibly observing localheat transfer variations) was determined by performing numericalsimulation of a fin with wall heat transfer boundary condition

obtained from prior solution (see Sec. 2) and is shown in Fig. 4. Itwas observed that it is improbable to capture local temperaturevariations using thermocouples near the dimpled regions on thefin owing to the small size of the dimples that results in negligibletemperature gradients across them. Therefore, the location of ther-mocouple tips on the fins was fixed at 13.5 mm in the height direc-tion i.e., on the horizontal centerline and they were placed at5 mm intervals from the inlet of the channel along the flowdirection.

The channel was attached to the outlet of the wind tunnel asshown in Fig. 3. Both the wind tunnel at the exit and the hub/baseof the channel at the inlet consisted of matching openings (equalto the channel cross-section) to enable for a smooth passage offlow at the inlet. All the junctions were completely sealed usinghigh-temperature silicone rubber to prevent any undesirable lea-kages. The mock channel (test-section) itself consisted of a holdermanufactured using stereolithography (SLA) to hold the alumi-num fins and the details are shown in Fig. 5.

Equations (6) and (7) were used to estimate the heat transfercoefficient from the experimental results.

Qs ¼ _mcpðTout � TinÞ (6)

Tf ¼ Tout þ Tinð Þ=2; hw ¼ qs= Tw � Tfð Þ (7)

Since it is computationally intractable to simulate the entire testchannel (as noted in Sec. 2), and since the flow will be stronglythree-dimensional with the presence of dimples, a two dimen-sional model was run simulating a smooth-walled test channelwith similar boundary conditions as in the actual experiments.

Fig. 3 Experimental setup for testing the overall performance of dimples

Fig. 4 Simulation showing negligible temperature gradients inthe vicinity of dimple

Fig. 2 Left SEM image of the milled dimple (�200 lm deep); Right: 200 lm deep dimples milled on a 600 lm thin aluminumsheet in a staggered pattern

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Comparison of temperatures obtained from the two dimensionalnumerical simulation of an ideal case (without heat loss) of thesmooth-walled channel, and the centerline temperatures measuredin the experiments for the corresponding case (shown in Sec. 4)showed that the loss, Qh, in the setup is less than 6% of the inputpower.

4 Results and Discussion

4.1 Design Optimization. Various dimple configurationswere simulated based on the cases generated by the CCD modeland the performance for each case was directly compared withthat of a smooth channel using Eq. (1) to obtain PF. Each of theperiodic simulation took about 72 h on an average to converge. ALinux based computing cluster, in the Data Center Laboratory atthe Georgia Institute of Technology, with 14 parallel dual core64-bit Xeon processors was used to run the simulations. Table 1provides the complete design space with key dimple geometricalparameters, and the performance numbers. Figure 6 shows the

dependence of PF on xþ, yþ and zþ in the considered designspace. A value of �0.96 was obtained for the coefficient of deter-mination (R2) for the curve fit, which was deemed reasonable con-sidering the inherent numerical simulation errors in the analysis.

It was found that a particular configuration of dimples (xþ:�0.5, yþ: 4, and zþ: 0.2) yielded the best overall performance forthe considered application. While xþ showed an optimum value,PF was found to monotonically increase and decrease respectivelywith yþ and zþ. Other variations in the dimple geometrical param-eters within the design space were found to affect the perform-ance, notably in some cases in Fig. 6. This can be ascribed to thedependence of heat transfer augmentation and pressure drop onthe vortex dynamics (both interaction and intensity), which in turndepend on the flow regime of operation as well as the flow veloc-ity within a particular regime. For example, vortex interaction fora particular flow velocity depends on the dimple geometrical fea-tures (relative depth and spacing). Similarly, for a particular opti-mized dimple configuration, changing the flow velocity couldalter the vortex interaction mechanism (discussed again inSec. 4.3). Hence, it is desirable to perform an application-specificoptimization for selecting the configuration of dimples that pro-vide a beneficial overall performance. In general, from Table 1, itis evident that both heat transfer coefficient and pressure dropwere proportional to the roughness of the surface, here, character-ized by the number of dimples. For dimples characterized by asmall yþ and D (cases with more number of dimples), significantimprovement in heat transfer performance was observed butaccompanied by an undesirable pressure loss. From the analysisof results (for estimating PF) in Table 1, it was observed that theoverall performance is more sensitive to pressure drop than heattransfer coefficient, i.e., an increase in the pressure drop affectsthe performance more compared to an equivalent augmentation inthe Nusselt number. This finding also suggests the importance ofchoosing an appropriate numerical model based on the prevalentflow regime.

Table 1 Parameter and result data for the DOE cases

xþ (¼d/W) yþ (¼sc/D) zþ (d/D) d (lm) D (lm) hwall (W/m2 � K) DP/m (103 � Pa/m)

0.2625 4 0.3 105 350.00 110.5 16.40.5 2.1 0.4 200 500.00 113.8 14.10.025 2.1 0.2 10 50.00 256.0 175.20.025 4 0.2 10 50.00 229.7 117.00.025 4 0.4 10 25.00 297.7 233.20.2625 2.1 0.3 105 350.00 102.6 20.60.5 3.05 0.3 200 666.67 105.2 16.20.5 4 0.2 200 1000.00 104.7 8.00.2625 3.05 0.4 105 262.50 114.2 23.10.2625 3.05 0.2 105 525.00 105.7 13.80.5 4 0.4 200 500.00 108.3 14.00.2625 3.05 0.3 105 350.00 115.2 20.60.5 2.1 0.2 200 1000.00 107.6 16.90.025 2.1 0.4 10 25.00 544.7 4699.00.025 3.05 0.3 10 33.33 491.0 3844.1

Fig. 5 Test-section with SLA fabricated holders and dimpledfins

Fig. 6 Response function (PF) trend

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Another key observation from the analysis is that, in the consid-ered space of dimple design parameters under the transitional flowconditions, dimple depth relative to the channel width is a crucialfactor in governing the effectiveness of dimples. Shallow dimpleswere found to generate vortices that are incapable of affecting themainstream fluid flow, resulting in only a marginal improvementin heat transfer compared to a smooth channel without dimples.But as discussed before, shallow dimples that are sparsely spacedwere found to provide better overall performance owing to adecrease in the number of dimples resulting in a reduction in thepressure drop compared to configurations with large number ofdimples. The resulting dimple dimensions of the optimum config-uration were as follows: d¼ 200 lm, sc¼ 4 mm, and D¼ 1 mm.With these dimensions, a total of 84 dimples arranged in a stag-gered configuration were found to fit on a wall of the consideredheat sink channel.

For validating the numerical model in the high velocity transi-tional flow regime, a simulation of flow in a smooth channel(which is not computationally as intense as a dimpled channel)was performed for comparison with experimental results. A devel-oping flow simulation was also performed to verify the model forsimulating flow in the dimpled channels and the model wasfound to satisfactorily match the measured results (discussed inSec. 4.3). From the decent matching obtained between the simula-tion and experimental results, it can be concluded that modelingtransitional flow conditions (occurring even without dimples dueto possible flow instabilities occurring at the inlet of the test-sec-tion) were reasonable. Therefore, a laminar flow assumption fornumerical simulations (especially with surface features like dim-ples), if not appropriate, might result in an inaccurate predictionof pressure; drop and hence, possible over-prediction of overallperformance.

4.2 Performance Assessment Using Numerical Simulation.Figure 7 shows the Nusselt number enhancement at the exits ofthe dimples for the optimum case corresponding to the values ofxþ, yþ, and zþ (shown in Fig. 6). It was noted that the localNusselt number values are lowest in the upstream halves of thedimples, which are located in a region of recirculating air flow,where convection velocities in the flow located adjacent to thesurface are very low. Local Nu then increase progressively withstreamwise distance along the dimpled surface. The improvementin the local Nu at dimple downstream locations and on the flatsurfaces at the exits of the dimples can be attributed to the bound-ary layer reattachment and local vortex generation.

Figure 8 shows the recirculation of the velocity vectors and theassociated mixing of flow within the dimple. It can be observedthat large flow separation occurs at the inlet of the dimple, whichis more specific to the high velocity flow conditions. Therefore,the extent of the separation zone, shear layer reattachment lengthand flow interaction between dimples, all depend on the flow

velocity as well (as noted in Sec. 4.1) in addition to the flow re-gime. Figure 9 shows the decrease in local pressure because offlow recirculation at the dimple inlet and increase in local pressureat the dimple exit due to streamwise vortex generation.

Another observation from the results (e.g., Fig. 7) is the mini-mal vortex interaction between dimples in this case, which impliesweak local vortex strength. For the optimum configuration, up to30% heat transfer improvement in the fully developed region wasobserved with the presence of dimples compared to a smoothchannel. Since, it is well known that heat transfer improvement ininternal flows is difficult to obtain under fully developed condi-tions; the result is remarkable especially considering the passivenature of the enhancement features. Therefore, it can be con-cluded that, with further optimization based on shape, dimpleshave the potential to improve thermal performance in the transi-tional flow regime and form an attractive candidate to augmentheat transfer in the fully developed region. Prior literature hasindicated that oval dimples (with major axis aligned perpendicularto the flow) facilitate in achieving better performance compared tocircular dimples [27]. Circular dimples were considered in thepresent study owing to their simplicity in manufacturing com-pared to other complicated shapes; and hence, provide scope forpracticality of demonstration.

Since dimples consume solid fin material to implement, fin effi-ciency (that was isolated from the performance analysis of dim-ples) was also estimated. Applying a constant heat transfercoefficient to the fin surface (obtained from the periodic flow sim-ulation of dimples as described before) and a constant heat flux atthe base of a fin helped in the calculation of fin efficiency. Alumi-num was assumed as the fin material. The presence of dimples(based on the optimized configuration) on the fin was found tolower its conduction efficiency by less than 5% compared to asmooth fin (without dimples).

4.3 Performance in Bench-Scale Experiments. Temperaturemeasurements in all the experiments were made after allowing

Fig. 7 Enhanced local wall Nusselt number at dimple exits

Fig. 8 Velocity (in m/s) vectors showing secondary flow in thedimple

Fig. 9 Local pressure (in Pa) rise at dimple exit

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sufficient time (usually after one hour) for the system to reach asteady state. Both smooth and dimpled fins consisted of dedicatedSLA holders, which enabled convenient switching of the channelsat the wind tunnel outlet for performance comparison. Figure 10shows the measured wall temperatures of the smooth and dimpledchannels. Temperature profile obtained from the simulation of asmooth channel was also plotted in the figure for comparison withexperiments. It must be noted that performing numerical simula-tion of the entire dimpled channel with 84 dimples (with �5� 106

mesh elements for each periodic dimple domain) was almostimpossible using the available computing resources and hence

could not be plotted in the figure. Therefore, a developing flowsimulation was performed in the periodic domain of the optimumdimple configuration (sc¼ 4 mm) for comparison with experi-ments (Fig. 11). The extrapolated air inlet temperature obtainedfrom the experiments was found to satisfactorily match the corre-sponding value in the simulation. In addition, the slopes of thetwo wall temperature curves in Fig. 11 also compared reasonablywell instilling confidence in the numerical model.

It was observed from the data in Fig. 10 that dimples keep thewall almost 2.2 �C cooler than a smooth wall without dimples. Animprovement of �10.5% in the wall heat transfer coefficient (asagainst a numerically predicted value of 30% in the fully devel-oped region) was observed while pressure drop increased by�12%, which corresponds to an overall performance gain(Eq. (1)) of �6.5%. This shows that performance of dimples isalso dependent on the flow development characteristics. While,the effect of dimples on heat transfer is less significant in thedeveloping flow, it can be notable in the fully developed flowowing to the local flow disturbances caused by dimples which areotherwise absent (in smooth channels). This effect can also beunderstood by comparing the slopes of the curves in Fig. 10 andby observing the local wall Nu distribution (shown on the rightsymmetry face; refer to Fig. 1(b)) for a dimpled wall in Fig. 12.While Nu is a constant for a smooth channel under fully devel-oped flow conditions, it is evident from the figure that Nu showedan increase at the dimple downstream locations. This localincrease in Nu as a result of boundary layer separation andreattachment is periodic; and thus, proliferates resulting in a con-siderable improvement in the overall heat transfer performance. Inthe developing flow regime, where the Nu for a smooth channel isalready substantial, the local vortex formation at the dimple exits(for a dimpled channel) only might contribute to a marginal heattransfer augmentation.

Since it was predicted through numerical simulations thatflow velocity might govern the vortex strength and interactionbetween dimples, experiments were performed at Re other than1650. The results are plotted in Fig. 13. It is evident from theplot that performance of dimples suffers at other Re. The differ-ence between the wall temperature curves for the smooth anddimpled channels was found to be maximum (�2.2 �C) at theoriginal Re of 1650 under which the geometry was optimized.Key experimental results as a function of flow Re are given inTable 2. PF was estimated from the performance numbers inTable 2 and plotted as a function of flow Re in Fig. 14. It canbe seen that even though PF is not a strong function of Re(considering the scale of the y-axis), it still showed a peak atRe of 1650 and a decrease of up to 2%–7% (compared to themaximum value) at other Re.

Fig. 10 Measured wall temperatures; x is the axial location inthe flow direction

Fig. 11 Comparison of wall temperature profile obtained fromthe numerical simulation and experimental results for the dim-ple walled channel; experiment: wall temperature 5 321.26 K atx 5 0, simulation: wall temperature 5 321.55 K at x 5 0

Fig. 12 Local wall Nu plotted on the right symmetry face (see Fig. 1)

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5 Conclusions

Three-dimensional numerical simulations and experiments ofhigh velocity, transitional flow through a dimpled channel wereconducted, reminiscent of conditions in future high-performanceair-cooled heat sinks (e.g., centrifugal heat sinks). Ease of manu-facturability and implementation of microscale dimples on thinheat sink fins (200 lm depth and 1 mm footprint diameter dimpleson a 600 lm thin aluminum fin) was also demonstrated in thepaper. Geometry optimization was performed numerically usingdesign of experiments with response surface analysis, andthe optimum geometry was found to be application-dependent.For the best configuration of dimples found in this study, an over-all performance improvement (considering the simultaneousimprovement in heat transfer coefficient, pressure drop and

surface area) of �6.5% (under the condition of constant pumpingpower) was observed compared to a smooth channel. The follow-ing key conclusions could be drawn from the paper:

(a) It was found that the performance of dimples, in addition todepending on the flow regime, also depends on the velocityand the flow development characteristics. Here, dimples inaerodynamically fully developed flow region were found toyield better thermal performance compared to those in thedeveloping region.

(b) Under the considered transitional flow operating conditions(Re �1650) in a narrow heat sink channel (0.8 mm wide,27.4 mm tall, and 30 mm long) with a high inlet flow veloc-ity (17 m/s), dimple depth relative to the channel width wasfound to be a key design parameter that governs the overallperformance.

(c) In addition, dimple depth and spacing also affect the per-formance, especially with their impact on the pressuredrop, and vortex strength and interaction. A right selectionof these parameters is crucial to reap the maximum benefitof using dimples on the fins/walls of heat sinks.

(d) In addition to the practical conditions surrounding electron-ics, it was observed that dimples themselves will also resultin premature flow transition in internal flows and must beconsidered during simulations for an accurate performanceprediction.

(e) Under the considered flow conditions, performance of dim-ples was found to be more sensitive to pressure drop thanheat transfer coefficient.

(f) Unlike flow through dimpled channels in the laminarregime where the pressure drop could be only slightlyhigher (or even lower) compared to a smooth-walled chan-nel, or in the fully turbulent regime where significant heattransfer enhancements could be obtained, optimization ofdimples and obtaining considerable overall performanceimprovements in the transitional regime is an arduous(though not impossible) task. This difficulty is compoundedby the fact that future compact, air-cooled heat sinks willhave very narrow channels with microsized dimples, whichusually affect the flow only weakly/locally.

Acknowledgment

This material is based upon work supported by the DARPAunder Contract No. W31P4Q-09-C-0067. The authors wish toacknowledge Dr. Thomas Kenny, Program Manager at DARPAMTO, for funding the work through the MACE program. Thanksto Dr. Scott Kaslusky and Brian St. Rock at the United Technolo-gies Research Corporation (UTRC) for participating in numeroustechnical discussions which were useful in laying the scope of thiswork. Special thanks to John Whiton of UTRC for providing help-ful suggestions during numerical modeling; to Dr. Pablo Hidalgoand Professor Ari Glezer at the Georgia Institute of Technologyfor providing drawings for the wind tunnel components used inthe experiments; to Dr. Florian Herrault, Dr. Chang-Hyeon Ji, andProfessor Marc Allen at the Georgia Institute of Technology formeasuring the geometrical features of the dimples.

Nomenclature

A ¼ fin area, m2

D ¼ dimple footprint diameter, md ¼ dimple depth, m

hw ¼ average heat transfer coefficient on the wall, W/m2 �Khwall ¼ average heat transfer coefficient on the surface of the

dimpled wall in the numerical simulations, W/m2 �K_m ¼ air mass flow rate, kg/s

Nu ¼ Nusselt numberP ¼ pressure, Pa

PF ¼ performance factor

Fig. 13 Experimentally measured wall temperatures ofdimpled and smooth channels at various flow Re

Table 2 Key experimental results as a function of flow Re

Average heat transfercoefficient (W/m 2 �K)

Pressuredrop (Pa)

ReDimpledchannel

Smoothchannel

Dimpledchannel

Smoothchannel

2063 163.55 150.97 532 4491856 161.52 148.45 460 4001650 156.92 142.33 385 3471444 149.08 139.96 330 2971238 136.75 131.06 270 2451031 133.42 129.19 230 211825 125.86 123.44 188 173

Fig. 14 Performance of a dimpled channel (as characterized byPF obtained from experiments) a function of flow Re

111005-8 / Vol. 135, NOVEMBER 2013 Transactions of the ASME

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Q ¼ heat input measured at the power supply, WQh ¼ heat loss from the channel setup, WQs ¼ heat supplied (¼ (Q – Qh)), Wqs ¼ heat flux (¼ Qs/A), W/m2

Re ¼ Reynolds numbersc ¼ dimple center-to-center spacing, m

Tw ¼ average wall Temperature, KTin ¼ fluid inlet temperature, K

Tout ¼ fluid outlet temperature, KTf ¼ average fluid temperature, KW ¼ channel half-width, mx ¼ axial location on the fin along the flow direction, m

xþ ¼ nondimensional response variableyþ ¼ nondimensional response variablezþ ¼ nondimensional response variable

Subscripts

D ¼ dimpled channelin ¼ inlet

out ¼ outletS ¼ smooth channel

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