Eﬀects of jet pattern on single-phase cooling performance ... Publications/133.pdf · contributions of jet impingement and micro-channel ﬂow in various regions of the micro-channel

Available online at www.sciencedirect.com

www.elsevier.com/locate/ijhmt

International Journal of Heat and Mass Transfer 51 (2008) 4614–4627

Effects of jet pattern on single-phase cooling performanceof hybrid micro-channel/micro-circular-jet-impingement

thermal management scheme

Myung Ki Sung, Issam Mudawar *

Boiling and Two-Phase Flow Laboratory (BTPFL), Purdue University International Electronic Cooling Alliance (PUIECA),

Mechanical Engineering Building, 585 Purdue Mall West Lafayette, IN 47907-2088, USA

Received 19 December 2007; received in revised form 1 February 2008Available online 28 April 2008

Abstract

This study explores the single-phase cooling performance of a hybrid cooling module in which a series of micro-jets deposit coolantinto each channel of a micro-channel heat sink. This creates symmetrical flow in each micro-channel, and the coolant is expelled throughboth ends of the micro-channel. Three micro-jet patterns are examined, decreasing-jet-size (relative to center of channel), equal-jet-sizeand increasing-jet-size. The performance of each pattern is examined experimentally and numerically using HFE 7100 as working fluid.Indirect refrigeration cooling is used to reduce the coolant’s temperature in order to produce low wall temperatures during high-flux heatdissipation. A single heat transfer coefficient correlation is found equally effective at correlating experimental data for all three jet pat-terns. Three-dimensional numerical simulation using the standard k–e model shows excellent accuracy in predicting wall temperatures.Numerical results show the hybrid cooling module involves complex interactions of impinging jets and micro-channel flow. Increasingthe coolant’s flow rate strengthens the contribution of jet impingement to the overall cooling performance, and decreases wall temper-ature. However, this advantage is realized at the expense of greater wall temperature gradients. The decreasing-jet-size pattern yields thehighest convective heat transfer coefficients and lowest wall temperatures, while the equal-jet-size pattern provides the greatest uniformityin wall temperature. The increasing-jet-size pattern produces complex flow patterns and greater wall temperature gradients, which arecaused by blockage of spent fluid flow due to the impingement from larger jets near the channel outlets.� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Micro-channel and jet-impingement cooling

Micro-channel flow and jet-impingement are undoubt-edly two of the most powerful thermal solutions for situa-tions demanding high-flux heat removal. This includeshigh-performance computer chips, hybrid-vehicle powerelectronics, military avionics, radars, and defense laserand microwave directed-energy weapon systems [1].

Micro-channel heat sinks have been studied extensivelyfor electronics cooling. In an often-cited study, Tuckerman

0017-9310/$ - see front matter � 2008 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijheatmasstransfer.2008.02.021

* Corresponding author. Tel.: +1 765 494 5705; fax: +1 765 494 0539.E-mail address: [email protected] (I. Mudawar).

and Pease [2] were able to dissipate up to 790 W/cm2 using awater-cooled micro-channel heat sink. They pointed outtwo key problems of micro-channel heat sinks, high pres-sure drop and large temperature gradients along the flowdirection. Bowers and Mudawar [3] achieved single-phasecooling heat fluxes as high as 3000 W/cm2 in micro-tubesusing water as working fluid. Both numerical and analyticalmethods have been used to model single-phase fluid flowand heat transfer in micro-channel heat sinks [4–6]. Quand Mudawar [4] showed the pressure drop and heat trans-fer characteristics of micro-channel heat sinks could beaccurately predicted by solving the conventional Navier–Stokes’ and energy equations.

Single-phase jet-impingement cooling has also beeninvestigated both experimentally [7–9] and numerically

mailto:[email protected]

Nomenclature

At top test surface area of copper heating block(1.0 � 2.0 cm2)

C1, C2, C3 empirical constantsDjet Diameter of micro-jetH height of unit cellHch height of micro-channelHjet height (length) of micro-jetHth height from thermocouple hole to unit cell bot-

tom boundaryHw height from unit cell bottom boundary to bot-

tom wall of micro-channelh height of wall jet; convective heat transfer coef-

ficient, q00eff=ðT s � T inÞ�hch1 mean convective heat transfer coefficient for mi-

cro-channel region 1�hch2 mean convective heat transfer coefficient for mi-

cro-channel region 2�hjet mean convective heat transfer coefficient for jet-

impingement region�hL mean convective heat transfer coefficient inside

micro-channelk thermal conductivityl parameter used in determining laminar layer

thicknessL length of unit cell (also length of micro-channel)Ljet,i length of micro-channel associated with jet iLjet pitch of micro-jetL1, L2, L3, L4 distance between thermocouple holes_m mass flow rate of entire cooling moduleNi number of jets of size i in single micro-channelNjet total number of jets in single micro-channelNu Nusselt numberNuL average Nusselt numberph perimeter of micro-channel, 2(Wch + Hch)P PressurePin fluid pressure at test module inletPout fluid pressure at test module outletPr Prandtl numberPW total electrical power input to cartridge heaters

q00eff effective heat flux based on top test surface areaof copper block, Pw/At

r radius measured from jet centerlinerb radial location where boundary layer reaches

film thicknessrc critical radius corresponding to onset of turbu-

lent zoneRe Reynolds numberRejet jet Reynolds number, UjetDjet/mf

Rejet,m jet Reynolds number based on mean velocity ofall jets in a given jet pattern

rj radius of circular jetrs radial extent of stagnation zoneT TemperatureTin fluid temperature at test module inletTout fluid temperature at test module outletTtci temperature measure by thermocouple i

(i = 1–4)Ujet mean jet velocityW width of unit cellWch width of micro-channelWw half-width of copper wall separating micro-

channelsx Cartesian coordinatey Cartesian coordinatez Cartesian coordinate

Greek symbols

d hydrodynamic boundary layer thicknessdth thermal boundary layer thicknessm kinematic viscosityq density

Subscriptsch channelf liquidin test module inletout test module outlettci thermocouple i (i = 1–4).

M.K. Sung, I. Mudawar / International Journal of Heat and Mass Transfer 51 (2008) 4614–4627 4615

[10–12]. Wadsworth and Mudawar [9] conducted confinedslot jet experiments using FC-72 as working fluid anddeveloped a superpositioning scheme for correlating sin-gle-phase heat transfer coefficient data. Baydar and Ozmen[12] demonstrated that the k–e model accurately predictsthe flow characteristics of confined air jets.

Overall, micro-channel heat sinks offer several impor-tant attributes, including the ability to dissipate very largeheat fluxes from small surface areas, compactness andsmall coolant inventory. A key drawback of single-phasemicro-channel heat sinks is the coolant temperature risealong the micro-channel can cause appreciable temperaturegradients in the heat-dissipating device to which the heat

sink is attached. Another drawback is large pressure drop.Jet-impingement cooling has the capacity to dissipate verylarge heat fluxes corresponding to relatively small pressuredrop. However, jets concentrate most of the cooling withinthe immediate vicinity of the stagnation zone. Multiple jetsare commonly used to diffuse this effect by creating severalhigh-flux impingement regions that are distributed alongthe surface of the heat-dissipating device.

1.2. Merits of low temperature refrigeration

Regardless which cooling scheme is used, dissipatingvery large heat fluxes can lead to unacceptably high device

4616 M.K. Sung, I. Mudawar / International Journal of Heat and Mass Transfer 51 (2008) 4614–4627

temperatures. All electronic devices have upper tempera-ture limits that are dictated by material and performanceconstraints. One effective means for maintaining the devicetemperature below this limit during high-flux heat dissipa-tion is to greatly decrease the coolant temperature. Oneexample of a successful low temperature cooling system isthe Kleemenko cooler, which provides 80 W of refrigera-tion for device cooling at �96 �C [13]. Aside from thermalbenefits, low temperatures provide significant enhancementin device functionality and reliability. Naeemi and Meindl[14] demonstrated 4.3 times higher CMOS chip perfor-mance at �100 �C than at 85�C. Schmidt and Notohardj-ono [15] showed low temperature cooling offers orders ofmagnitude improvement in reliability. Overall, low temper-atures facilitate faster switching times of semiconductordevices, increase circuit speed (due to lower electrical resis-tance of interconnecting materials), reduce thermallyinduced failures, and improve device performance bydecreasing current leakage.

Refrigeration cooling can be implemented in one of twoconfigurations, direct-refrigeration cooling and indirect-refrigeration cooling. Direct refrigeration involves insertingthe cooling module as an evaporator in a vapor compres-sion cycle, and using the refrigerant as coolant for the elec-tronic device. Indirect-refrigeration cooling involves usinga separate cooling loop in which a liquid coolant is usedto remove the dissipated heat, which is rejected a separatevapor compression cycle. While the direct-refrigerationsystem is simpler and more compact, the indirect-refrigera-tion system provides greater flexibility in coolant selection,as well as allows the use of a non-pressurized coolingmodule.

1.3. Objectives of study

Recently, the authors of the present study proposed ahybrid cooling scheme that combines the cooling benefitsof micro-channel flow and micro-circular-jet-impingement[16,17]. With this hybrid cooling scheme, the coolant isintroduced gradually as a series of jets into each micro-channel of a micro-channel heat sink, and is expelledsymmetrically through both ends of the micro-channel.Unlike conventional micro-channels, where the tempera-tures of both the coolant and the device to which themicro-channel heat sink is attached increase along thedirection of fluid flow, the hybrid scheme supplies lowtemperature coolant at various locations along themicro-channel. This helps to enhance temperature unifor-mity of both coolant and device. Another benefit of thehybrid scheme is a reduction in pressure drop comparedto conventional micro-channel heat sinks. The hybridcooling scheme is also superior to multi-jet-impingementmodules in its ability to better manage the flow of spentcoolant, prevent flow instabilities, and reduce flow block-age. The earlier authors’ studies involved equally-sizedmicro-circular-jets that are equally spaced along themicro-channel.

The present study is an extension of the authors’ earlierwork and aims to explore the benefits of utilizing differentlysized jets along the micro-channel. Three different jet pat-terns are compared. The first, decreasing-jet-size pattern,consists of jets that decrease in size symmetrically fromthe center of the micro-channel towards the two ends.The second, equal-jet-size pattern, consists of jets of equalsize uniformly distributed along the micro-channel, likethose used in the authors’ earlier studies. The third,increasing-jet-size pattern, consists of jets that increase insize from the center of the micro-channel towards thetwo ends. The same total flow area of all jets is used foreach jet pattern. The key objective in examining these threeconfigurations is to explore any potential cooling benefitsthat may be realized as a result of modulating the relativecontributions of jet impingement and micro-channelflow in various regions of the micro-channel. To furtherenhance cooling performance, the three jet patterns aretested in an indirect-refrigeration cooling system. Two ulti-mate cooling objectives are to achieve, for a given flow rate,the highest possible heat transfer coefficient (i.e., lowestwall temperature) and lowest wall temperature gradients.Numerical simulation is used to predict both the complexmicro-jet/micro-jet flow interactions and wall temperaturedistribution. Also presented is a simple, yet very effectivescheme for correlating single-phase heat transfer coefficientdata.

2. Experimental methods

2.1. Test module

The layered construction and assembly of the test mod-ule are illustrated in Fig. 2. The test module consists of acopper heating block, a micro-jet plate, an upper housing,a bottom housing, lower support plates, and 16 cartridgeheaters. Liquid HFE 7100 is supplied from the upper hous-ing into a plenum in the upper housing above the micro-jetplate. The coolant flows through holes in the micro-jetplate in the form of jets that impinge inside the micro-chan-nels. The flow splits into two equal and opposite parts inthe micro-channels, each is expelled into one of two ple-nums in the bottom housing. The micro-channels areformed by cutting five 1.0-mm wide and 3-mm deep slotsequidistantly within the 1.0-cm width of the top1.0 � 2.0 cm2 test surface area of the copper block. Thecopper block is tapered in two steps to help ensure uniformtemperature along the top surface. The heights of thesesteps are based on numerical three-dimensional simulationof the test module. Heat is supplied to the micro-channelsfrom the 16 cartridge heaters that are inserted into theunderside of the copper block. The total electrical powerinput to the cartridge heaters is measured by a YokogawaWT 210 wattmeter. Both the upper and bottom housingsare machined from high-temperature G-11 fiberglass plas-tic. Four stainless steel pins are inserted between the


micro-jet plate and the bottom housing to accurately alignthe jets relative to the micro-channels. The copper heatingblock is wrapped in multiple layers of ceramic fiber, andmounted atop a solid ceramic plate to help minimize heatloss. Four type-T thermocouples are inserted below themicro-channel bottom wall to monitor stream-wise temper-ature distribution. An absolute pressure transducer and atype-T thermocouple are connected to the inlet plenum ofthe test module. Another absolute pressure transducerand a second thermocouple are each connected to one ofthe outlet plenums.

2.2. Jet patterns

Three different micro-jet patterns are examined; eachpattern is formed in a separate micro-jet plate. In the firstmicro-jet plate, jets decrease in size along each side of themicro-channel. The second plate has equally-sized jets,and, in the third plate, jets increase in size along each sideof the micro-channel. In each plate, five parallel arrays ofcircular holes are drilled within the 1-cm width facing thefive micro-channels. It is important to emphasize that thesum of flow areas of all jets is the same for all threemicro-jet plates. The micro-jet plates are fabricated fromoxygen-free copper.

Table 1Experimental operating conditions

Workingfluid

Inlet temperatureTin (�C)

Inlet flow rate_m (g/s)

Effective heat fluxq00eff ðW=cm2Þ

HFE 7100 �40 to 20 11.1–55.9 16.1–304.9

2.3. Flow loop

Fig. 1 shows a schematic diagram of the cooling systemthat is configured to deliver low temperature HFE 7100liquid at the desired pressure and flow rate to the testmodule. Heat is rejected from the HFE 7100 liquid to a

Fig. 1. (a) Test module construction. (b

secondary refrigeration system via a heat exchanger. Therefrigeration system uses feedback control to regulate thetemperature of the HFE 7100 liquid at the heat exchangeroutlet to within ±0.5 �C. The coolant flow rate and pres-sure are controlled by two needle valves situated upstreamand downstream of the test module, as well as a bypassvalve. The coolant flow rate is measured by a Coriolis flowmeter.

Electric power is supplied to the test module andincreased in small increments after the desired test moduleinlet conditions are reached. Once steady-state is reachedfollowing each power increment, the module inlet pressure,Pin, outlet pressure, Pout, inlet temperature, Tin, outlet tem-perature, Tout, heating block temperatures, Ttc1–Ttc4, andelectrical power input, PW, are all recorded for later pro-cessing. Measurement uncertainties associated with thepressure transducers, flow meter, wattmeter, and thermo-couples are 0.5%, 0.1%, 0.5%, and 0.3 �C, respectively. Anumerical 3-D model of the entire test module yielded aworst-case heat loss (corresponding to the lowest coolantflow rate tested) of less than 8% of the electrical powerinput. The heat fluxes reported in the present paper aretherefore based on the measured electrical power input.The experimental operating conditions of this study arelisted in Table 1.

) Cross-section of module assembly.

Fig. 2. Schematic of flow control system.


3. Numerical scheme

Fig. 3a shows a unit cell consisting of a single micro-channel, portion of the micro-jet plate facing the samemicro-channel, and surrounding solid. This figure showsthe different geometrical parameters of the unit cell as wellas locations of the thermocouples in the copper block. Dueto symmetry, a computational domain consisting of onlyone quarter of the unit cell is required. Fig. 3b shows thedetail geometrical parameters of the three micro-jet plates.Table 2 provides all dimensions of the unit cell and the jetplates.

FLUENT 6.2.16 [18] is used to compute flow fields andheat transfer characteristics of the hybrid cooling module.The computational mesh is constructed using Gambit2.2.30 [19]. The model used here assumes steady, turbulentand incompressible flow with constant properties. Thestandard two-equation k–e turbulent model [20] is usedfor closure of the Reynolds stress tensor. The governingconservation equations as well as boundary conditionsand the effects of mesh size are detailed in two previousstudies by the authors [16,17].

3.1. Determination of extent of laminar zone

Fig. 4 shows the flow field along a heated surface for acircular free jet. To determine the radial distance of the tur-bulent zone from the jet centerline, laminar flow is imposedon the computational domain from the jet inlet to the stag-nation zone, and a portion of the wall jet surrounding thestagnation zone. The procedure for determining theupstream radial location of the turbulent zone and laminarthickness is described in [17]. Key equations for wall layer

thickness and radial locations of the individual zones are asfollows:

h ¼D2

jet

8rfor 0 < r < rs; ð1aÞ

h ¼D2

jet

8r

!þ 1� 2p

3ffiffiffi3p

c2

� �d for rs < r < rb; ð1bÞ

h ¼ 8p

3ffiffiffi3p r3 þ l3

� �DjetRejetr

for rb < r < rc; ð1cÞ

where

d2 ¼ 1:402ð Þ3ffiffiffi3p

p� 1:402ffiffiffi3p r

DjetRejet

; ð2aÞ

l ¼ 0:3296DjetRe1=3jet ; ð2bÞ

and

rb ¼ 0:1834DjetRe1=3jet : ð2cÞ

The computational domain in FLUENT is therefore di-vided into two sub-zones, a laminar zone and a turbulentzone. For each jet pattern, the laminar thickness for eachjet-size is determined and the smallest laminar zone heightis used for all jets. Laminar flow is imposed on the flow do-main between the jet inlet and the stagnation zone, as wellas up to height h(r) from the well. Turbulence is permittedeverywhere else in the computational domain.

3.2. Determination of jet velocities

Jet velocities of differently sized jets can be related to oneanother by equating their pressure drop. Consider a cool-

Fig. 3. Schematic of unit cell illustrating (a) overall dimensions and thermocouple locations and (b) jet patterns.


ing module that contains three different jet sizes, Djet1, Djet2

and Djet3. Equal pressure drop requires that

DP 1 ¼ DP 2 ¼ DP 3 ¼ fH jet

Djet1

qf U 2jet1

2

¼ fH jet

Djet2

qf U 2jet2

2¼ f

H jet

Djet3

qf U 2jet3

2; ð3Þ

where the pressure drop coefficient, f, is inversely propor-tional to jet Reynolds [21]

f ¼ KRe�1jet ; ð4Þ

and K is fairly constant for the conditions of the presentstudy. Eqs. (3) and (4) allow the jet velocities to be relatedto one another.

U jet2 ¼D2

jet2

D2jet1

U jet1 ð5aÞ

and

U jet3 ¼D2

jet3

D2jet1

U jet1: ð5bÞ

Tab

le2

Dim

ensi

on

so

fu

nit

cell

L(m

m)

L1

(mm

)L

2

(mm

)L

3

(mm

)L

4

(mm

)W

(mm

)W

ch

(mm

)W

w

(mm

)H (m

m)

Hje

t(m

m)

Hch

(mm

)H

w

(mm

)H

th

(mm

)D

jet1

(mm

)D

jet2

(mm

)D

jet3

(mm

)D

jet4

(mm

)L

jet1

(mm

)L

jet2

(mm

)L

jet3

(mm

)L

jet4

(mm

)L

jet5

(mm

)

20.0

04.

006.

003.

006.

001.

831.

000.

4214

.27

1.65

3.00

7.62

5.08

0.60

0.45

0.30

0.42

1.84

1.62

1.44

1.23

1.43

Fig. 4. Fluid flow regimes for free circular impinging jet with Prf > 1.


Then Ujet1 can be determined from continuity.

_mtotal ¼ N 1qf

pD2jet1

4

!U jet1

þ N 2qf

pD2jet2

4

!D2

jet2

D2jet1

U jet1

!

þ N 3qf

pD2jet3

4

!D2

jet3

D2jet1

U jet1

!; ð6Þ

where Ni is the total number jets of diameter Djeti. Thevelocities of the other jets can be determined using Eqs.(5a) and (5b).

4. Correlation of heat transfer data

A superpositioning technique is used to correlate the sin-gle-phase heat transfer data for the three jet patterns. Thistechnique seeks to assign dominant heat transfer mecha-nisms to different portions of the heat transfer area. Thistechnique, which was originally developed by Wadsworthand Mudawar [9] for confined slot jets, was very effectiveat correlating the present authors’ single-phase data for ahybrid micro-channel/micro-jet-impingement module withequal-jet-size [16].

The superpositioning technique consists of applying dif-ferent correlations of the general form

Nu

Pr0:4f

¼ f ðReÞ ð7Þ

to the different surface regions. Fig. 5 illustrates the differ-ent regions associated with a single jet. The surface consistsof an impingement region, two identical bottom wall

Fig. 5. Schematic of superpositioning technique for correlating single-phase heat transfer data.


regions, and a micro-channel flow region. Assuming sur-face temperature is uniform across the entire wetted sur-face, the superpositioning technique yields the followingrelation for overall heat transfer coefficient, �hL:

�hLphL ¼XN jet

i¼1

�hjet;i

pD2jet;i

4

" #þ �hch1;i W chDjet;i �

pD2jet;i

4

!" #(

þ�hch2;i phLjet;i � W chDjet;i þpD2

jet;i

4

!" #); ð8Þ

where Njet is the number of micro-jets for a single micro-channel and ph the micro-channel perimeter. Since channelvelocity increases away from the central jets towards theoutlet due to the increasing flow rate, Eq. (8) is writtento allow for variations in the values of heat transfer coeffi-cients between successive jet cells similar to those depictedin Fig. 5. Eq. (8) assumes jets are symmetrically situatedaround the center of the micro-channel. As shown inFig. 3, this is the case for both the equal-jet-size andincreasing-jet-size patterns examined in this study. How-ever, the decreasing-jet-size pattern includes a jet at thecenter of the micro-channel, which does not conform toEq. (8). Following is a correlation technique for symmetri-cal jet patterns that do not include a central jet. Variationsin the correlation for patterns including a central jet will bediscussed afterwards.

Eq. (8) can be represented in the dimensionless form

NuL ¼�hLLkf¼XN jet

i¼1

�hjet;ipD2

jet;i

4ph

� �kf

2664

3775þ

�hch1;iW chDjet;i�

pD2jet;i4

ph

!

kf

266664

377775

8>>>><>>>>:

þhch2;i Ljet;i � W chDjet;i

ph1þ pD2

jet;i

41

W chDjet;i

� � kf

2664

37759>>>>=>>>>;: ð9Þ

The Reynolds numbers used to characterize heat transfer inthe different surface regions depicted in Fig. 5 are definedas

Rejet;i ¼U jet;iDjet;i

mf; ð10aÞ

Rech1;i ¼U ch1;i

W chDjet;i�pD2

jet;i4

ph

!

mfð10bÞ

and

Rech2;i ¼U ch2;i Ljet;i � W chDjet;i

ph1þ pD2

jet;i

41

W chDjet;i

� � mf

: ð10cÞ

Due to the Bernoulli effect, the sidewall characteristicvelocity is assumed equal to the jet velocity. The channelvelocity can be determined from mass conservation,accounting for the gradual increase in flow rate away fromthe center of the micro-channel.

U ch;i ¼ U jet;i ð11aÞand

U ch2;i ¼Xi

j¼1

U jet;jpD2

jet;j

4

W chH ch

: ð11bÞ

Therefore, the heat transfer correlation can be written as

NuL

Pr0:4f

¼XN jet

i¼1

C1Reajet;i

Djet;i

ph

� �þ C2Reb

ch1;i þ C3Recch2;i

� �

¼XN jet

i¼1

C1Reajet;i

Djet;i

ph

� �þ C2Reb

jet;i

W chDjet;i �pD2

jet;i

4

phDjet;i

0@

1A

b8><>:

þC3Recjet;i

Xi

j¼1

U jet;j

U jet;i

� �pD2

jet;j

4

W chH ch

8><>:

9>=>;

264

� Ljet;i

Djet;i� W ch

ph

1þpD2

jet;i

4

1

W chDjet;i

!375375

c9>=>;:

264 ð12Þ

Eq. (12) can also be written as

NuL

Pr0:4f

¼XN jet

i¼1

Xi

j¼1

C1Reajet;i

Djet;i

ph

� �1

i

� �8><>:

þC2Rebjet;i

W chDjet;i �pD2

jet;i

4

phDjet;i

0@

1A

b

1

i

� �

þC3Recjet;i

U jet;j

U jet;i

� �pD2

jet;j

4

W chH ch

Ljet;i

Djet;i� W ch

ph

264

264

� 1þpD2

jet;i

4

1

W chDjet;i

!375375

c9>=>;: ð13Þ

As indicated earlier, Eqs. (12) and (13) are valid for jet pat-terns that do not include a central jet. For patterns with a

Fig. 6. Comparison of predictions of single-phase heat transfer correla-tion and experimental data.

Fig. 7. Comparison of numerical predictions of temperatures alongthermocouple line and measured temperatures.


central jet, these equations must be modified by includingthe following term for each side of the micro-channel.

C1Reajet;1

Djet;1=2� �

ph

� �

þ C2Rebjet;1

W ch Djet;1=2� �

� p Djet;1=2ð Þ24

phDjet;1

0@

1A

b

þ C3Recjet;1

p Djet=2ð Þ4

W chH ch

Ljet;1=2� �

Djet;1

8<:

� W ch

ph

1

2þ

p Djet;1=2� �2

4

1

W chDjet;i

!#)c

: ð14Þ

The rest of the single-phase correlation can be obtained bysimply setting Ujet,1 = Ujet,1/2 and Djet,1 = Djet,1/2 to thethird term in Eqs. (12) and (13).

As indicated in [16] and recommended earlier by Wads-worth and Mudawar [9], the impingement term should befitted with the exponent a = 0.5. The remaining empiricalconstants are obtained with a least-squares’ fit to the sin-gle-phase heat transfer data. The following correlationwas obtained for the micro-channel/micro-circular-jet-impingement module with equal-jet-size [16],

NuL

Pr0:4f

¼XN jet

i¼1

63:41Re0:5jet;i

Djet;i

ph

� �8><>:

þ 0:183Re0:199jet;i

W chDjet;i �pD2

jet;i

4

phDjet;i

0@

1A

0:199

þ 0:197Re0:654jet;i

Xi

j¼1

U jet;j

U jet;i

� �pD2

jet;j

4

W chH ch

8><>:

9>=>;

264

� Ljet;i

Djet;i� W ch

ph

1þpD2

jet;i

4

1

W chDjet;i

!375375

0:654264

9>=>;;ð15Þ

which can also be expressed as

NuL

Pr0:4f

¼XN jet

i¼1

Xi

j¼1

63:41Re0:5jet;i

Djet;i

ph

� �1

i

� �8><>:

þ 0:183Re0:199jet;i

W chDjet;i �pD2

jet;i

4

phDjet;i

0@

1A

0:199

1

i

� �

þ 0:197Re0:654jet;i

U jet;j

U jet;i

� �pD2

jet;j

4

W chH ch

Ljet;i

Djet;i� W ch

ph

264

264

� 1þpD2

jet;i

4

1

W chDjet;i

!375375

0:6549>=>;: ð16Þ

Fig. 6 shows Eqs. (15) or (16) fit the single-phase data forall three micro-jet patterns with a mean absolute error(MAE) of 5.26%, with all data points falling within a±20% error band. This is proof of the universal validityof this correlation.

5. Numerical predictions of the effects of micro-jet pattern

5.1. Validation of numerical predictions

Fig. 7 compares numerical predictions of the tempera-ture distribution along the thermocouple line in the copperblock with the thermocouple measurements for the three jet


patterns. The numerical scheme appears equally effective atpredicting the temperature variations for the different jetpatterns corresponding to different heat fluxes and flowrates. The agreement between the measured and predictedtemperatures demonstrates the effectiveness of the presentnumerical scheme using the standard k-e model and therelations used to determine the extent of the laminar zone.

Fig. 8. Streamlines and wall temperature plots at q00eff ¼ 36:0 W=cm2, _m ¼ 11:1

5.2. Predicted trends of cooling performance

Figs. 8–10 show flow streamlines and channel bottomwall temperature distribution for one-fourth the unit cellillustrated in Fig. 3. Results for the three jet patterns areprovided for low, medium, high flow rates in Figs. 8–10,respectively.

g=s for (a) decreasing-jet-size, (b) equal-jet-size, and (c) increasing-jet-size.

Fig. 9. Streamline and wall temperature plots at q00eff ¼ 67:6 W=cm2, _m ¼ 33:6 g=s for (a) decreasing-jet-size, (b) equal-jet-size, and (c) increasing-jet-size.


For the decreasing-jet-size pattern with a low flow rate,Fig. 8a shows the large jets near the center of the channelare easily able to reach the channel bottom wall, yieldinglowest temperatures near the center of the channel. Thespent fluid from the first jet and second jet makes it difficultfor the downstream jets to reach the bottom wall. How-ever, the heat transfer coefficient increases with increasing

flow rate along the flow direction. The decreasing-jet-sizepattern appears to effectively utilize both the jet flow andthe channel flow to achieve excellent bottom wall tempera-ture uniformity. Fig. 8b shows that heat transfer for theequal-jet-size pattern is dominated more by channel flowthan by jet-impingement. Since the flow rate increasesalong the flow direction, the lowest temperature is

Fig. 10. Streamlines and wall temperature plots at q00eff ¼ 121:5 W=cm2, _m ¼ 55:9 g=s for (a) decreasing-jet-size, (b) equal-jet-size, and (c) increasing-jet-size.


encountered near the channel outlet. For the increasing-jet-size pattern, Fig. 8c shows the flow is complicated by inter-actions between neighboring jets. Large jets near the chan-nel outlet create appreciable blockage to coolant flow fromthe upstream small- and medium-sized jets. Overall, theincreasing-jet-size pattern provides the poorest cooling per-

formance of the three jet patterns, evidenced by the highestwall temperatures and largest wall temperature gradients.

Figs. 9 and 10 show, for medium and high flow rates,respectively, similar cooling trends for each jet patterns.One obvious difference from the low flow rate case is agreater influence of jet-impingement compared to micro-

Fig. 12. Variation of heat transfer coefficient with mean jet Reynoldsnumber for different jet patterns.


channel flow for all jet patterns. Strong impingement of thelargest jets reduces surface temperature for the decreasing-jet-size pattern, Figs. 9a and 10a, and the increasing-jet-sizepattern, Figs. 9c and 10c, compared to the equal-jet-sizepattern, Figs. 9b and 10b. Because of the increasing flowrate along the flow direction, fairly uniform temperatureis achieved with the decreasing-jet-size pattern as shownin Figs. 9a and 10a. Excellent surface temperature unifor-mity is achieved with the equal-jet-size pattern at mediumand high flow rates as shown in Figs. 9b and 10b. Forthe increasing-jet-size pattern, the increasing flow rate esca-lates the aforementioned blockage effect, causing apprecia-ble recirculation in the flow from the upstream small jets asshown in Figs. 9c and 10c. Despite the ability to achieverelatively low overall wall temperatures, the flow blockageinduces large wall temperature gradients for the increasing-jet-size pattern.

Fig. 11. Variation of wall Wadsworth and Mudawar [x]. temperaturealong micro-channel for (a) q00eff ¼ 36:0 W=cm2, _m ¼ 11:1 g=s, (b)q00eff ¼ 67:6 W=cm2, _m ¼ 33:6 g=s, and (c) q00eff ¼ 121:5 W=cm2,_m ¼ 55:9 g=s.

Fig. 11 shows the effects of flow rate on temperature dis-tribution along the centerline of the channel’s bottom wall.For the three jet patterns, increasing flow rate decreases thebottom wall temperature at the expense of a higher temper-ature gradient. The medium and high flow rate cases man-ifest the strong impingement effects of the large jets in theform of low upstream temperatures for the decreasing-jet-size pattern, Fig. 11a, and low downstream temperaturesfor the increasing-jet-size pattern, Fig. 11c. Fig. 11 shows,for all flow rates, the highest single-phase heat transfercoefficients (i.e., lowest wall temperatures) are achievedwith the decreasing-jet-size pattern. However, the greatesttemperature uniformity is realized with the equal-jet-sizepattern. These trends point to important practical trendsin cooling system design. The increasing-jet-size pattern ispreferred for high-heat-flux removal, while the equal-jet-size pattern is preferred for devices demanding greater tem-perature uniformity.

The flow rate trends depicted in Fig. 11 are further sub-stantiated in Fig. 12, which shows the heat transfer coeffi-cient data plotted against Rejet,m, the jet Reynolds numberbased on mean velocity of all jets in a micro-jet plate.Clearly evident in Fig. 12 is the advantageous effect ofincreasing Rejet,m for all jet patterns, as well as the superiorheat transfer performance of the decreasing-jet-sizepattern.

6. Conclusions

This study examined a hybrid thermal managementscheme that combines the cooling benefits of micro-channelflow and jet-impingement. Indirect refrigeration cooling isused to achieve low coolant temperatures in order todecrease wall temperature during high-flux heat dissipa-tion. Three micro-jet patterns are examined, decreasing-jet-size, equal-jet-size and increasing-jet-size. The perfor-mance of each pattern is examined experimentally andnumerically using HFE 7100 as working fluid. Key findingsfrom the study are as follows:


1. A single-phase correlation is developed using a superpo-sitioning technique that assigns different heat transfercoefficient values to different regions of the micro-chan-nel based on the dominant heat transfer mechanism foreach region. A single correlation is found equally effec-tive at fitting experimental data for all three micro-jetpatterns.

2. Excellent agreement between numerical predictions andtemperature measurements proves the standard k–emodel and the criteria adopted to determine the extentof the laminar zone are very effective at predicting theheat transfer performance of the hybrid cooling schemeregardless of micro-jet pattern.

3. The three hybrid module configurations involve com-plex interactions of impinging jets with micro-channelflow. Increasing the flow rate (and therefore jet speed)strengthens the contribution of jet impingement to theoverall cooling performance, resulting in lower overallbottom wall temperatures. However, this advantage isrealized at the expense of greater wall temperaturegradients.

4. The highest convective heat transfer coefficients andlowest bottom wall temperatures are achieved with thedecreasing-jet-size pattern, rendering this pattern mostsuitable for applications demanding high-heat-fluxremoval. The equal-jet-size pattern provides the smallestgradients in bottom wall temperature; this pattern istherefore better suited to devices demanding tempera-ture uniformity. The increasing-jet-size pattern producescomplex flow patterns and greater wall temperature gra-dients, which are caused by blockage of the spent fluidby larger jets near the channel outlets.

Acknowledgement

The authors are grateful for the financial support of theOffice of Naval Research (ONR).

References

[1] I. Mudawar, Assessment of high-heat-flux thermal managementschemes, IEEE Trans. Compon. Pack. Tech. 24 (2001) 122–141.

[2] D.B. Tuckerman, R.F.W. Pease, High-performance heat sinking forVLSI, IEEE Electron Device Lett. EDL-2 (1981) 126–129.

[3] M.B. Bowers, I. Mudawar, High flux boiling in low flow rate, lowpressure drop mini-channel and micro-channel heat sinks, Int. J. HeatMass Transfer 37 (1994) 321–332.

[4] W. Qu, I. Mudawar, Experimental and numerical study of pressuredrop and heat transfer in a single-phase micro-channel heat sink, Int.J. Heat Mass Transfer 45 (2002) 2549–2565.

[5] S.J. Kim, D. Kim, Forced convection in microstructures for electronicequipment cooling, J. Heat Transfer 121 (1999) 639–645.

[6] A.G. Fedorov, R. Viskanta, Three-dimensional conjugate heattransfer in the microchannel heat sink for electronic packaging, Int.J. Heat Mass Transfer 43 (2000) 399–415.

[7] H. Martin, Heat and mass transfer between impinging gas jets andsolid surfaces, Adv. Heat Transfer 13 (1977) 1–60.

[8] L.M. Jiji, Z. Dagan, Experimental investigation of single-phase multi-jet impingement cooling of array of microelectronic heat sources, in:Proceedings of the International Symposium on Cooling Technologyfor Electronic Equipment, Honolulu, HI, 1987, pp. 265–283.

[9] D.C. Wadsworth, I. Mudawar, Cooling of a multichip electronicmodule by means of confined two-dimensional jets of dielectric liquid,J. Heat Transfer 112 (1990) 891–898.

[10] T.J. Craft, L.J.W. Graham, B.E. Launder, Impinging jet studies forturbulence model assessment – II. An examination of the performanceof four turbulence models, Int. J. Heat Mass Transfer 36 (1993) 2685–2697.

[11] T.H. Park, H.G. Choi, J.Y. Yoo, S.J. Kim, Streamline upwindnumerical simulation of two-dimensional confined impinging slot jets,Int. J. Heat Mass Transfer 46 (2003) 251–262.

[12] E. Baydar, Y. Ozmen, An experimental and numerical investigationon a confined impinging air jet at high Reynolds numbers, App.Thermal Eng. 25 (2005) 409–421.

[13] W.A. Little, Low temperature electronics workshop: recent advancesin low cost cryogenic coolers for electronics, in: Proceedings of 16thIEEE Semi-Therm Symposium, San Jose, CA, 2000, pp. 110–111.

[14] A. Naeemi, J.D. Meindl, An upper limit for aggregate I/O intercon-nect bandwidth of GSI chips constrained by power dissipation, in:Proceedings of IEEE International Interconnect Technology Confer-ence, San Francisco, CA, 2004, pp. 157–159.

[15] R.R. Schmidt, B.D. Notohardjono, High-end server low-temperaturecooling, IBM J. Res. Dev. 49 (2002) 739–751.

[16] M.K. Sung, I. Mudawar, Single-phase hybrid micro-channel/micro-jet-impingement cooling, Int. J. Heat Mass Transfer 51 (2008) 4342–4352.

[17] M.K. Sung, I. Mudawar, Single-phase and two-phase heat transfercharacteristics of low temperature hybrid micro-channel/micro-jet-impingement cooling module, Int. J. Heat Mass Transfer 51 (2008)3882–3895.

[18] Fluent 6.2.16. User’s Guide, Fluent Inc., Lebanon, NH, 2005.[19] Gambit 2.2.30. User’s Guide, Fluent Inc., Lebanon, NH, 2006.[20] B.E. Launder, D.B. Spalding, The numerical computation of turbu-

lent flows, Comput. Meth. Appl. Mech. Eng. 3 (1974) 269–289.[21] F.P. Incropera, Liquid Cooling of Electronic Devices by Single-phase

Convection, Wiley, New York, NY, 1999.

Documents

Eﬀects of jet pattern on single-phase cooling performance ... Publications/133.pdf · contributions of jet impingement and micro-channel ﬂow in various regions of the micro-channel