Hight Flux Minicanal

8/12/2019 Hight Flux Minicanal

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Int. J, Heat Muss Transferr. Vol. 37, No. 2, pp. 321-332, 1994 M)17-9310/94 6.00+0.00Printed inGreatritain 1993PergamonPressLtd

High flux boiling in low flow rate, low pressuredrop mini-channel and micro-channel heatsinksM. B. BOWERS and I. MUDAWART

Boiling and Two-phase Flow Laboratory, School of Mechanical Engineering, PurdueUniversity, West Lafayette, IN 47907, U.S.A.Receiv ed 20 August 1992 and i~ ~~a l~ or~ 1 M arch 1993)

Abstract-Due to the need for practical cooling technologies which could dissipate high heat fluxes, anexperimental study of pressure drop and CHF in mini-channel (L) = 2.54 mm) and micro-channel (0 = 510pm) heat sinks of 1 cm heated length was performed using R-l 13. Test conditions included inlet subcoolingranging from 10 to 32C and a range of low flow rates up to a maximum of 95 ml min-. The tests yieldedCHF values for both heat sinks in excess of 200 W cm-* with the advantage of both low flow rates andlow pressure drops (AP i 0.32 bar) as compared to high-flux, single-phase micro-channel heat sinks. Keyfeatures of the miniature heat sinks include a lack of inlet subcooling effect on CHF and superheated outletconditions at the lowest flow rates. A single CHF correlation was developed for both heat sinks. The paperwill iIlustrate the use of the CHF correlation and a generalized model for pressure drop as predictive toolsin assessing the merits of different channel sizes in incorporating miniature heat sink technology into highheat flux cooling schemes. Overall, the mini-channels performance proved superior to the micro-channeldue to pressure drops less than 0.01 bar for comparable CHF values as well as the reduced likelihood ofclogging and the relative ease in fabricating the mini-channel.

1. INTRODUCTION

INCREASED demands for dissipating high heat fluxesfrom electronic, power, and laser devices creates theneed for new cooling technologies as well as improve-ments in existing technologies. To meet such demands,miniature heat sinks of roughly one square centimeterin heated surface area are in the development stages.Such heat sinks consist of a thin block of metal thatcontains small channels for the flow of cooling fluid,which acts as a sink for heat supplied to the surfaceof the block. The heat sinks are typically characterizedby channel hydraulic diameters ranging from roughly90-550 pm [1,2] and are referred to as micro-channels.The small hydraulic diameter insures a thin thermalboundary layer and results in a large heat transfercoefficient; however, the dissipation of high heatfluxes is accompanied by large pressure drops. Tuck-erman and Pease [I] performed optimization studiesfor laminar flow of water through micro-channels of1 O cm* heated surface area. For a heat Aux of 18 1 Wcm . the corresponding pressure drop was 1 O bar. Ina separate study, Phillips [2] developed a computercode to predict both laminar and turbulent flow pres-sure drop and heat transfer characteristics for variousliquids and micro-channel sizes. The reference casefor water flow yielded heat fluxes of 100 W cm- andgreater in a 1 O cm long channel with a pressure dropof 0.69 bar.--._-..____

t Author to whom all correspondence should beaddressed.

In order to increase the heat flux from a micro-channel with single-phase cooling while maintainingpractical limits on surface temperature, it is necessaryto increase the heat transfer coefficient by eitherincreasing the flow rate or further decreasing thehydrauiic diameter. Both are accompanied by verylarge increases in pressure drop. However, two-phaseheat dissipation can achieve very high heat fluxes fora constant flow rate while maintaining a relativelyconstant surface temperature, and the surface tem-peratures magnitude is generally determined by thesaturation properties of the cooling fluid. The limitingfactor for most convective boiling situations is thecritical heat flux, CHF. When CHF is approached fora flow boiling system, there is a sudden dryout atthe heat transfer surface which is accompanied bya drastic reduction in heat transfer coefficient andcorresponding rise in surface temperature.

There are several advantages to utilizing two-phaseminiature heat sinks over their single-phase counter-parts. Key advantages are as follows :

(1) Single-phase miniature heat sinks compensatefor high surface heat fluxes by a large stream-wiseincrease in coolant temperature and a correspondingstream-wise increase in the heat sink temperature.This increase is often very detrimental to temperature-sensitive devices such as electronic chips. Two-phaseheat sinks, on the other hand, rely upon latent heatexchange which maintains stream-wise uniformityboth?n the coolant and the heat sink temperatures ata level set by the coolant saturation temperature.

321


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322 M. B. BOWEKS nd I. MLIIAWAR

i

NOMENCLATUREA,. heat sink total flow area normal to How, A r,,,, liquid subcooling, 7;,, - 7

N(7cDL,4) I mean liquid velocity at channel inlet(UP specific heat 1 specific volumeD channel inside diameter (I.$ difference in specific volumes of saturated,;

Fanning friction factor liquid and vaporc; two-phase friction facto] \ width of heat sinks heated upper surface.mass velocity. p @r/n ,. fir,II,-, latent heat of vaporization WK

Webcr number, G L/(al~,)empirical constant .\- mass vapor quality

L heated length of heat sink channel .s, thermodynamic equilibrium qualityL,, boiling length of channels heated section X, equilibrium quality at the channel inlet1 0 outlet length of heat sink channel -YI equilibrium quality at the end of theL * length of channels inlet single-phase heated lengthregion 3 coordinate in flow direction.L 101 total length of channeliv number of channels in heat sinkP pressure Greek symbolsAP pressure drop P density

m surface tension.Y heat flux based upon I an-heated uppersurface of heat sink(/,I, CHF based upon I cm heated upper Subscriptssurface of heat sink A accelerationI,1 heat flux based upon the heated channel exp cxpcrimcntal datainside ;trca. (I,,,u/( NnD) r liquid%1,.p CHF based upon the heated channel F frictioninside area ; vaporq,,_ CHF based upon channel inside area for gravity

condition of zero inlet subcooling i inletPT total volumetric flow rate of heat sink 111 maximum (critical heat flux)t thickness of cell containing one channel 0 outlett I width of cross sectional cell containing P heat flux area based upon channel insideone channel areaT temperature pred analytical predictionT, reference surface temperature used in sat saturatedboiling curves sub subcooled.

(2) In order to lessen the detrimental effects of A generalized correiation of CHF for forced con-stream-wise incrcascs in coolant and heat sink vection boiling in vertical tubes was later devised bytemperatures, larger flow rates are often needed with Katto [5. 61. Data for different liquids from varioussingle-phase micro-channel heat sinks. Two-phase sources were separately analyzed and correlated forheat sinks. on the other hand, permit the con- four distinct regimes called the L-, H-, N-, and HP-sumption of all liquid by evaporation, thus requiring regimes. CHF for zero inlet subcooling, Y,,,~,,~,wasminimal coolant flow rates. correlated as

An early study of CHF by Gambill and Greene [3]examined the flow of water through 7.74 mm i.d.vertical tubes of 4.73 cm length and greater. Therewas an increase in CHF values with increases in bothexit subcooling and mean flow velocity, and areduction in CHF with incrcascd L/D. The CHF datawas correlated in the form of Gunthers equation 141which accounts for the effect of velocity and sub-cooling at L,/D = 6 : however, to increase the rangeof applicability. Gambill and Greene modified thecorrelation with a term which accounted for vari-ations in LlD.

$j =.+I, ,r;. ;]. (I)

For most regimes, there was a linear rise in CHF withincreased inlet subcooling ; therefore, subcooling wasaccounted for by the following equation

where K was empirically determined from the database for each regime. Katto also concluded from his


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Experimental study of mini- and micro-channel heat sinks 323study that, for the special case of a very long tube,CHF seemed to occur for the condition of exit qualityequal to one.

The effect of inlet subcooling on CHF was laterexplored in a separate study by Katto 171. In hisrevised correlation he utilized the boiling length, L,,which is the heated length for a uniformly heated tubefrom the location where x, = 0 to the end of the heatedlength or the location of x, = 1 for the case of totaldryout. The study defined a specific range where sub-cooled flow CHF can be found using the correlationdescribed in equation (1) by replacing L with Lb.Additional studies on CHF in vertical upflow havebeen performed using R-l 13 as the working fluid.Weede and Dhir [8] performed an experimental studyfor 1.73 cm id., uniformly heated tubes varying inL / D from 5.1 to 17.6. The data showed the commontrends of increasing CHF with increasing inlet sub-cooling, decreasing L / D , and/or increasing mass vel-ocity. Based upon the experimental trends, the datawere correlated according to equations (1) and (2).Lazarek and Black [9] performed CHF studies withR-113 in a 12.6 cm long tube having an i.d. of 3.15mm. They correlated their data in the form of a criticalexit quality which was hypothesized as the trigger forthe onset of CHF. The experimental values of criticalquality covered a broad range with some as high as89%.

Flow boiling can achieve high values of heat flux,but there are practical concerns in the design of highflux heat sinks other than CHF. A problem unique toflow boiling is the production of vapor bubbles thatleads not only to increased heat transfer but alsoincreased pressure drop. This is not unlike single phaseflow in micro-channels where pressure losses are aproblem ; however, achieving high fluxes with flowboiling requires neither the relatively high flow ratesfor equal channel diameters of single-phase heat sinksnor the ultra small diameters that lead to very highpressure losses. The channel diameters required forcomparable two-phase heat dissipation are on theorder of 10-50 times larger than the micro-channels,thus referred to hereafter as mini-channels. Anadditional advantage of mini-channels is the ease offabrication, whereas micro-channels require specialmanufacturing technology.

In this paper flow boiling in both mini-channelD = 2.54 mm) and micro-channel D = 510 pm) heatsinks will be demonstrated as means of achieving high

values of heat flux. The mini-channel diameter waschosen based upon manufacturing ease and tube flowCHF predictions. However, the micro-channel wasselected from several provided by 3M and was specifi-cally chosen for a practical comparison of boilingperformance relative to the mini-channel. The flowboiling experiments were performed with R-113 at1.38 bar to determine CHF for a range of inlet sub-coolings and flow rates, and simultaneously, a database was acquired for pressure drop as a function ofboth flow rate and heat flux. Based upon the exper-

imental findings, a general description and com-parison of the hydrodynamic and flow boiling charac-teristics of both the mini- and micro-channel heatsinks are presented. The experimental work is comp-lemented by the development of a generalized pressuredrop model for miniature heat sinks and a correlationfor the CHF data base. Also included in this paper isa discussion on the use of the model and correlation aspredictive tools for incorporating this technology intoany high flux cooling scheme.

2. EXPERIMENTAL APPARATUSIn order to investigate mini- and micro-channel

two-phase flow and heat transfer characteristics, theflow loop illustrated in Fig. l(a) was constructed. R-113, the dielectric coolant chosen for this study, waspumped from the bottom of the loop reservoir andcirculated through the loop by a magnetically coupledcentrifugal pump. Exiting the pump, the liquid passedthrough a 5 pm cartridge filter followed by a heatexchanger where it was heated or cooled dependingupon the test subcooling conditions. The appro-priately metered volume flow rate then entered thetest loop while the remaining flow was routed to thereservoir through a by-pass loop. The volume flowrate of R-l i3 that entered the test module was mea-sured with a rotameter, and its magnitude was con-trolled by adjusting valves located in both the testloop and by-pass line.A cartridge heater was used to fine tune the testloops stream temperature, which was measured atboth the inlet and exit of the test module with ther-mocouples located, respectively, in the tubingupstream and downstream of the test module. Exitingthe module, the fluid flowed through a cooler to con-dense the large vapor fraction and then into the res-ervoir where the stream remixed with the by-passedliquid. To control the loop pressure, a liquid-vapormixture was maintained in the pressure control tank,and loop pressure was adjusted by either heat additionor removal. Also connected to the pressure controltank was a reflux condenser which was used duringdeareation of the fluid.Test m odule

The test module in Fig. l(b) was used for both heatsinks, and consisted of a housing and cover madefrom G-10 fiberglass plastic, which was chosen forboth its insulating properties and dimensionalstability. The mini- or micro-channel heat sink wasfitted in the housing and held securely in place by thecover. The housing possessed both inlet and outletplenums that were large enough to insure a uniformpressure in the plenum at the entrance to the heat sinkand at the exit where the streams from the heat sinksflow channels remixed. This assured equal flow ratesthrough the individual flow channels. Incorporatedinto the cover were pressure taps located at the inlet


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324 M. 5. BOWEKSnd I. MLJDAWAK

Test Loop

rai

Pressure Forts

(a) (b)Frc:. I. (a) Flow loop and jb) test module.

and outlet plenums for me~~surement of both inletpressure and pressure drop.

The miniature heat sinks are illustrated in Fig. 2.The mini-channel heat sink, Fig. 2(a), was machinedfrom one block of oxygen-free copper, It consisted ofa 10 x 10 mm top section, to which a thick-filmresistor was soldered, and a 28.6 x 28.6 mm bottomplate through which the mini-channels weremachined. The top section protruded 3.18 mm fromthe bottom plate and was designed to provide a uni-form heat flux for a I cm area. The thick-film resistorwas powered by a Cl-240 V a.c. variac. Directly belowthe top section and equidistant within a I cm widthwere three 2.54 mm i.d. channels that ran the entirelength of the bottom plate, which had area largerthan the heated top due to the necessity of providingmechanical seals. A 0.13 mm thermocouple for pro-viding a reference tem~er~~ture was located at the mid-point of the mini-channels top section. The ther-mocouple was placed inside a 0.81 mm hole whichwas then filled with a thermally-conducting epoxycontaining boron nitride.

The micr[~-channel heat sink, Fig. 2(b), was verysimilar to the mini-channel ; however, it consisted ofa separate nickel plate and a copper conducting block.The inicr~)-channel plate, which contained 510 /lrn i.d.channels, required special manufacturing technologyand was provided by 3M. The top section of the con-ducting block duplicated that of the mini-channel heatsink with the lower part serving as a spacer, and toprovide a low thermal contact resistance between the

conducting block and nickel plate, the two parts weresilver-soldered together. To insure that channelswithin only a 1 cm width directly below the heat sourcewere active, all channels except the middle 17 werefilled with solder at both the channel inlets and outlets.

Before performing experimenta. tests, the flow loopwas prepared for operation which included periodicdeareation of the fluid. This procedure was performedby vigorously boiling the R-l 13 to force the vaporand other entrained gases into the reflux condenserwhere the R-l 13 vapor condensed and drained backinto the pressure control tank as the other non-con-densable gases escaped freely to the ambient. Also ona periodic basis, the channels of the ~~~ni-channel heatsink were cleaned with cotton swabs and acetone,and the channels of the micro-channel heat sink werereamed with a small wire to preclude any buildup ofdeposits.

For normal testing procedure, the electrical powerto the heater was adjusted by the variac to the desiredlevel, and the heat sink was then allowed to reachsteady conditions, which were achieved withinminutes once the flow conditions were stabilized.However, due to the large vapor fractions producedwithin the nucleate regime, 15-20 min were oftenrequired to stabilize the flow loop conditions. Steadystate was assumed when the standard deviation overa period of 30 s for 15 samples of the heat sinksthermocouple was less than 0.2G ; however, this con-


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Experimental study of mini- and micro-channel heat sinks

60

325Think-~lrnResIstor

FIG. 2. (a) Mini-channel and (b) micro-channel heat sinks.

dition was relaxed for the very high fluxes (closeto CHF) due to larger temperature fluctuations. Atsteady state, readings from all thermocoupies, the wattmeter, and both differential and absolute pressuretransducers were recorded with a Keithley series 500data acquisition system as directed by a Compaq mic-rocomputer. Manual heat flux adjustments were donein increments of 10-20 W cm-* in the nucleate regime,followed by 2 W cm-or less as CHF was approached.Boiling curves required 3-4 h and ended with CHF,which was identified by a sudden unbounded rise inthe heat sinks temperature.Measurement uncertaintiesErrors associated with the thermocouples are esti-mated to be less than 0.2C; however, due to the highheat fluxes, the heat sink thermocouple was facinglarge temperature gradients. The additional errorassociated with large temperature gradients was esti-mated to be less than 1.2C at a heat flux of 200W cm -. The un~rtainty associated with differentialpressure measurement was estimated to be less than5% for the low pressures (AP < 0.02 bar) and lessthan 1% for the higher differential pressures, anduncertainty in the absolute pressure was 1%. Error inflow rate measurement was estimated to be less than4% with the greatest uncertainty being for the flowrates less than 34 ml min-.Heat losses from the heat sink were numerically

estimated to be less than 3% ; therefore, electricalpower measurement, which had an uncertainty of lessthan I%, was used for heat flux calculations. Thenumerical predictions of heat loss were madeassuming free convection boundaries for exposed sur-faces and zero contact resistance between surfaces,thereby yielding conservative estimates of heat loss.

3. DISCUSSION OF RESULTSBoiling data for flow of R-113 through both themini-channel and micro-channel heat sinks were taken

for a range of flow rate from 19 to 95 ml min- andinlet subcooling from 10 to 32C while maintainingan inlet pressure of 1.38 bar. Tests were conducted toexplore the effects of velocity and inlet subcooling onCHF as well as to compare the thermal and hydro-dynamic performances of the two heat sinks.

Figure 3(a) compares the boiling curves of the mini-and micro-channel heat sinks for a Aow rate of 64 mlmin.- and inlet subcooling of 20C. For the single-phase portion of the curves, there is a distinct of&etbetween the heat sinks curves with the micro-channelexhibiting a lower thermal resistance. These resultsare to be expected since a small hydraulic diameterassures a thin thermal boundary layer, resulting in alarger heat transfer coefficient for the micro-channel.Also, the thermal resistance is further reduced by thelarger number of channels in the micro-channel heat


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326 M. B. B~WEKSand I. MLD W K

111 I O 100 500

1. - T, W64

0.35jifsj j,0.25 c

cp 0. 15 -Pcl

0.05 -

QT = 64 t im n_ '(0.017QpmATsub,i = 20C

PI _ 1. 38bar I(200 psi @ I~~~~ ___

1 10 100 500q (W cmw2)@I

FIG. 3. Comparison of mini- and micro-channel (a) boiling curves and (b) pressure drops for a. Aow rateof 64 ml min- and 20 C inlet subcooling.

sink which results in a 14% increase in total cir-cumferential area available for heat transfer. Figure3(a) shows a slight hysteresis at incipience for themini-channel ; however, within the nucleate boilingregime, the distinction in thermal behavior subsidesfor all heat fluxes less than approximately 150 Wcm- Above this flux, the boiling curves diverge, withthe mini-channels curve displaying much more of thecharacteristic necking before approaching CHF at200 W cm- as compared to 256 W cm- for themicro-channel.Pressure drop

For a flow rate of 64 ml rnin-- , the micro-channelyielded a 28% increase in CHF as compared to themini-channel; however, as illustrated in the cor-responding pressure drop curves of Fig. 3(b), thisrequired a substantial increase in pressure drop, from0.008 bar for the mini-channel to 0.32 bar (3900%difference) for the micro-channel. Under single-phaseconditions, the mini-channel pressure drops were neg-ligible (AP < 0.003 bar), as were the micro-channels(BP z 0.007 bar), due to the low flow rate employed.Once in the nucleate regime, the micro-channel pres-sure drops were observed to rise drastically withincreased heat flux. A comparison of pressure drop inthe nucleate boiling regime (y = 100 W cm- ), wherethe thermal characteristics are indistinguishable,yields a AP z 0.003 bar for the mini-channel andBP z 0.07 bar for the micro-channel. These resultsdearly demonstrate a need for predictive tools forboth the two-phase hydrodynamic and thermalbehavior of mini- and micro-channel heat sinks. Suchtools are of utmost importance in aiding the adap-tation of miniature heat sink technology into any highflux application.

The effect of subcooling on the boiling chardc-teristics is demonstrated in Fig. 4. Included on the

figure are schematics of the heat sinks illustrating thereference temperatures, r,, used in the presentationof the boiling curves and was calculated by assumingone-dimensional conduction from the plane of thethermocouple to the plane of T,. The boiling curvesare for a flow rate of45 ml min and inlet subcoolingsof 10, 20, and 3OC. These plots illustrate a distinctoffset between each subcooling in the nuclcatc boilingregime : however, this offset is simply a result of usinginlet temperature in the temperature difference of theplot abscissa. The curves for each subcooling convergeat high fluxes and yield the same values of CHF foreach respective heat sink. As expected, the micro-channel yielded a larger CHF than the mini-channelsCHF. An explanation for this behavior is availablefrom Fig. 5, which shows the outlet temperatures thatcorrespond to the heat fluxes of Fig. 4. For heat fluxesbelow 20 W cm *, the outlet temperatures dis-tinctivcly correspond to each value of inlet sub-cooling; however, for heat fluxes above 40 W cm 2.the outlet temperature shows little dependence on inletsubcooling. The exit temperature corresponding todifferent subcoolings is indistinguishable for thehigher heat fluxes because of the fluid being at satu-rated conditions. Therefore. the outlet temperature jsthe saturation temperature that corresponds to theexit pressure. The behavior described was charac-teristic of both heat sinks; however, the micro-chan-nel, unlike the mini-channel, experienced a decreasein outlet temperature with increasing heat flux. Fig-ures 6(a) and (b) demonstrate that this phenomenonis a result of the large rise in pressure drop in themicro-channel with increasing heat flux. The pl otsshow the variation in outlet saturation temperatureas a result of the decrease in outlet pressure as pre-dicted by the model presented in the next section. Ineach case, the outlet subcooling reduces to zero forrelatively very low values of heat flux; therefore. folthe low flow lates considered in this study, there wasa negligible effect of inlet subcooling on CHF.


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Experimental study of mini- and micro-channel heat sinks 327

1 10 100 500T, - T, (2

(a)

500

100

N-' 5e= 10

11 10 100 500

Ts- T, ( C)NO

FIG. 4. Comparison of boiling curves for the (a) mini- and (b) micro-channel heat sinks for inlet subcoolingsof lo,20 and 30C at a flow rate of 45 ml min-I.

Superheated exi t condit io nsFor test cases at the lowest flow rates (Qr < 19 ml

min-), the flow not only reached saturation con-ditions and possibly total dryout, but also superheatedconditions as illustrated in Fig. 7. The plot is for themicro-channel at a flow rate of 19 ml min- and inletsubcooling of 20C. The exit temperature is shownexceeding the outlet saturation temperature andassuming superheated values for heat fluxes evensmaller than CHF. Superheated conditions at the out-let were observed not only for the micro-channel, butalso for the mini-channel ; however, superheated exittemperatures were encountered at lower flow rateswith the mini-channel heat sink. These results suggestCHF is not always triggered by total dryout at theexit. This issue will be discussed in a later section.

30' ' , . , . . I , , . , . ' . 11 10 100 500

q ( W cm-?)(a)

4. PRESSURE DROPTo aid in the design of mini- and micro-channel heat

sinks, a hydrodynamic model for predicting pressuredrop was developed. With reference to Fig. 8, theheat sink is modeled as having N circular channels ofdiameter D, and each channel is contained within arectangular cell with sides of lengths t and t,.

Tw o-phase pressure dropEvaluation of the pressure drop through a channel

is based upon the homogeneous two-phase flowmodel. The model accounts for the total pressuregradient as the sum of contributions from friction,acceleration, and gravity, where the gravitationalcomponent is negligible for the heat sinks considered.

60

35

301 10 100 500

q (W cm-)(b)

FIG 5 Comparison of (a) mini- and (b) micro-channel outlet temperatures for inlet subcoolings of 10, 20,and 30C at a flow rate of 45 ml min-.


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328 M. B. Bowels and I. MUDAWAK60

55

50o^e 45I-O

40

35

30 t I I I11 10 100 500

q W cm.*)a)

55 -

50 -Ge 45-co

40 -

35 ^

301 10 100 500

q W cm-)bJ

FIG. 6. Measured exit fluid temperatures and predicted exit saturation temperatures for (a) mini-channelwith negligible pressure drop and (b) micro-channel with large pressure drop.

For the purposes of the present analysis, all propertiesare assumed constant. This assumption yields [lo]

and

The flow quality, X. is assumed equal to the equi-librium quality, s,, for 0 < .Y, < 1. The equilibriumquality is determined by employing conservation ofenergy on a differential control volume along thechannel. The resulting differential expression for theequilibrium quality is

75706560

Ce 55co

504540351 ,.,.I ,,,,,I ,i1 10 100 500

q W cm-*)FIG. 7. Superheated exit conditions for flow rate of 19 mlmin- as illustrated with measured exit fluid temperaturesand predicted exit saturation temperatures.

Integrating the enthalpy gradient in equation (4) withthe assumptions of constant heat flux and constantproperties yields

Substituting equations (5) and (4) in equations (3a)and (3b), respectively, the frictional and accelerationalpressure drops are found by integrating over the chan-

FIG. X. Schematics illustrating mim- or micro-channel heatsink geometry with uniform heat flux, y, applied along theupper surface. Cross section in (a) defines the mean heat flux.qr, around the channel inside area. The channel side view (b)

defines the model nomenclature for a subcooled inlet.


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Experimental study of mini- and micro-channel heat sinks 329nels boiling length, &,. Rewriting in terms of xL, theequilibrium quality at the end of the heated length,yields

(6b)The total pressure drop in the boiling region(0 < X, < 1) is the sum of the contributions of accel-eration and friction.

AP, = AP, +AP,. (7)The mass velocity, G, can be defined in terms of the

total flow rate and flow area which is then substitutedinto equations (6a) and (6b). Regrouping yields

and

@b)which are dimensionless relations for the frictionaland accelerational pressure drops.Comparison with experimental dataIn order to accurately determine the total pressuredrop for the mini- or micro-channel heat sinks, thepressure drop from the entrance and exit lengths mustbe included as well as the heated length upstream ofthe point where x, = 0. To account for each con-tribution, the total pressure drop is written as

AP = AP, +AP, +AP,, 9)where the respective subscripts refer to single-phase,boiling, and outlet sections of the channel. The single-phase length of the channel, L,, is the sum of theunheated entrance and the heated section up to thelocation of X, = 0 (see Fig. 8(b)) which can be deter-mined from equation (8).

The single-phase pressure drop is given by2f,G2L,AP,=- P,D (10)

where fS is the Fanning friction factor whose value isdetermined from the Reynolds number for each of the

unheated lengths as found in ref. [111. The remainingportion of the heated length is the boiling length, Lb,for which 0 < x, < 1. The two-phase pressure droprelationships derived for frictional and accelerationalpressure drop are valid within the convective boilingregion; thus, equations (6a), (6b), and (7) are used tocalculate the pressure drop for the remaining heatedsection assuming no superheating takes place withinthe heated section.Over the length L,, which extends from the end ofthe heated section through the channel outlet, thequality remains constant at a value equal to x,_. Thetwo-phase frictional pressure drop is found by inte-grating equation (3a) for the exit length of the channel.This yields

AP, = (2;~;Lo)[l+~L t$)], (11)which is also the total pressure drop in the exit lengthin the absence of any acceleration.Pressure drop predictions based on equation (9) arecompared with experimental data in Fig. 9. For thetwo-phase friction factor, Collier [lo] gives a rangefrom 0.0029 to 0.005 ; therefore, a conservative valueof fTp = 0.005 was used. Excluded from the datashown are those for which x, > 1 at the end of theheated section. Also, calculations of the two-phaseMach numbers yielded a maximum value of 0.46 with90% of the data having Mach numbers less than 0.28.Therefore, the assumption of constant properties isjustified due to the small compressibility effects. Theexperimental pressure drop data are for mean valuesof 15 samples over a period of 30 s. The use of meanvalues is due to pressure drop fluctuations duringtesting. The standard deviations of these fluctuationsfor the micro-channel were generally around 2% upto a high of 8% at the lower values of pressure drop.The mini-channel yielded the greatest percentage fluc-tuation with standard deviations as high as 30% for

s ss*,-1 as*, -

0.001 0.01 0.1 0.5APprw bar)

FIG. 9. Comparison of theoretical predictions of pressuredrop with experimental data.


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330 M. 3. BOWERSnd I. MUDAWAKAP c 0.01 bar due, in part, to the limited resolutionof the differential pressure transducer for these verylow pressures. The plot includes 73 data points ; how-ever, most are for the micro-channel because of itsbroader range of pressure drops. The model closelypredicts the pressure drops as iilustrated by the k 30%error band with the best predictions being for pressuredrops exceeding 0.06 bar. Heat sink inlet and outletpressure losses between the channel and the plenumsare not included in the model ; however, calculationsshow that the net contribution from both the accel-eration or deceleration and form pressure drops is lessthan 0.7% of the total pressure drop. Based upon themodel, the major contributor to the total pressuredrop was determined to be the two-phase accel-erational component calculated from equation (hb).For the micro-channel, the acceleration accounted forapproximately 75% of the total pressure drop, com-pared to approximately 90% for the mini-ch~lnnel.These results are to be expected due to the low massvelocities yielding low frictional losses. For the highflow qualities produced, a departure from the homo-geneous assumption of dispersed flow to an annularflow would be expected ; however, with the large liquidto vapor density ratio, evaporation is accompanied bya large acceleration in the flow that is accounted forin the model.

5. CHF CORRELATIONThe CHF data base exhibited a lack of subcoolingeffect on CHF for both heat sinks and all operating

conditions. The effect of mass velocity on CHF isillustrated in Fig. 10(a). The data base covers a massvelocity range from 31 to 150 kg m s-l for the mini-channel and 120 to 480 kg mm s - for the micro-channel. The data points follow a well defined trendwith mass velocity with a high degree of repeatability.

There is a distinct separation between the mini- andmicro-channel curves as is expected due to the largedifference in heated length-to-diameter ratio, 3.94 forthe mini-channel compared to 19.6 for the micro-channel.Due to a lack of CHF correlations for boiling in~nicro-cllannels. the CHF dcpendcnce on mass vel-ocity for each heated length-to-diameter ratio wasused to corretate the data. Since CHF is not sensitiveto inlet subcooling, the standard CHF correlationform presented in equation (1) was used and resultedin the following correlation :

as shown in Fig. IO(b), where ljn,.r is CHF based uponthe heated channel inside area. Heat flow predictionsmade using a finite element code with a constant sur-face heat flux and constant channel wall temperaturerevealed that 99% of the heat passes through theupper half of the channel for both the mini- and micro-channel heat sinks. Therefore, the channel inside areawas used in the correlation to represent an averageheat flux. Also included in Fig. 10(b) is the equilibriumquality that corresponds to each CHF value, and des-ignated on the plot are values of CHF where super-heated exit conditions similar to those shown in Fig.7 were measured. For the mini-channel, only data forthe lowest flow IXteS produced .Y& > 1. whereas thernicro-~~d~ln~l exhibited .Q > 1 for all data except thehighest flow rate. This is expected since the micro-channel achieved higher CHF values than the mini-channel at ail vatues of flow ram.These CHF results point to unique fcaturcs ofminiature channel heat sinks not available in mostother boiling systems. Of special importance to highflux cooling applications are the following features :

4 ,,.. 8. . ..i b.,. ,J o.ooL ,,,. /... ,,.. I.... ,.~o,5*100 200 300 ml 500 00 01 0.2 0.5 0.6

G kg mm2-

FIG. IO. (a) Effect of mass velocity on CHF for mini-channel and micro-channel heat sinks and (b) theresulting correlation of CHF data and corresponding values of outlet equilibrium mass vapor quality forAT,,,, = 20C.


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Experimental study of mini- and micro-channel heat sinks 331

(1) The two heat sinks demanded minima1 flowrates evidenced by the values of .xt approaching orexceeding unity.(2) The small diameters of the mini- and micro-channels suggest an increased frequency and effec-tiveness of droplet impact with the channel wall inregions of high xL values. This may have greatlyincreased the heat transfer coefficient in that region,and enhanced CHF, compared to droplet flow regionsin large diameter tubes.(3) The small overall size of the heat sink seems togreatly contribute to delaying CHF by conductingheat away from the downstream region undergoingeither partial or total dryout to the boiling region ofthe channel. No other system known to the authorshas produced values of xL exceeding unity at CHF.

6. DESIGN CONSIDERATIONSPractical design tools have been estabhshed in the

form of a CHF correlation and pressure drop modelapplicable to the mini- and micro-channel heat sinksof this study as well as miniature heat sinks of varyingsizes. Figure 11 presents curves that characterize bothCHF and the corresponding pressure drop for themini- and micro-channel heat sinks at conditions forwhich xL < 1. The CHF curves were constructed usingthe correlation of equation (12), and the pressure dropcurves were constructed from equations (6) and (7).For illustrative purposes, a maximum heat fluxrequirement (i.e. CHF) of 500 W cm- based on the1 cm2 heater surface area has been assigned. To ach-ieve 500 W crne2 with the mini-channel necessitates aflow rate of approximately 270 ml min- as comparedto a flow rate of roughly 200 ml min- for the miero-channel. Both flow rates are low considering the highheat flux required. However, the slight advantage ofa lower flow rate with the micro-channel heat sink isrecognized with a very high penalty in pressure drop,

25 -

20 -

=jj 5

10 -

5-

OL0.05

/0 100 150 260 250 300 3509 (ml mid)I , , I I I I I 1 , I I I I I0.02 .03 0.04 0.05 0.06 0.07 0.08 0.09

QT (gPm>FIG. 11. Design plot illustrating Aow rate and pressure dropcharaeterjstics to achieve a CHF of 500 W cmm2 with mini-channel and micro-channel heat sinks with .q < 1.

I .7 bar compared to only 0.1 bar for the mini-channelheat sink. As demonstrated by the plot for this par-ticular example, the mini-channel clearly possessessuperior overall performance. Furthermore, mini-channels are much less likely to promote flow cloggingthan micro-channels. However, as evident by thediverging CHF curves, higher heat flux values maynecessitate the use of the micro-channel, if the highpressure drop can be tolerated, or a heat sink withchannel diameters between those considered in thepresent example due to constraints such as maximumflow rate.By generating plots similar to those of Fig. 11 fora variety of heat sink channel sizes, a good comparisonof performance characteristics can be obtained. Plotsof this type do not yield a single optimum heat sinksize ; however, optimization schemes do not accountfor important practical concerns. Cooling schemesare generally limited by flow rate and pressure dropconstraints as well as issues such as ease of fabricationand maintenan~ of the device. The above constraintsare unique to each cooling scheme and must be care-fully evaluated by the designer. Thus, the findings ofthis study provide information that is imperative to adesigner incorporating mini- or micro-channel heatsinks into a high flux cooling scheme.

7. CONCLUSIONSAn experimental study of CHF in mini-channel(D = 2.54 mm) and micro-channel (D = 5 10 pm) heatsinks of f cm in heated length was conducted. Tests

were performed for a range of inlet subcooling andAow rate. Complementing the experimental work area pressure drop model and CHF correlation whichprovide analytical tools for heat sink design. Keyfindings of the study are as follows :

I. Flow boiling in mini- and micro-channel heatsinks is an effective means of achieving high heat tluxes(q > 200 W cm-*) coupled with low flow rates(Q, < 65 ml min-) and low pressure drops(AP < 0.35 bar). In comparison, single-phase micro-channel technology reported in ref. [I] required a pres-sure drop of 1 bar to achieve a heat Aux of 181 W cm-using water which has far superior thermal propertiesthan the dielectric liquid utilized in the present study.

2. Reference [3] hypothesized that CHF was trig-gered by critical exit qualities ; qualities as high as89% were reported in that study with R-l 13 in 3.15mm i.d. tubes of 12.6 cm heated length. Reference [6]afso reported that CHF in long tubes appeared tooccur at an exit quality approaching unity. However,the present study employed heat sinks which reliedupon heat exchange with an array of small diameterchannels with short heated lengths that were formedin a the~ally-conducting metallic block. Thisallowed the spread of heat to surface locations whereit could be dissipated rather than creating a large


12/12

332 M. B. BOWERS and 1 MW W Rrise in surface temperature. The net result was totaldryout, and, at the Iowest flow rates, superheatedexit conditions before CHF which suggests CHF was

1,triggered at a location upstream of the exit. This isevidence that, unlike most other boiling systems. 2.cooling with miniature heat sinks is possible with anevaporation efficiency of unity (i.e. minimal coolantflow rate).

. CHF for mini-channel and micro-channel heat

REFERENCES

sinks is not a function of inlet subcooling at low flowrates due to the fluid reaching the saturation tcm- 4.perature a short distance into the heated section ofthe channel. 54. The homogeneous equilibrium model accuratelypredicts the pressure drop for flow boiling in minia-ture heat sinks at low Row rates. The major corn-ponent of pressure drop was the acceleration which 6,accounted for roughly 90 and 75% of the mini-channel and micro-channel pressure losses, respcct-ivcly. I.

5. The flow boiling performances of both the mini-and micro-channel heat sinks are superior to com-parable single-phase technology ; however, the mini-channel &arly has the practical advantage over themicro-channel. Mini-~~annei CHF values as high as200 W cm- were achieved with a negligible pressuredrop of less than 0.01 bar compared to 0.23 bar for themicro-channel. Furthermore, the mini-channel heatsink could bc fabricated using conventional drillingwhile fabrication of micro-channel heat sinks requiresspecial manufacturing technalogy and is more proneto flow clogging.

D. B. Tuckerman and R. F. W. Pease, High-performanceheat sinking for VLSI, IEEE Elecrron Dmiw Ltrrt. EDL-2.126 129 (1981).R. J. Phillips, Forced-convection, hquid-cooled micro-channel heat sinks, M. S. Thesis, Department of Mech-anical Engineering, Massachusetts Institute of Tech-nology. Massachusetts (1987).W. R. Cambill and N. D. Greene. Boiling burnout withwater in vortex flow, Chem. B qng Prtj,c). 54. 68--76(10X9.F. C. Gunther, Photo~raplli~ study nf surface-boilil?~heat transfer to wafer with forced convection. Tr~,r.s..4SMI:73(2), 115- 123 (1951).Y. Katto. A generalized correlation ofcritical heat ituxfor the forced convection boiling in vertical uniformlyheated round tubes, Int. .I. Hecct Mass TF~UL Y 21, 15271542 (1978).Y. Katto, A generalized correlation of critical heat Huxfor the forced convection boiling in vertical uniformlyheated round tubes--a supplementary report. Ittt. d.Hm Mms Trmsfcr 22, 7833794 ( 1979).Y. Katto, An analysis of the etTect of nlet subcooling onzriticat heat flux of forced convection boiling in verticaluniformly heated tubes. hf. J. Hrut Mus.s ?rnn,~f~~r 22,156i- 1575 (1979).

X. J. Wcede and V. K. Dhir, Experimeiltal study of thecnh~~n~~rnent of criticai heat flux usine, tangential flow

9. G. M. Lazarek and S. H. Black, Evaporative heat trans-fer. pressure drop and criticai heat flux in a small verticaltube with R-l 13, ht. J. Hew Mcrss Trunsfipr 25, 945960 (1982).

IO. J. G. Collier, Con~ec(it~c &i&g urltl (onc/e~str(io,~ (2ndEdn). McGraw-Hill, London (I98 I ).I I K. W. Fox and A. T. McDonald. lt7/,orlz4crion io Lhiti

Mec~hnrc~.~ (3rd Edn) Wiley. Ncu York (1985).

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