A novel thermo-hydraulic test platform for micropillared array thermal wick optimization

Proceedings of the ASME 2012 10th International Conference on Nanochannels,Microchannels, and Minichannels

ICNMM2012July 8-12, 2012, Rio Grande, Puerto Rico

ICNMM2012-73192

A NOVEL THERMO-HYDRAULIC TEST PLATFORM FOR MICROPILLARED ARRAYTHERMAL WICK OPTIMIZATION

Collier Miers, Geoff Wehmeyer, and Carlos H. HidrovoMultiscale Thermal Fluids Lab (MTFL)

Department of Mechanical EngineeringThe University of Texas at Austin

Austin, Texas

ABSTRACTHeat pipes have immense potential in the future of thermal

management in electronic devices. As a passive device, they relysolely upon capillary forces to recirculate the coolant from thecondenser to the evaporator via a wicking structure. In interme-diate temperature heat pipes the limiting factor for heat removalis the capillary limit, which indicates the maximum recirculationrate that the capillary forces can induce. This capillary limitmust be increased to allow heat pipes to remain a viable op-tion for heat management within electronic devices. The aim ofthis work is to characterize and optimize the capillary limit ofmicropillared thermal wicks for heat pipe application in micro-electronics cooling.

Towards this goal, an analytical model, and a novel thermo-hydraulic experimental setup was developed. The analyticalmodel of the micropillared array wicking structure provides atheoretical basis from which the pillar geometry and arrange-ment can be optimized. A capillary limit model was used to de-termine the geometric relationship between the pillar arrays andthe maximum capillary flow rate through the wick. This modelconsiders the effects of gravity and mass transfer due to evapo-ration.

Finally, the thermo-hydraulic characterization setup, de-signed to minimize environmental losses, was used to experi-mentally determine the capillary limits of different silicon basedmicropillared wick samples. The heater and wicking structurewere enclosed in a temperature and humidity controlled vacuum

chamber. The results obtained from this setup were used to vali-date the analytical model shown in this paper.

INTRODUCTIONIn accordance with Moore’s Law, electronics have steadily

increased in power while decreasing in size over the last fiftyyears [1, 2]. However, future technologies will need new meth-ods for heat dissipation in electric devices to continually advanceat this pace. Heat pipes are an attractive technology for the pas-sive cooling of such electronic devices, but it has been theorizedthat current heat pipe technology cannot function effectively forheat fluxes exceeding 100 W

cm2 [3, 4].The limiting factor for intermediate temperature heat pipes

used in electronic cooling is the capability of the wick to returnfluid to the evaporator [5]. This capillary limit occurs when thecapillary pressure is less than the sum of the pressure drops dueto losses in the wick, thus barring any increase in the mass flowrate through the wick.

Performance of intermediate temperature heat pipes can alsobe hampered by boiling phenomena. Boiling can occur at thebottom of the liquid film within the evaporator segment of thewick. The bubbles formed during this process decrease the flowarea in the wick, resulting in vapor blockages of the micropillararray and a decreased recirculation rate. At high heat fluxes aphenomenon called dry-out occurs. The onset of dry-out is in-dicated by an increased superheat and results in no enhancement

1 Copyright c© 2012 by ASME

of the capillary flow rate despite added heat flux at the evapo-rator [6–8]. Due to the complexities accompanying boiling inthe wicking structure, most heat pipe designers take measures toavoid the occurrence of boiling. This paper focuses solely on thecapillary limitation of the wick.

Heat pipes have generally been examined for optimizationas a whole system [9]. This approach leaves aspects of the in-dividual component interactions incompletely explained. Isolat-ing the wicking structure to find optimal pillar geometries anddistributions can lead to a greater understanding of how to max-imize heat removal in heat pipes. Recently, much attention hasbeen focused on characterizing flow through micropillar wickingarrays, with a particular emphasis being placed on tracking ini-tial fluid penetration distances into unwetted pillar arrays. Ishinostudied the effects that varying pillar height and array spacinghad on the fluid’s impregnation speed [10]. Srivastava has usedfinite-element methods to expand on this approach, predictingpenetration velocities based on COMSOL simulations and sur-face energy minimization techniques [11]. Nam uses capillaryrate of rise experiments and numerical methods to find an effec-tive wick permeability through hydrophilic copper microposts,which is then used to find an effective capillary pressure [12].Xiao uses numerical methods and experimental observations tofind a driving pressure force for initial penetration into an un-wetted porous array, and solves a form of the Brinkman’s equa-tion to find the viscous losses [13]. The proposed model andexperimental method are intended to more closely mirror con-ditions for wicking structures in heat pipes, where continuousflow through wetted pillar arrays occurs because an applied heatflux at one end of the wicking structure is evaporating the liq-uid. Rather than focusing on initial penetration distances, thethermo-hydraulic test platform allows the direct measurement ofthe effective heat load capacity of a given wicking structure.

Isolation of the wicking geometry will occur both analyti-cally and experimentally in this study. The aim of the analyticalmodel is to investigate the forces driving the capillary flow us-ing an ab initio approach. Utilizing this approach avoids the useof the empirically determined permeability information requiredfor Darcy’s Flow law. Validation of this model will be accom-plished through the use of an original experimental set up thatallows for control of the wick conditions as well as the test en-vironment. Normalizing the test conditions further isolates theindividual geometric differences between the wicks.

NOMENCLATUREP Pressure of fluidg Gravityh Convective heat transfer coefficientk Thermal conductivitym Mass flow rates Spacing of pillars in x-dimentionu Fluid velocity in flow directionθ Contact angleµ Fluid dynamic viscosityρ Fluid densityσ Surface tensionAc Cross-sectional area of the wickAsur f Surface areadn Diameter of pillarhn Height of pillarLevap Length of evaporative regionLwick Length of wickQNE Volumetric flow rate in non-evaporative regionQvol Volumetric flow rateQevap Evaporation rate per unit length of wickqconv Convective heat transferqwick Conductive heat transfer through the wickq′′evap Heat flux through the wickwn Width between pillarswwick Width of wick∆Pcap Capillary pressure∆Pevap Pressure drop over the evaporative region∆Pwick Pressure drop over the entire wick

THEORETICAL MODEL

FIGURE 1: APPROXIMATION OF FLUID FLOW THROUGHMICROPILLAR ARRAY


Capillary Limit ModelThe capillary limit model predicts the maximum mass flow

rate through a homogenous array of micropillars using a bal-ance between capillary pressure, gravitational forces, and vis-cous losses. For the pillar geometry shown in Fig. 1, the Laplacedriving pressure can be expressed as [14]:

∆Pcap =2σ cosθ

wn(1)

The effective contact angle is influenced by the geometry of therough surface, and is larger than the intrinsic contact angle be-tween the fluid and smooth solid [15]. Bico has derived an equa-tion determining the contact angle for hydrophilic surfaces usingthe solid fraction of dry area and solid roughness of the struc-ture [16]. For a composite surface consisting of the pillars andthe surrounding substrate, the fraction of dry area is found by di-viding the dry pillar top area by the wetted pillar sides and thesubstrate. The surface roughness is found from the ratio of theactual surface area to the projected area. The contact angle thendepends on the pillar spacing, height, and diameter.

The balancing losses can be derived from the general two-dimensional Navier-Stokes equations. Due to the low Reynoldsnumber of the flow, entrance effects are neglected, and the mo-mentum equilibrium yields:

∂P∂x

+ρg = µ

(∂ 2u∂y2 +

∂ 2u∂ z2

)(2)

In steady-state conditions, the volumetric flow rate is constantover the portion of the wick removed from the heat source. Asthe fluid evaporates out of the wicking structure near the heatsource, the flow rate will decrease. In the evaporative region, thismodel assumes that the flow remains at the constant height ofthe pillars while decreasing in velocity to account for the evap-orated mass. A constant fluid evaporative rate per unit length ofthe wick, Qevap is found by dividing the total entering volumet-ric flow rate by the length of wick in which evaporation occurs.Although there are actual variations in the rate of evaporation,this first order approximation gives insight into for the decreas-ing viscous stresses associated with the decreased liquid flowrate. From conservation of mass analysis, the volumetric flowrate along the wick is given by:

Qvol = QNE − Qevapxe (3)

Here, xe is the distance from the initiation of evaporation on thewick and QNE is the incoming flow rate from the non-evaporativeregion. As Fig. 2 shows, there are two distinct regions of thepillar structures with different boundary conditions. In Region

FIGURE 2: REGIONS A AND B AND THEIR VELOCITYPROFILES

A, the liquid only experiences viscous losses from the wick sub-strate, while in Region B the fluid is also constrained by pillars oneach side. Region A is modeled similarly to forced flow betweeninfinite parallel plates, and the pressure drop over one Region Asection is [17]:

∆PA =3µ

h3nwn

∫ x+s

xQvoldx+ρgs (4)

The pillars constraining the liquid in Region B are treated as flatplates, modeling the flow similarly to forced flow through halfof a rectangular duct. Though this approximation ignores thetwo-dimensional effects of flow around a submerged cylinder,the Stokes flow conditions prevalent in these tests indicates thisapproximation gives reasonably accurate results for low-speedflow interactions with the curved surfaces. The velocity distribu-tion is then governed by a partial differential equation that canbe solved using a separation of variables technique that yields aFourier series expression for the pressure drop [17]. The Fourierseries solution was nondimensionalized and graphed such thata linear relationship between the nondimensionalized flow ratesand the pillar aspect ratio could be found. Using this solution inthe momentum equation yields a pressure drop over Region B of:

∆PB =12µ

hnw3n

∫ x+dn

xQvoldx+ρgdn (5)


FIGURE 3: ETCHED MICROPILLAR ARRAY

To find the pressure drop over the entire evaporative region of thewick, the pressure drop over a given segment consisting of adja-cent Regions A and B is first calculated. The pressure drop overthis segment varies with the segment’s location on the wick. In-tegrating these segmented pressure drop over the number of seg-ments in the evaporative region produces the evaporative regionpressure drop. The pressure drop in the nonevaporative regioncan be evaluated using the same method where Qevap is 0. Thesummation of these pressure drops is equivalent to the Laplacepressure at the maximum flowrate.

Incorporating the width of the wick and the packing den-sity of the micropillars allows the capillary limitation of the massflow rate to be calculated as:

m = ρ

(wwick

wn +dn

)QNE (6)

This mass flow rate ultimately implies the maximum heat loadcapability of the wick, since the latent heat of vaporization is theprimary method of heat removal.

THERMO-HYDRAULIC EXPERIMENTAL SETUPMeasurement of Thermal Flux

Sample wicks, such as the one shown in Fig. ( 3), werefabricated at the Center for Nano and Molecular Science andTechnology (CNM) of the University of Texas at Austin usingphotolithography and deep reactive ion etching (DRIE) to cre-ate homogeneous arrays of micropillars on the surface of siliconwafers. Wicks were fabricated containing pillars with diametersof 30µm, heights of 40µm, and spacings of 120µm and 160µm.

A thermo-hydraulic experimental setup was designed andconstructed to validate the proposed analytical model. This setup

FIGURE 4: ENVIRONMENTAL CONTROL CHAMBER TOHOUSE SETUP

allowed for the measurement of capillary flow through the wick-ing media and control of the heat load supplied to the evaporator.A chamber was designed for the purpose of housing the setup toallow precise control of both the temperature and relative humid-ity for the test environment.

Temperature within the chamber was controlled using adhe-sive film heaters to raise the temperature of the metal walls andfinned resistance heaters were utilized as convection heaters forthe space. Both types of heaters were controlled using a highwattage external power supply in conjunction with a PID con-troller to regulate the chamber temperature to a consistent 30◦C.

Control of the relative humidity was accomplished usingseparate air inlet lines, one for dry air and another for saturatedwater vapor. Once inside the chamber the dry and humid airmixed to establish the desirable relative humidity. LabVIEW wasused to construct a control program to regulate the humidity levelinside of the chamber via the flow controls for the air lines andhumidity probes located within the chamber. The feedback pro-vided by the probes allowed the program to adjust the flow ratesof the inlet lines to compensate for any deviation from the targetof 55% relative humidity.

One end of the wick was secured to a copper block extru-sion, while the central portion was left exposed and the bot-tom was submerged in a reservoir of distilled water as shown inFig.( 5b). This positioning corresponds to the evaporator, the adi-abatic transport length, and the condenser regions of a heat pipe.Thermal grease was used between the wick and block to reducecontact resistance. Leaving the wick exposed to the air created anopen loop system that prevented vapor saturation within the wickin addition to circulation effects encountered in a closed loop


(a) ILLUSTRATION OF SETUP INSIDE OF THE CONTROLCHAMBER

(b) BLOCK HEATER AND WICK ASSEMBLY

FIGURE 5: EXPERIMENTAL SETUP

heat pipe wicking system. However, the open loop system re-sults in natural evaporation from the water reservoir, which mustbe accounted for in calculating the mass flow rate of the wick.

The reservoir rested on top of a load cell, which communi-cated change in mass to the computer to be logged against theelapsed time of the experiment, yielding the mass flow rate. Theactual mass flow for the wick was found by subtracting the nat-ural evaporation rate observed before the start of the experimentfrom the mass flow recorded by the load cell. While the naturalevaporation experienced at the wick did contribute to the mass

flow rate registered by the load cell, by controlling both the tem-perature and the humidity surrounding the wick, this rate wasessentially constant across all tests.

The copper block extrusion contained four 100W cartridgeheaters and acted as the heat flux source. The heating block washoused in an enclosure insulated with mineral wool to direct theheat flux of the cartridge heaters through the wick-block interfaceto induce a mass flow through the wick. The area of the housingthat surrounded the interface and the frame which secured thewick were constructed of a low-conduction machined ceramic,MACOR R©. The power supplied to the heaters was controlledby a variable autotransformer. Due to the thermal mass of thecopper block it was necessary to wait for the system to reachsteady state at each wattage before measurements could be taken.Once steady state conditions were reached for the block heater,data samples were recorded every two or four seconds for fifteenminutes.

It was necessary to gather temperature information about thecopper block, housing, reservoir, and wick. Twenty type K ther-mocouples were installed on different surfaces through out thesystem to construct a thermal map of the system. Heat loss couldthen be determined permitting corrections for the thermal energydissipated through the insulation and ceramic frame. An infrared(IR) camera was utilized for gauging the temperature profile andconduction along the wick.

FIGURE 6: LabVIEW VI

Data acquisition for the experiments was executed using aLabVIEW VI tailored to the setup. A wattage transducer wasused to convert the power supplied to the heaters to a scaled 0-10V signal which allowed LabVIEW to record the input powerlevels. The voltage readings from the twenty thermocoupleswere interfaced with the LabVIEW VI. The data recorded fromthe thermocouples allowed for accurate measurements of the heatflux experienced at the wick-block interface. The LabVIEW VIwas also used to interface with a scaled output voltage signalfrom the load cell. This allowed the change in mass of the reser-


voir to be recorded over time. This measurement provided thenet mass flow rate of the liquid leaving the reservoir.

Plotting this adjusted change in mass as a function of theheater input power supplied a linear relationship between heatinput and mass removal. This plot was used to chart when thewick deviated from linear behavior, thus signifying a limitationof the mass flow rate.

Pictures of the wicking structure were collected throughoutthe testing process to compliment the data collected. Images col-lected allow a visual aid for the behavior of the flow within thewicking structure while also serving as another check for wickdry-out.

Heat Loss Through InsulationThe function of the mineral wool insulation was to direct the

heat flux provided by the cylindrical cartridge heaters throughthe extruded portion of the copper block toward the wick. Theinsulation thickness was maximized to the size constraints ofthe thermo-hydraulic experimental setup, but was still not thickenough to completely redirect all of the heat flux from the heatersto the wick.

To observe the thermal losses to the environment six ther-mocouples were placed on the main body of the copper blockand six additional thermocouples were attached to the outside ofthe enclosure. These thermocouples provided a surface temper-ature profile for both the copper block and the exterior of theenclosure. Having both surface temperatures yielded the thermalgradient across the insulation to be used with a conduction modelto quantify actual heat loss.

Shape factors were employed in the conduction analysis toaccount for losses through the edges and corners of the enclo-sure [18]. The heat loss from the faces, edges, and corners wassummed to yield the total heat loss through the insulation.

Wick Conduction LossesThe purpose of a wicking structure in a heat pipe is to trans-

port heat away from the evaporator. In light of this, wicks gen-erally are very good thermal conductors to aid in this process.While beneficial for operation in a heat pipe, this conduction losshad to be accounted for in the experimental model to ensure ac-curate measurements were collected for the heat removed fromthe evaporator solely via capillary flow.

An assumption was made that air acted as an insulator to thewick, because relative to water, air acts as a poor heat transfermedium. This assumption allowed the system to be modeled asexperiencing one dimensional conduction. An IR camera wasemployed to collect temperature profiles along the portion of thewick exposed to air. This data was then plotted as temperature asa function of distance from the water interface. The near unityvalue for the coefficient of determination

(R2)

justifies the onedimensional conduction assumption. Heat transfer from the wick

FIGURE 7: BLOCK-WICK PROFILE WITH HEAT TRANS-FER

FIGURE 8: EXPERIMENTAL DATA DEPICTING THE TEM-PERATURE PROFILE IN EXPOSED SEGMENT OF THEWICK

to the water reservoir could then be calculated with the funda-mental conduction equation [19]:

qwick = kAcdTdx

(7)

where k is the thermal conductivity of the silicon wick obtainedfrom literature [18,20], Ac is the cross-sectional area of the wick,


and dTdx is the temperature distribution deduced from the slope of

the linear fit seen in Fig.( 8).

Corrected Thermal Flux through the WickThe actual heat dissipated by the wick was found by com-

bining the power input to the heaters with the heat losses for thesystem. The result was the heat that actually worked to evaporatethe water within the wicking structure, found by the equation:

qevap = qmeasured−qinsulation−qwick (8)

where qevap was the net heat dissipated by the wick, qmeasured wasthe power input to the heaters recorded by LabVIEW, qinsulationwas the totaled heat loss through the insulation, and qwick wasthe heat loss by means of conduction along the wick. The heatflux exerted on the wick was calculated by dividing the total heatapplied to the wick-block interface by the contact area.

q′′evap =qmeasured−qinsulation−qwick

Asur f ,wick(9)

Where q′′evap is the heat flux through the wick and Asur f ,wick is thesurface area of the wick in contact with the face of the copperheating block. All of q′′evap goes into vaporizing the water withinthe exposed portion of the wick.

RESULTSTwo wicking geometries were tested using this setup. Both

geometries used pillars with a height of 20µm and diameter of30µm, but the spacing was varied, with one wick having 120µmspacing and one with 160µm spacing. As seen in Fig.( 9), theexperimental results correlated well with predictions by the ana-lytical model. When the capillary limit is reached, the transitionfrom convective heat transfer to conductive heat transfer throughthe wick is apparent. The capillary limit model predicts a slightlyhigher maximum flow rate than was seen in tests. The assump-tion of a constant evaporation rate per unit length of the wickwith a constant liquid height results in a smaller driving pres-sure requirement than that required if the height of the liquid wasdecreasing to account for the evaporated mass. This smaller re-quired Laplace pressure results in a larger predicted mass flowrate.

CONCLUSIONSThis paper presented a robust analytical model for the simu-

lation of capillary flows through an array of micropillars etchedon an everted wick. Additionally, a novel test setup was devel-oped allowing for the increased isolation of the test wick, thus

normalizing test conditions between wicks and improving over-all results. The experimental data collected was shown to corre-spond well to the proposed model for the prediction of the capil-lary limit in micropillar array heat pipe wicks.

(a) 120µm PILLAR SPACING

(b) 160µm PILLAR SPACING

FIGURE 9: EXPERIMENTAL MASS FLOW AND EVAPORA-TOR SURFACE TEMPERATURE AS FUNCTIONS OF HEATFLUX

ACKNOWLEDGMENTThe authors would like to thank Conan Zhang for his previ-

ous work and contributions to the project.


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A novel thermo-hydraulic test platform for micropillared array thermal wick optimization

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