TCPT-2006-096.R2: Micro Scale pin fin Heat Sinks \u0026#x2014;Parametric Performance Evaluation Study

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IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES 1

TCPT-2006-096.R2: Micro Scale pin fin Heat Sinks—Parametric Performance Evaluation Study

Ali Kosar and Yoav Peles

Abstract—A parametric study of heat transfer and pressure dropassociated with forced flow of deionized water over five micro pinfin heat sinks of different spacing, arrangements, and shapes wasconducted experimentally. Nusselt numbers and friction factorswere obtained over Reynolds numbers ranging from 14 to 720. Thethermal and hydraulic results were obtained to evaluate and com-pare the heat sinks performances at fixed mass flow rate, fixed pres-sure drop, and fixed pumping power. Two distinct regions of theNusselt number dependency on the Reynolds number separatedby a critical Reynolds number have been identified for unstream-lined pin fin devices while the streamlined device showed no slopechange. The effects of spacing, shape of pin fins, and arrangementon friction factor and heat transfer were in agreement with ex-isting literature. The results indicate that utilizing streamlined pinfin heat sinks can significantly enhance the thermal-hydraulic per-formance of the heat sink, but only at moderate Reynolds numbers.

Index Terms—Cross flow, heat sink, microelectromechanical sys-tems (MEMS), pin fin, single-phase, thermal-hydraulic.

NOMENCLATURE

Base area ( surface area without pin fins) m .

Fin surface area m .

Fin cross-sectional area m .

Minimum cross-sectional area m .

Planform area (surface area of silicon block) m .

Total heat transfer area ( ) m .

Specific heat at constant pressure kJ kg C .

Pin fin diameter, vertical projected length of pinfin m.

Friction factor.

Mass velocity based on minimum cross-sectionalarea kg m s .

Manuscript received June 1, 2006; revised October 20, 2006. This work wassupported by the Office of Naval Research through the Young Investigator Pro-gram under Contract N00014–05–1–0582 and by the Cornell NanoScale Fa-cility (a member of the National Nanotechnology Infrastructure Network) whichis supported by the National Science Foundation under Grant ECS-0335765.Recommended for publication by Associate Editor R. Culham upon evaluationof the reviewers comments.

A. Kosar is with the Department of Mechatronic Engineering, Sabancı Uni-versity, Istanbul 34956, Turkey.

Y. Peles is with the Department of Mechanical, Aerospace and Nuclear En-gineering, Rensselaer Polytechnic Institute, Troy, NY 12180 USA (e-mail: [email protected]).

Digital Object Identifier 10.1109/TCAPT.2007.906334

Average heat transfer coefficient at a definite flowrate W m C .

Channel height, fin height m.

Average heat transfer coefficient at a definite heatflux W m C .

Thermal conductivity of the fin (Silicon) Wm C .

Thermal conductivity of the fluid W m C .

Thermal conductivity of the Silicon block Wm C .

Channel length m.

Constant.

Number of data points at fixed flow rate.

Number of data points.

Mass flow rate kg s .

Fin parameter.

MAE Mean absolute error.

Number of pin fins in a single row.

Nusselt number.

Average Nusselt number at a definite Reynoldsnumber.

Average Nusselt number at a definite heat flux.

Electrical power W.

Prandtl number.

Heat flux W cm .

Volumetric flow rate m s .

Heat loss W.

Electrical resistance .

Convective part of total thermal resistance KW .

Thermal resistance due to heating of fluid K W .

Total thermal resistance K W .

Dimensionless total thermal resistance.

Reynolds number based on the vertical projectedlength.

1521-3331/$25.00 © IEEE


2 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES

Longitudinal pitch m.

Transverse pitch m.

Thickness of the silicon block m.

Temperature C.

Average surface temperature C.

Exit temperature C.

Average heater surface temperature C.

Inlet temperature C.

Channel width m.

Greek:

Pressure drop kPa.

Fin efficiency.

Pumping power W.

Viscosity kg m s .

Density kg m .

Subscript:

Ambient.

Average.

Critical.

Exit.

Fluid.

Fin.

Inlet.

Index.

Surface.

I. INTRODUCTION

RESEARCH efforts aimed at developing prodigious ad-vancement of the current state of affairs concerning

cooling of ultra high power electronic components utilizingmicroelectromechanical systems (MEMS) technology are cur-rently being conducted in academia and industry. As part ofthese efforts, micro pin fin heat sinks are being studied [1], [2].Micro pin fins formed from various cross-sectional shapes canprovide increased surface area and enhanced heat transfer coef-ficient with respect to microchannel based heat sink. However,the pressure drop required to deliver the flow can adverselyaffect the potential benefit of such cooling schemes. Therefore,performance evaluation criteria must be developed or adoptedfrom conventional scale to fully assess the enhancement capa-bilities of various micro scale pin fin heat sinks.

In conventional scale, numerous recent studies on heattransfer and/or pressure drop of cross flow, jet impingement,and pool boiling have been conducted. These investigationshave demonstrated the importance of different factors such asthe Reynolds number, thermophysical properties of the flow,and various geometrical parameters in dictating the Nusselt

number and the friction factor. In general, densely packed andlong pin fins are desirable to enhance heat transfer for both jetimpingement and cross flow. However, elevated pressure dropis required to propel the flow through densely populated pinfin heat sinks, and it has been found that the thermal-hydraulicperformance is dependent on both the evaluation criterion [1],[3], [4] used in the performance analysis and the experimentalconditions [5] (e.g., dimensions of the pin fin heat sink).

Kosar and Peles [1] and Kosar et al. [4] have shown that undervarious conditions, pertaining to micro scale heat sinks, avail-able large scale correlations provide poor prediction of the heattransfer coefficient and friction factor. Besides, microfabrica-tion technology presents an effective means to form heat sinksfrom unconventional shapes for which available data are verylimited. Therefore, in the current scenario it is indeed ambitiousto presume that available large scale correlations and the lim-ited data available on micro scale systems [1], [4] are adequateto fully assess the thermal and hydraulic characteristics of microheat sinks. Furthermore, adaptation of large scale performanceevaluation criteria of heat exchangers [6] to micro systems hasto be implemented in order to fully evaluate and compare thethermal-hydraulic performance of heat sinks made of silicon.The current report presents and discusses experimental resultsof heat transfer and pressure drop of cross flow over five microscale pin fin heat sinks formed from a range of pin fin shapes,spacing, and arrangements. The data are then used to obtain thethermal resistance and compare the thermal-hydraulic perfor-mance of the heat sinks based on three criteria, namely, totalthermal resistance at fixed mass flow rate, at fixed pressure drop,and at fixed pumping power. This kind of performance evalua-tion study on micro scale pin fin heat sinks is performed for thefirst time.

II. DEVICE OVERVIEW AND MICROFABRICATION

PROCESS FLOW

A. Device Overview

Fig. 1 displays a CAD model of a micro pin fin sink. De-ion-ized water is forced through the inlet plenum into the pin fins,absorbs the heat dissipated by the heater residing on the oppo-site side [Fig. 1(b)], and leaves the heat sink through the exitplenum. The heater also serves as a thermistor for temperaturemeasurements. In order to minimize ambient heat losses, an airgap is formed on the two ends of the side walls, and an inletand exit plenum, 4 mm long each, are etched on the thin siliconsubstrate ( 147 m). A Pyrex cover seals the device from thetop and allows flow visualization. Pressure taps are created atthe inlet and exit of the device.

Five different micro pin fin heat sinks were tested in the cur-rent study and are given in Fig. 2 and Table I. The geometricaldesign of the pin fins provides a range of shapes, configurations(inline/ staggered) and spacings (densely/ sparsely populated).The pin fin shapes can be divided into two categories; stream-lined (e.g., hydrofoil) shapes, and pins formed from objects thatpromote flow separation (e.g., circular). To balance between therequirement for very high pressure drops due to frictional losses(very low Reynolds numbers) with diminishing hydraulic diam-eter on one hand, and to promote high heat transfer coefficientand increased surface area on the other hand, the vertical pro-jected length of all devices is 100 m (Fig. 2). To maximize


KOSAR AND PELES: MICRO SCALE PIN FIN HEAT SINKS 3

Fig. 1. (a) CAD model of a micro pin fin heat sink (1CD), (b) heater dimensions(dimensions in �m), and (c) top view of the device (dimensions in �m).

Fig. 2. Geometry and arrangements of pin fins employed in the current study(the vertical projected length of a micro pin fin is 100 �m for all devices).

the pin fin height (increase heat transfer area) while maintainingthe structural integrity of the devices, the pin fin height is set to243 m.

B. Microfabrication Process Flow

The micro scale device is micromachined on a polisheddouble-sided n-type 100 single crystal silicon wafer em-ploying techniques adapted from IC manufacturing.

First, a 1 m thick high quality oxide film is deposited on bothsides of the silicon wafer to protect the bare wafer surface duringprocessing, and serves as an electrical insulator. The heater andthe vias are then formed on the backside of the wafer (on top ofthe thermistors) by sputtering. A 70 thick layer of titaniumis initially deposited to improve adhesion characteristics, whichis followed by sputtering a 1 m thick layer of aluminum con-taining 1% silicon and 4% copper. Subsequent photolithographyand concomitant wet bench processing create the heater on thebackside of the wafer. A 1 m thick plasma enhanced chem-ical vapor deposition (PECVD) oxide is deposited to protect theheater during further processing.

Next, the micro pin fins of the desired geometry are formedon the top side of the wafer. The wafer undergoes a photolithog-raphy step and an oxide removal process (reactive ion etching)to mask certain areas on the wafer which are not to be etchedduring the deep reactive ion etching (DRIE) process. Thewafer is subsequently etched in a DRIE process, and siliconis removed from places not protected by the photoresist/oxidemask. The DRIE process forms deep vertical trenches on thesilicon wafer with a characteristic scalloped sidewall pos-sessing a peak-to-peak roughness of 0.3 m. A profilometerand scanning electron microscope (SEM) are employed tomeasure and record various dimensions of the device.

The wafer is flipped and the backside is then processed tocreate an inlet, outlet, side air gap, and pressure port taps forthe transducers. Photolithography followed by a buffer oxideetching (BOE) (6:1) oxide removal process is carried out tocreate a pattern mask. The wafer is then etched-through in aDRIE process to create the fluidic ports. Thereafter, electricalcontacts/pads are opened on the backside of the wafer by per-forming another round of photolithography and RIE processing.Finally, the processed wafer is stripped of any remaining re-sist or oxide layers and anodically bonded to a 1-mm thick pol-ished pyrex (glass) wafer to form a sealed device. After the suc-cessful completion of the bonding process, the processed stackis die-sawed to separate the devices from the parent wafer.

The device is packaged by sandwiching it between two plates.The fluidic seals are forged using miniature “o-rings,” while theexternal electrical connections to the heater are achieved frombeneath through spring-loaded pins, which connect the heaterand thermistors to electrical pads residing away from the mainmicrochannel body. Fig. 3 presents a summary of the processflow outlined above.

III. EXPERIMENTAL TEST SETUP AND PROCEDURE

A. Experimental Test Setup

The setup, shown in Fig. 4, consists of the flow loop sec-tion, instrumentation, and a data acquisition system. The testsection includes the MEMS based micro pin fin devices and itsfluidic and thermal packaging module (Fig. 5), which deliversthe working fluid to the microchannels and allows access to thepressure transducers.



TABLE IDEVICES TESTED IN THE CURRENT STUDY

Fig. 3. Micro pin fin heat sink fabrication process (not to scale).

The main flow loop contains the micro pin fin device, a pulse-less gear pump, and flow meter. The micro heater was con-nected to a power supply with an adjustable dc current to pro-vide power to the device. Prior to the experiments, calibrationof the heater temperature was done by placing the device in anoven, heating it at the desired temperature, recording the corre-sponding resistance value, and establishing the resistance-tem-perature curve for the heater. The calibration curve for device3H is depicted in Fig. 6. Resistance, pressure, and flow mea-surements were taken at a fixed flow rate in the loop. The elec-trical power was supplied to the device with an INSTEK pro-grammable power supply, while electrical current and voltagewere measured using a HP3457A digital multimeter. An HNPMikrosysteme micro annular gear pump and a 180 Series Mi-cropump annular gear pump capable of generating flow rates upto 18 ml/min and 145 ml/min, respectively, were used to propelthe liquid from a reservoir through the MEMS devices at var-ious flow rates, while the inlet temperature was measured by anOmegaette HH308 Type K Thermometer. Inlet and exit pres-sures were measured via PX303- Omega pressure transducers ofvarious ranges depending on the operating conditions. OmegaF-111, F-112, and F-113 flow meters were used for flow rate

measurements. Pressure and flow rate data were acquired to-gether with the voltage and current data and were transferred tothe spreadsheet file for data reduction.

B. Experimental Procedure

The deionized water flow rate was fixed at the desired value,and experiments were conducted after steady flow conditionswere reached at atmospheric exit pressure and ambient roomtemperature. To measure pressure drops, the flow rate is in-creased in a controlled manner, and pressure and flow ratedata are collected from pressure and flow sensors through theLabView interface at ambient temperature and stored for furtheranalysis. For the heat transfer measurements, first, the electricalresistance of the device was measured at room temperature.Thereafter, voltage was applied in 0.5 V increments to theheater, and the current/voltage data were recorded once steadystate was reached. Flow visualization through the high-speedcamera and microscope complements the measured data. Theprocedure was repeated for different flow rates for each device.

To estimate heat losses, electrical power was applied tothe test section after evacuating the water from the test loop.Once the temperature of the test section became steady, thetemperature difference between the ambient and test sectionwas recorded with the corresponding power, so that the plot ofpower versus temperature difference was generated to calculatethe heat loss ( ) associated with each experimental datapoint. Heat loss calibration curve and heat losses for 112in device 1CD are shown in Fig. 7(a) and (b), respectively.

IV. DATA REDUCTION AND UNCERTAINTIES

This section consists of two subsections. The first subsectionpresents the hydrodynamic and the thermal analysis of micropin fin heat sinks. Important parameters for the evaluation ofthermal hydraulic performance are introduced and expressed.The second subsection discusses uncertainties in experiments.

A. Data Reduction

The data obtained from the voltage, current, flow rate, andpressure measurements were reduced to the average walltemperatures, heat transfer coefficients, Nusselt numbers andsingle-phase friction factors. The electrical input power andresistance were calculated using the measured voltage andcurrent values. The average heater temperature was calculatedusing the electrical resistance. Under 1-D steady state heat



Fig. 4. Experimental setup.

Fig. 5. Device package.

conduction assumption, the surface temperature at the base ofthe micro pin fin device is expressed as

(1)

The heat transfer coefficient at a given heat flux for a fixedflow rate was obtained using Newton’s law of cooling jointlywith 1-D steady-state adiabatic tip fin equation as follows:

(2)

Fig. 6. Heater electrical resistance–temperature linear calibration curve of de-vice 3H.

where , , and.

Equation (2) was solved iteratively to obtain . The Nusseltnumber corresponding to each net input power at a fixed flowrate was calculated using the average heat transfer coefficientobtained from (2) as

(3)

An average value of the heat transfer coefficient and Nus-selt number for a fixed Reynolds number was then calculated



Fig. 7. (a) Heat loss calibration curve. (b) Heat loss curve for Re = 112 ofdevice 1CD.

according to

(4)

(5)

( number of data at a fixed flow rate).The friction factor, , is a nondimensional form of the pres-

sure drop and is defined as

(6)

where and are the fluid density and number of pin finrows, respectively. Various correlations have been developed topredict the friction factor in conventional [7], [8]–[10] as wellas in micro scale [4] systems, and it was found that dependson the pin fin configuration (in-line/ staggered)/spacing/shape,and Reynolds number.

The pumping power ( ) is another hydrodynamic character-istic that is commonly sought in the design of heat exchanger,and is expressed as the product of the pressure drop and the vol-umetric flow rate ( )

(7)

The heat transfer performance of heat sinks are commonly ex-pressed in terms of their total thermal resistance in C W.

TABLE IIEXPERIMENTAL UNCERTAINTIES

To enhance heat transfer should be minimized. The totalthermal resistance ( ) can be expressed [11], [12] as the sumof three components that account for conduction through thesilicon substrate excluding the fin region ( ), convectionto the flow ( ), and thermal resistance due to an increasein the flow temperature as it flows through the fins and absorbsheat ( ). , and are expressed as

(8)

(9)

(10)

( total heat transfer area).To enhance the thermal-hydraulic performance should

be minimized.

B. Uncertainties

The uncertainties of the measured values, given in Table II,were obtained from the manufacturer’s specification sheets,while the uncertainties of the derived parameters were calcu-lated using the method developed by Kline and McClintock[13], and the comparison of the experimental data with theorywas accomplished through the mean absolute error (MAE),defined as

MAE (% ) (11)

( number of total data points).

V. RESULTS AND DISCUSSION

A. Thermal Characteristics

Average Nusselt number as a function of the Reynoldsnumber for all five devices is shown in Fig. 8. The character-istic trends of the current devices are generally in accordancewith large scale findings in terms of the effect of pin fin shape,spacing and configuration. Nonetheless, previous results per-formed on micro scale pin fin devices have shown that theheat transfer coefficients are not well predicted by large scale



Fig. 8. Nusselt numbers of micro pin fin devices.

correlations, particularly at low Reynolds numbers ( 100)and for intermediate height-to-diameter pin fin bundles [1].

Two distinct regions of the Nusselt number dependency onthe Reynolds number are apparent for four of the devices (1CD,2CLD, 4C, 5R) while device 3H showed consistent trend overthe entire Reynolds number range. This deviation manifests it-self at a critical Reynolds number, which varies between 35 and205 depending on the pin fin shape (Table III). is ob-tained by taking the best curve fits for the low data and forhigh data and marking the intersection point. The Reynoldsnumber corresponding to the intersection point is assigned as

. While the values [where is the slope of versus(i.e., )] at Reynolds numbers lower than

are significantly higher than those of large scale correlations, atReynolds numbers higher than the values are general inagreement with those obtained from long tubes [7], [14], [15].Kosar and Peles [1], [16] have attributed such dependency totwo factors: endwall effects and a delay in flow separation inlow aspect ratio and densely populated pin fins. While end-walls should affect all devices indiscriminately, flow separa-tion delay should not affect streamlined pin fin devices. Sincethe dependency of the Nusselt number on the Reynolds numberaffected only devices that promote flow separation (significantdifferent values at Reynolds numbers lower and higher thanthe ), endwall effects do not seem to dominate the tran-sition in the Nusselt number. Thus, flow separation can be as-sumed to control the transition Reynolds numbers. The criticalReynolds numbers for devices 1CD and 4C are in the vicinity of

60, which can be attributed either to the formation of attachedvortices or von Kármán vortex street and/or alternate shedding,which for unconfined and isolated long cylinders are prevalent atReynolds numbers of 4 40 [17], 40 60–100 [18],and 60–100 200 [19], respectively. However, compre-hensive flow visualization or micro particle image velocimetry( PIV) studies are required to fully assess the flow characteris-tics in the vicinity of the critical Reynolds number.

1) Spacing Effect: The effect of pin fin spacing is evidentwhen comparing the heat transfer coefficients of devices 1CDand 2CLD. Heat transfer coefficients of device 1CD are greaterthan for device 2CLD over Reynolds numbers ranging from 30to 112. This is in agreement with the literature for conventionalscale pin fins [20]–[23]. The reason may lie in the pronouncedwake-pin fin interaction in device 1CD. Because of the densespacing, the wake formed downstream a pin fin may interact

TABLE IIIRe AND THE DEPENDENCE OF Nu ON Re FOR EACH PIN FIN DEVICE, m IS

THE SLOPE OF Nu VERSUS Re (i.e., Nu� Re )

Fig. 9. Pressure drop as a function of volumetric flow rate.

with the pin fins in the following row, so that mixing (advec-tion) and heat transfer are enhanced. This is reflected as higherheat transfer coefficients in device 1CD. Since at low Reynoldsnumbers the wake-pin fin interaction moderates, deviations be-tween the Nusselt numbers of the two devices diminish.

2) Shape Effect: Pin fin geometry strongly affects the Nus-selt number. Since the pin fins of device 3H are streamlined,flow separation is suppressed. As a result, the wake formeddownstream of a pin fin is minor (if at all present), and theheat transfer coefficients are lower than for the other pin fin de-vices for Reynolds numbers above 50. The Nusselt numberof the cone shaped pin fin device (4C) increases rapidly withthe Reynolds number. Although, device 4C is sparsely popu-lated (compared to device 1CD), the heat transfer coefficientsare comparable to device 1CD. This is perhaps because the sharppointed regions connecting the semicircle with the triangle partof the pin fin promote flow separation and result in an extendedwake region. A similar argument has been used to relate the in-creased wake region of diamond shape pin fins compared to cir-cular ones [24]. The Nusselt numbers for the rectangular pinfin device (5R) are relatively low. This can be related to largespacing between the pin fins and the device configuration (in-line). As stated in several studies [20]–[23], large spacing be-tween pin fins and in-line configurations result in lower heattransfer coefficients compared to densely populated and stag-gered arrangements.

B. Hydrodynamic Characteristics

The pressure drop-volumetric flow rate demand curve for allfive devices is shown in Fig. 9. As expected the pressure droprequired to propel the flow is significantly lower for the hydro-foil pin fin device than all other staggered devices. The denselypopulated circular pin fin device requires higher pressure dropsthan the more sparsely populated pin fins of device 2CLD.

The friction factors (Fig. 10) are comprised from two com-ponents, one accounting for the drag due to flow separation andthe other stemming from viscous forces. Streamlined objects



Fig. 10. Friction factor as a function of Reynolds number.

tend to have relatively large surface areas, which elevate frictiondrag, while flow separation tends to diminish on these objects.Since form drag gradually dominates the pressure drop with in-creasing Reynolds numbers, the friction factor of the stream-lined pin fin (hydrofoil) diminishes more rapidly than the otherdevices. It should be noted that due to pin-wall interaction, forintermediate pin fin height-to-diameter ratios, such as in the cur-rent study, endwalls significantly affect the friction factor at lowReynolds numbers [4], [24], [25].

The effect of spacing is evident when comparing the fric-tion factors of device 1CD and device 2CLD. Device 1CD haslarger friction factors than device 2CLD, which suggests thatdensely populated pin fins lead to higher friction factors. Thisis in agreement with previous conventional scale [15], [20] andmicro-scale [20] studies. Wakes behind pin fins form due to flowseparation. For densely populated pin fins the wake generateddownstream of a pin fin interacts more rigorously with pin finsin the following row. As a result, friction factors are higher forclosely packed objects.

The friction factor for device 5R is larger than all other stag-gered devices, due to the large surface area of the individualpillar, which increases friction drag. Furthermore, as discussedby Munson et al. [26] and White [27] drag over rectangular pinfins tends to be higher than for circular configurations, whichpromotes an increase in the friction factor. Drag coefficient ofcross flow over circular object is larger than for conical object[27]. Thus, since device 4C and 2CLD have similar pin fin ar-rangement and spacing it is expected that device 2CLD will gen-erate larger friction factors than device 4C. However, Fig. 10shows opposite trend. As discussed in the previous section thepin fins of device 4C promote longer wakes, which results in in-tensified wake-pin interaction and pressure losses leading to anamplification of the friction factor.

C. Thermal-Hydraulic Performance Evaluation

As discussed in the previous sections heat transfer coefficientof flow over streamlined pin fins tends to be lower than for moretortuous objects which promote flow separation and wakes. Onthe other hand, flow over nonstreamlined objects requires sig-nificant increase in the pressure drop to deliver the flow. There-fore, from the practical point of view, independent evaluation ofthe thermal and hydraulic characteristics is not sufficient to fullyprovide guidelines to optimize the performance of heat sink fora particular engineering task. Various performance evaluationcriteria [6] have been utilized to aid the selection of a heat ex-changer. Adaptation of three such criteria is used in the current

Fig. 11. Thermal resistance as a function of mass flow rate.

study. However, it is useful first to present the concept of totalthermal resistance, which is often employed to evaluate the per-formance of micro scale heat sinks [12], [28], [29], [30]. Totalthermal resistance is the sum of three components which ac-count for conduction through the silicon substrate excluding thefin region ( ), convection to the flow ( ), and thermalresistance due to an increase in the flow temperature as it flowsthrough the fins and absorbs heat ( ).

The total thermal resistance of the five pin fin devices testedin this study is evaluated based on three performance categories,namely, for fixed mass flow rate, fixed pressure drop, and fixedpumping power. While comparing the performance of variousheat sink devices it is often desirable to minimize the totalthermal resistance. Therefore, for a specific criterion the devicewhich provides the lowest thermal resistance should be favored.

D. Fixed Mass Flow Rate

Fig. 11 presents the total thermal resistance as a function ofmass flow rate. For a fixed flow rate and the conductionresistance ( ) are independent of the heat sink configura-tion, and the reciprocal of the product solely dictates anydeviations of the total thermal resistance between various de-vices. Since the heat transfer coefficient and the surface area ofthe hydrofoil pin fin device are smaller than the circular pin findevice 2CLD the results favor the circular pin fin heat sink.

The relative importance of the three thermal resistances,the sum of which is the total thermal resistance, is shown inFig. 12 as a function of mass flow rate. For low mass flow rates( 5 10 kg/s), predominates the total thermalresistance. With an increase in flow rate, the dominance of theconvection resistance gradually increases since decreaseslinearly (simple calorimetric balance), while the reduction of

is more moderate since the Nusselt number is correlatedthrough ( is lower than 1 for ). Therefore,the heat transfer coefficient is proportional to , and theconvective thermal resistance has the following proportionalitylaw (assuming the effective heat transfer area is unchanged):

. On the other hand and therefore. Moreover, fin efficiencies of

micro pin fins become smaller with mass flow rate as shown



Fig. 12. Fractions of R , R , and R in R .

Fig. 13. Fin efficiencies of micro pin fin devices.

in Fig. 13. As a result, the total effective heat transfer areadecreases which in turn further increases with respectto . Assuming the thermal conductivity is independent oftemperature the term remains constant at any workingcondition, thus, with increasing mass flow rate, the importanceof the conduction thermal resistance gradually increases (since

and decreases), although it never assumes domi-nance (at least under the conditions tested in the current study).

1) Fixed Pressure Drop: As can clearly be seen in Fig. 14,significant different trends are obtained for fixed pressure dropcompared to fixed flow rate. The hydrofoil-based pin fin deviceoutperformed all other devices, primarily because with a givenpressure drop considerable higher mass flow rates can be pro-pelled through the device. However, with increasing flow rate,

gradually dominates over , which results in mod-eration of the slope at pressure drops higher than

10 kPa. A similar trend is observed for the rectangular pinfin device (5R). Since the tortuous flow path of device 1CDdictates stringent demand for pressure drop, is elevated,

Fig. 14. Thermal resistance as a function of pressure drop.

which in turn magnifies the total thermal resistance. Although,for the more sparsely populated devices (devices 2CLD and 4C)the convective thermal resistance is high the increased flow ratelowers (compared to device 1CD) which is dominated atlow pressure drops. Thus, lower thermal resistances are obtainedfor device 2CLD and 4C compared to device 1CD. However, thedifferences weaken with increasing pressure drop (decreases) which is evident by the steeper slope of thecurve of device 1CD compared to devices 2CLD and 4C. Al-though, not demonstrated in the current study at sufficiently highpressure drops device 1CD should be favored even over the hy-drofoil pin fin device.



TABLE IVBEST PERFORMANCE PIN FIN HEAT SINK AS A FUNCTION OF THE PRESCRIBED OPERATING CONDITION AND PERFORMANCE EVALUATION

Fig. 15. Thermal resistance as a function of pumping power.

Since larger mass flow rates can be obtained for device 2CLDthan for device 4C for a given pressure drop, its is lower.However, device 4C has higher fin efficiency and a higher heattransfer coefficient, which in turn reduces . Apparentlythese two adverse effects are balanced and the total thermal re-sistances of both devices are comparable.

2) Fixed Pumping Power: Fig. 15 shows thermal resistanceas a function of pumping power. At the same pumping power,the mass flow rate is higher for streamlined pin fins. Since forlow flow rate, (and thus, low pumping powers), is thedominant component, streamlined pin fins have superior perfor-mance. However, as pumping power increases, begins topredominate the total thermal resistance. Since is higher

for streamlined pin fins (lower heat transfer coefficient), the dif-ference between un-streamlined and streamlined pin fins dimin-ishes with the increase in the pumping power, and at sufficientlyhigh pumping powers un-streamlined pin fin device (4C) mightoutperform the streamlined heat sink (3H).

As a general remark, it can be stated that the trends at the fixedpumping power are similar to the fixed pressure drop since massflow rates have similar trends at a fixed pressure drop. The re-duced differences between the thermal resistances for the fixedpumping power compared to the fixed pressure drop implies thatdeviations in the thermal resistance of various devices are lesspronounced for the fixed pumping power criterion.

3) Summary of Results for Performance Evaluation Trends:It is evident from the discussion presented in previous sectionsthat the evaluation criteria used in the performance analysis andhydrodynamic conditions impact the device which yields thebest performance. A summary of the trends for various perfor-mance evaluation criteria at different hydrodynamic conditionsis presented in Table IV.

VI. CONCLUSION

Heat transfer and pressure drop experiments of cross flowover five micro scale pin fin heat sinks have been conducted.Three performance criteria, namely, total thermal resistance atfixed mass flow rate, at fixed pressure drop, and at fixed pumpingpower have been used to evaluate the performance of the heatsinks. The main conclusions drawn from this study are as fol-lows.

• The merits of using micro pin fin device are dependent onthe performance evaluation criterion used, as well as on thehydrodynamic conditions. In general, for a fixed pressuredrop and pumping power, utilizing streamlined pin fin heatsinks is favored at moderate pressure drops and flow rate,



while for very high and low pressure drops and flow ratespin fins promoting flow separation should be favored. Forfixed mass flow rate streamlined pin fins provide inferiorperformance.

• Two distinct regions of the Nusselt number dependencyon the Reynolds number separated by a critical Reynoldsnumber are apparent for unstreamlined pin fin deviceswhile the streamlined pin fin device showed no slopechange over the entire Reynolds number range.

• Large spacing between pin fins and inline configurationsresults in lower heat transfer coefficients compared todensely populated and staggered arrangements, which isin agreement with existing literature.

• Micro pin fins having sharp pointed regions generatehigher heat transfer coefficients than streamlined pin fins.This is associated with separation effects mitigated bysharp points as well as extended wake regions, whichincrease the mixing and heat transfer.

• Higher density pin fins and sharp point pins result in largerfriction factors. The latter augment wake-pin interactionand introduce more pressure drop.

REFERENCES

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Ali Kosar received the B.S. degree in mechanicalengineering from Bod-aziçi University, Istanbul,Turkey, in 2001 and the M.S. and Ph.D. degreesfrom the Department of Mechanical Engineering,Rensselaer Polytechnic Institute, Troy, NY, in 2003and 2006, respectively.

He joined the Department of Mechatronics Engi-neering, Sabancı University, Istanbul, in 2007. His re-search interests lie in heat and fluid flow in micro heatsinks. He has been conducting pioneering research onsingle-phase and boiling heat transfer, single-phase

and two-phase pressure drop, critical heat flux (CHF), and cavitation in MEMS-based pin fin and second generation microchannel heat sinks.

Yoav Peles received the Ph.D. degree in mechanicalengineering from the Technion-Israel Institute ofTechnology, Haifa, in 2000.

He then joined the Massachusetts Institute ofTechnology (MIT), Cambridge, to work in the GasTurbine Laboratory (GTL) and the MicrosystemsTechnology Laboratory (MTL), on the micro engineproject. He joined the Department of Mechanical,Aerospace, and Nuclear Engineering, RensselaerPolytechnic Institute (RPI), Troy, NY, in 2002.

Dr. Peles received the ONR Young InvestigatorAward in 2005 and the DARPA/MTO Young Faculty Award in 2007.

Documents

TCPT-2006-096.R2: Micro Scale pin fin Heat Sinks \u0026#x2014;Parametric Performance Evaluation Study