Dusˇan
Coso
Vinod Srinivasan
Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740
Ming-Chang Lu
Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30010
Je-Young Chang
Intel Corporation, 5000 W. Chandler Boulevard, CH5-157, Chandler, AZ 85226Arun Majumdar
Advanced Research Projects Agency-Energy (ARPA-E), US Department of Energy, Washington, D.C. 20585 e-mail: [email protected]
Enhanced Heat Transfer
in Biporous Wicks in the Thin
Liquid Film Evaporation and
Boiling Regimes
Biporous media consisting of microscale pin fins separated by microchannels are exam-ined as candidate structures for the evaporator wick of a vapor chamber heat pipe. The structures are fabricated out of silicon using standard lithography and etching techni-ques. Pores which separate microscale pin fins are used to generate high capillary suc-tion, while larger microchannels are used to reduce overall flow resistance. The heat transfer coefficient is found to depend on the area coverage of a liquid film with thickness on the order of a few microns near the meniscus of the triple phase contact line. We manipulate the area coverage and film thickness by varying the surface area-to-volume ratio through the use of microstructuring. Experiments are conducted for a heater area of 1 cm2with the wick in a vertical orientation. Results are presented for structures with approximately same porosities, fixed microchannel widths w 30 lm and w 60 lm, and pin fin diameters ranging from d¼ 3–29 lm. The competing effects of increase in surface area due to microstructuring and the suppression of evaporation due to reduction in pore scale are explored. In some samples, a transition from evaporative heat transfer to nucleate boiling is observed. While it is difficult to identify when the transition occurs, one can identify regimes where evaporation dominates over nucleate boiling and vice versa. Heat transfer coefficients of 20.7 (62.4) W/cm2-K are attained at heat fluxes of 119.6 (64.2) W/cm2until the wick dries out in the evaporation dominated regime. In the nucleate boiling dominated regime, heat fluxes of 277.0 (69.7) W/cm2can be dissipated by wicks with heaters of area 1 cm2, while heat fluxes up to 733.1 (6103.4) W/cm2 can be dissipated by wicks with smaller heaters intended to simulate local hot-spots. [DOI: 10.1115/1.4006106]
Keywords: biporous wick structure, heat transfer coefficient, dryout heat flux, hot-spot, heater area, evaporation, boiling
1
Introduction
The integration of graphical processing units with central proc-essing units as well as the use of multicore processors can pose two severe challenges in thermal management, namely: (i) how to cool local hot-spots on the order of 1 mm in size with power den-sities exceeding 500 W/cm2; and (ii) how to dissipate more than 100 W over a chip area of about 1 cm2, i.e., for average chip power densities exceeding 100 W/cm2[1,2]. Vapor chamber heat pipes have received attention for thermal management of these processor chips since they have a high heat transfer coefficient for heat spreading and require no external source of power or liquid pumping making them ideal for portable or handheld devices [3,4]. Ideally, a heat pipe spreader is designed such that it can dis-sipate a given heat flux while maintaining a minimal temperature rise. This heat dissipation capability depends significantly on the performance of the evaporator section of the heat pipe, which is typically composed of a porous wick.
In general, two factors restrict the operating envelope of a heat pipe, namely: (i) the capillary suction limited mass flow rate, and (ii) the initiation of nucleate boiling in the evaporator wick. Evap-orator wicks are typically made of sintered copper particles. In these types of structures, the twin goals of increasing both the dis-sipated heat flux and the overall heat transfer coefficient are in
conflict [4]. Reduction of particle size and increase in wick thick-ness favor higher capillary driven mass flow rate, thus increasing the heat flux dissipated. However, particle size reduction also increases liquid flow resistance and the density of point contacts between particles thus reducing the effective thermal conductivity of the wick. These and other factors for the optimal design of po-rous wick structures have been examined in great detail by Faghri [5]. With these tradeoffs in mind, there is likely an optimum parti-cle size, wick height, and wick porosity that maximize the heat transfer coefficient and the heat flux that can be dissipated.
During heat pipe operation, heat is conducted from the wick base through the particle matrix, and further into liquid toward the evaporating liquid–vapor interface. Due to the low conductivity of the liquid, most of the heat transfer at the top surface occurs in the liquid region (thickness few microns) near the triple-phase con-tact line [6–8]. The observed heat transfer coefficient is governed by the area coverage and thickness of this thin liquid film region, and the effective conductivity of the porous matrix [9]. Figure1 shows an idealized sketch of the thermal resistance network of a sintered copper particle wick. Here,Rsubstrateis the substrate ther-mal resistance on which the particles are sintered, Rmatrixis the effective thermal resistance of the particle/liquid matrix,Rfilm is the thermal resistance of the thin liquid film that forms at the me-niscus, andRintis the thermal resistance of the liquid/vapor inter-face. Additionally,Q, TvapTwall, andTsubstrateare the heat flow, vapor temperature, temperature at the wall in contact with the liq-uid, and temperature at the base of the substrate respectively. Thus, given that the interfacial thermal resistance is not the
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OFHEATTRANSFER. Manuscript received March 13, 2011; final manuscript received December 29, 2011; published online August 6, 2012. Assoc. Editor: Louis C. Chow.
dominant resistance in such a system [5], one can tune other resis-tances to maximize wick performance. Wicks with sintered par-ticles in the range 40–400 lm and typically of 1–4 mm thickness have been tested by several researchers [9–14]. The highest observed heat transfer coefficient in the evaporative mode of heat transfer using sintered particle wicks is 12.8 W/cm2-K at an applied flux of 8.3 W/cm2[10]. All other wicks that display capil-lary evaporation show values in the range 1–10 W/cm2-K.
In the past, biporous media consisting of large clusters of small particles have been shown to increase the heat dissipation capacity [11]. In these structures, the capillary suction is generated by the small pores inside the particle clusters while the viscous drag is reduced as a result of liquid flow through the large voids between the clusters, thereby extending the capillary limit. However, sig-nificant increases in evaporative heat transfer coefficient have not been demonstrated, presumably due to low solid thermal conduc-tivity of such structures and thus a large thermal resistance of the liquid/particle matrix (Rmatrix) as illustrated in Fig. 1. In other structures, nucleate boiling is observed at relatively low super-heats, accompanied by high heat transfer coefficients [12–16]. Semenic et al. [12] use a wick consisting of large clusters of small copper particles and suggest that the small pores serve to transport liquid to the boiling sections by capillary suction, while large pores between the clusters facilitate vapor transport away from the wick thus enhancing the overall heat transfer performance. Zhao and Chen [13] use a similar concept to explain improved heat transfer from a surface consisting of microchannels in which the walls are made of compacted sintered copper particles. In their study, samples with wider microchannels display higher dryout heat fluxes. Li et al. and Li and Peterson [15,16] stress the impor-tance of good thermal contact of the porous wick medium with the heated base and the resulting high effective thermal conductiv-ity. In their study, wicks consisting of multiple layers of sintered copper mesh displayed high boiling dryout heat fluxes as high as 370 W/cm2and heat transfer coefficients as high as 25 W/cm2-K. The dryout heat flux increased with wick thickness.
The present study implements designed biporous structures to simultaneously increase the heat dissipation capacity as well as the heat transfer coefficient of the evaporator wick. In order to avoid point contact between particles, establish greater control over porosity and pore size, and allow for a more systematic investigation of the performance, we use silicon wick structures composed of pin fin arrays periodically separated by large micro-channels. These structures are developed using standard microfab-rication techniques. We use these microporous structures in order
to increase capillary pressure and surface area for evaporation, as well as to reduce the maximum thickness of liquid film through which conduction occurs at the liquid–vapor interface near the meniscus. We quantitatively measure the heat transfer perform-ance in the evaporative and nucleate boiling regimes to identify the optimum wick parameters, such as pin fin characteristic size, pin fin spacing, wick height, and microchannel width for a given wick porosity. Furthermore, applicability of these geometries to amelioration of hotspot cooling in microprocessors is examined by considering heat sources of varying area.
2
Material and Methods
2.1 Parameter Range. As illustrated in Fig.2(a), the wicks of depthH are fabricated in the form of parallel microchannels of widthw that periodically separate arrays of micro pin fins. The pin fins of square cross section and sized (throughout the text we denote this sized as “diameter d”) and spacing p are arranged in an in-line array of widthD. Table1shows the parameter space over which the experiments are performed. Pin fin array widthD is varied from150 lm to 290 lm in order to maintain the same porosity among samples (/ 0.79 6 0.02). This is done so that the effective thermal resistance of the solid pin fin wickRpins, and the bulk liquid thermal resistanceRLin Fig.2(b)are approxi-mately constant among samples of similar depth H. In addition, samples are made so that the wick substrate thermal resistance Rsubstratein Fig.2(b)is not the dominant resistance in the network. In this way, by varying the size and thus the surface area of the pin fins it is possible to determine how the thin liquid film thermal resistance Rfilm affects the overall performance of the wick. To
Fig. 2 (a) Cross section and plan views of the evaporator ge-ometry showing arrays of pin fins with periodic microchannels; here d is the side length of a pin of square cross section, p is the pin spacing, H is the depth of the wick, w is the channel width, and D is the width of the pin fin array; (b) heat flow path and the corresponding thermal resistance network for the sili-con wick structures investigated here: Q is the applied power, Twallis the temperature at the base of the pin fin array, Tsubstrate
is the measured substrate temperature, Rsubstrateis the thermal
resistance of the substrate from which the pins are protruding, Rpinsis the thermal resistance of the pin array, RLis the bulk
liq-uid resistance which fills the pores, Rfilmis the resistance of the
liquid thin film that forms at the meniscus, Rintis the thermal
re-sistance of the liquid/vapor interface, and Tvap is the vapor
temperature Fig. 1 Thermal resistance network for a typical sintered
cop-per particle porous wick structure; Q is the applied power, Twall
is the temperature at the base of the particle matrix, Tsubstrateis
the temperature at the base of the wick substrate, Rsubstratethe
thermal resistance of the substrate, Rmatrixis the overall thermal
resistance of the particle/liquid matrix, Rfilmis the resistance of
the liquid thin film that forms at the meniscus, Rintis the
ther-mal resistance of the liquid/vapor interface, and Tvap is the
arrive at values for the pin fin diameterd and pore size p, we note that the thermal resistance of a 5 lm-thick planar layer of water is 0.074 cm2
-K/W (approximate value for the desired performance of the wick). By choosing the pore size p to vary from 28 lm down to 4.9 lm, we can generate a range of meniscus film thick-nesses that yield thermal conductances in the range of the desired performance.
2.2 Sample Preparation. Figure 3 illustrates the process used to fabricate test samples on a 100 mm diameter (525 lm thick) silicon wafer. Photolithography using positive photoresist is used to define regular pin fin array patterns over a 2 2 cm2
area. Subsequently, deep trenches are etched in the wafer using
induc-tively coupled SF6 plasma (Figs. 3(a)–3(c)). The photoresist is then removed by immersion in photoresist stripper (FujiFilm PRS3000) and cleaned with piranha and de-ionized water. A thin silicon dioxide layer is deposited on the wafer in order to increase wettability. This is achieved by plasma-enhanced chemical vapor deposition in oxygen plasma at 350C. Ellipsometry is used to measure the film thickness at the base of the microchannels of the pin fin array. The nominal measured thickness across samples is approximately 200 nm. This yielded an average contact angle of 12 6 2.5 deg measured by a Kruss goniometer among different samples in contact with deionized water (DIC) water. The oxide thickness is not measured along the side of the pins, but energy-dispersive X-ray spectroscopy is performed to confirm the pres-ence of oxide at multiple locations along the pins. Resistive heat-ing is accomplished by depositheat-ing a thin250 nm layer of indium tin oxide (ITO) on the back side of the silicon substrate. Lithogra-phy is used to define the heater area of 1 cm2(Fig.3(d)), and ITO is deposited using a radio frequency argon plasma sputtering chamber. A similar process is used to deposit1.5 lm of copper, overlapping the edge of the ITO heater, which defines the electro-des. An array of three special limit of error Omega Engineering T-type thermocouples spaced2 mm apart are bonded to the heater using electrically insulating epoxy (kepoxy 2.0 W/m-K).
3
Experimental
3.1 Experimental Setup. Figure4shows a schematic of the experimental system for measurement of wick performance. In order to ensure that the wick is not flooded with liquid, but draws up only as much liquid as necessary to maintain it wetted, the experiments are performed with the wick suspended in a vertical orientation. The test sample is immersed in a liquid reservoir (labeled A in Fig.4) such that the bottom edge of the ITO heater is 5 mm above the reservoir liquid level. The reservoir is replen-ished by liquid supply from another beaker (B) in which water is maintained at100C. The temperature of the reservoir is kept
constant by immersing the reservoir in a tank (C) maintained at 100C by a hot plate as well as immersed cartridge heaters. The
liquid level in the reservoir is maintained by using an overflow system.
To replicate the saturation conditions in a vapor chamber heat pipe, experiments are conducted in a saturated water vapor environ-ment atTsat 100C andPsat 1 bar. This is achieved by evacuat-ing the test chamber multiple times, sealevacuat-ing it, and boilevacuat-ing the water from the overflow tank to evaporate until the chamber pres-sure is close to 1 bar. Thermocouples monitor the temperatures at Table 1 Dimensions (in lm) of the various length scales defining
the wick geometry Pin fin array width D Microchannel width w Pin fin diameter d Pore size p Wick depth H 156 30 3.1 4.9 135 152 30 6.9 9.2 145 144 31 13.5 16.5 56, 145, 207, 243 232 61 7.1 8.5 150 272 61 15 16.8 149 264 61 22.5 24 152 288 61 29 28 158
Fig. 3 Schematic of fabrication process used to generate the evaporator wick geometries: (a) Photoresist (PR) is deposited. (b) Lithography is used to define and develop the pattern. (c) Deep silicon etching is used to obtain a wick of desired depth. (d) After cleaning, the sample is oxidized to improve wettability and an ITO heater is deposited subsequently. (e) Copper elec-trodes are deposited and the sample is cut to a desired size.
Fig. 4 Experimental apparatus used to measure the heat trans-fer performance of the evaporator wicks
multiple locations near the wick sample surface, in the water reser-voirs, and in the vapor atmosphere as illustrated in Fig.4. Typi-cally, the temperature everywhere inside the chamber attains a value between 96C and 100C after 6 cycles of pumping out the chamber. This is an indication that the chamber atmosphere con-sists mainly of water vapor. Electrical power is then applied via a power meter (Agilent N5750A DC Power Supply—150 V/5 A/750 W) at regular intervals to the ITO heater while simultaneously measuring temperature at various points along the height of the sample. Vapor is allowed to bleed out of the system through a one-way valve in order to maintain a constant pressure.
From these experiments, we extract the heat transfer coefficient based on the heater area as follows:
h¼ Q=Aheater Twall Tvap
(1)
Here,Twallis the wall temperature at the wick base in contact with the liquid,Tvapis the saturation temperature of water vapor at1 bar (Tvap 100C),Aheateris 1 cm2in all tests except when other-wise specified, and Q is the power dissipated by phase change heat transfer.
3.2 Uncertainty and Error Analysis. The primary error in measurement of heat transfer coefficient arises from uncertainty in temperature measurement and estimation of the heat losses to the ambient through nonevaporative heat transfer. The dominant mode of heat loss from the test sample is by conduction from the heater through the silicon wick substrate to the liquid reservoir. To estimate this, experiments are performed with a bare silicon surface with no wick structure and of the same dimensions as all other test samples, with power input and wick surface temperature measured as before. The power input to these bare samples reflects the losses associated with conduction through the wafer into the liquid reservoir, as well as radiation and convection heat transfer to the ambient at each measured substrate temperature. A schematic of the prepared test sample and a corresponding ther-mal resistance network are shown in Fig.5. For a typical epoxy thickness oftepoxy¼ 3 mm covering the back of the sample and a conservative estimate of the free convection heat transfer coeffi-cienthconv¼ 0.01 W/cm
2
-K over a 1 cm2area, the corresponding resistances turn out to beRepoxy¼ 15 cm
2
-K/W andRconv¼ 100 cm2-K/W. Therefore, the high evaporative/boiling thermal resist-ance of the wick always measured to be less than 0.5 cm2-K/W, and a high thermal resistance through the back side indicate that the heat lost through the back surface is no more than 1% of the input power for all the samples measured. Figure5also illustrates
the placement of the thermocouples on the sample heater used to measure the average substrate temperatureTsubstrate. From experi-mentally obtained results, the overall heat lossQlossis correlated as a function of the substrate temperature as
QlossðWÞ ¼ 4:5 105ðTsubstrate 100Þ 3 þ 3:5 103ðT substrate 100Þ 2 þ 3:32 102ðT substrate 100Þ þ 6:16 101 (2)
For the highest measured temperatures of 130C in the experi-ments, this value is about 3.5 W which is less than 3% of the peak heat flow through the samples with a 1 cm2heater size. Thus, the net power dissipated by phase change heat transfer is
Q¼ Qinp Qloss (3)
whereQinpis the electrical power applied to each sample. Here Qinpis also adjusted for the power dissipated in the leads that con-nect the samples to the power supply.
For all measured samples, we implement standard procedures for uncertainty propagation [17], where the uncertainty in a calcu-lated quantityS is given by
US¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi XN 1 @S @ai Uai 2 v u u t (4)
HereS is a calculated parameter, USis the uncertainty inS, aiis a measured parameter, andUaiis the uncertainty in parameter ai. Based on standard procedures in linear regression analysis for estimating the error in slope and intercept of Eq.(2), the uncer-tainty in estimating the heat loss (dQloss) is about 0.2 W for values ofTsubstrate¼ 130C. The measured heat flux is defined as q¼ Q/Aheater. For large heat fluxes,q > 100 W/cm
2
which are of particular interest, the total uncertainty in the heat flux measure-ment including uncertainty in heater area and heat losses is less than 3.9% for all samples with 1 cm2heaters.
In order to obtain the heat transfer coefficient of the wick, the temperature at the base of the wickTwallis calculated by account-ing for the temperature drop through the silicon wafer usaccount-ing a one dimensional conduction model to yield
Twall¼ Tsubstrate qðtwafer HÞ=kSi (5)
ThusTwallis defined in terms of the measured substrate tempera-ture Tsubstrate, the total heat flux q corrected for heat losses, the overall wafer thicknesstwafer, the wick heightH, and the thermal conductivity of siliconkSi. The manufacturer-specified uncertainty in temperature measurement of the thermocouple was 0.6 K. The uncertainty in the temperature drop through the substrate is 3.1% of its value. At the highest heat fluxes, this drop can be up to 5.4 K, leading to uncertainties of 0.16 K. The total uncertainty in Twall remains dominated by the manufacturer-specified uncer-tainty. The total measurement uncertainty in the heat transfer coefficient from Eq.(4)from a single sample is estimated using Eq. (1). This ranges from values of no more than 12.2% at low superheats (5 K) to no more than 9.5% at high superheats (>15 K) for all samples with 1 cm2heaters.
To verify the assumptions used in the uncertainty estimates, a fi-nite element calculation is performed for representative values of power and temperature observed in the experiment. A rectangular plate of silicon, with area of 2 2 cm2
and of thickness 525 lm is considered representing the entire sample containing the wick and substrate. The central area of 1 1 cm2
on one side of the wafer has an imposed heat flux of 100 W/cm2, while a heat transfer coef-ficient of 12 W/cm2-K is imposed resembling a measured evapora-tive heat transfer on the coinciding central area on the other side containing the wick. Additional boundary conditions are chosen so Fig. 5 Sketch of resistances to heat flow generated at the back
surface of the wick and the placement of the thermocouples for the wall temperature measurement
that one end face of the plate of dimensions 2 cm 525 lm is assumed to be maintained at 100C representing immersion in the large liquid reservoir. A free convection heat transfer coefficient of hconv¼ 0.01 W/cm2-K is imposed on all other faces of the plate for heat exchange with the ambient which is assumed to be at 100C. Figure6presents temperature contours on the substrate side of the wafer whereTsubstrateis measured. A sharp temperature gradient is observed on one side of the wafer, which corresponds to conduction away from the wick area towards the liquid pool. Numerical inte-gration of the resultant heat flux yields an overall heat loss of3.2 W (3.2% heat loss), which compares well with measured heat losses from bare silicon samples1.
4
Results and Discussion
4.1 Effect of Wick Depth on Performance: Predominantly Evaporative Regime. Wick samples are tested in a vertical ori-entation as depicted in Fig.4. When water saturates the wick, the thermal resistance of the bulk liquidRLbetween the pins as seen in Fig.2(b)is roughly two orders of magnitude higher than the re-sistance through the silicon pinsRpins. Therefore, most of the heat travels through the solid substrate and the pin structures to the thin liquid film that forms at the meniscus where the bulk of the evaporative heat transfer occurs. With these considerations in mind, the resistance network in Fig.2(b)can be simplified as a se-ries network withRLomitted and including the substrate, pin fin array, thin liquid film, and interfacial thermal resistances desig-nated asRsubstrate,Rpins,Rfilm, andRint, respectively. Furthermore, if we only consider the thermal resistances in the pin fin array of the wick of 1 cm2area we obtain
1 gpins
¼ H
ð1 /ÞkSi
(6)
where the term on the right hand side is the thermal resistance of the pin fin arrayRpins. Here,H is the depth of the pin array, / the porosity, kSi the thermal conductivity of silicon at 115C, and
gpinsis the thermal conductance of the pin fin array. As channel depth is increased fromH¼ 56 lm to H ¼ 243 lm in experiments considered here, the conductance of the solid pins with porosity / 0.79 drops from gpins¼ 1/Rpins¼ 43.2 W/cm2-K down to gpins¼ 9.9 W/cm2-K. For the range of pore sizes investigated here, the effective liquid film thickness at the meniscus has been estimated by several investigators to be under 5 lm [9,18], giving a thin film conductance to be gfilm¼ 1/Rfilm¼ 13.6 W/cm2-K. Therefore, pin fin arrays deeper than 145 lm (gpins¼ 1/Rpins < 15.9 W/cm2
-K) contribute the dominant thermal resistance. This implies that in the range of depths considered here, a transi-tion is likely to occur in the thermal resistances that dominate (betweenRfilm andRpins) and thus yield different trends in heat transfer performance among samples investigated.
Figure8(a)shows the effect of varying the depthH of the micro pin fin structures on wick performance for the cased¼ 13.5 lm, p¼ 16.5 lm, w ¼ 31lm and porosity / 0.79. Predominantly evaporative heat transfer is observed only in wicks of depth H¼ 145 lm and below. Here we presume that bubble nucleation at the measured temperatures is suppressed due to high wettability of water on SiO2precluding vapor trapping [19]. For these sam-ples, the pin array conductance estimated by Eq.(6)(gpins> 15.9 W/cm2-K) remains comparable or larger than the liquid film con-ductance gfilm. In this scenario, the film conductance governs the heat transfer and the initial slope of the curves remains independ-ent of wick depth (similar slopes forH¼ 56 lm and H ¼ 145 lm). At low to moderate heat fluxes, when the wick is saturated with liquid (Fig.7), the liquid film conductancegfilmis a function of thin liquid film thickness and the total length of the contact line, i.e., the total area of the thin liquid film surrounding the pin. As the applied heat flux and mass flow rate increase, the capillary limit is reached near the center of the heater and local dryout occurs evinced by a visible dry spot on the wick surface. We con-jecture that there must be a radial variation of the liquid level away from the dry spot, rising from zero at the edge of the spot to the top of the pin fins far away from the spot, as depicted in Fig.7. As a result, the effective area of thin film is significantly enhanced just prior to dryout, with evaporation occurring in the thin film around the pin fins as well as from the base on which the pin fins stand. In addition, at high heat fluxes the contact angle is at the minimum possible value, the receding contact angle for water on SiO2. It is possible that this recession further thins down the liquid film where the bulk of the evaporation occurs, and slightly increases the film thermal conductance. We presume that these two effects working in tandem increase the slope at high heat fluxes, most clearly apparent forq> 90 W/cm2in a wick of H¼ 145 lm (Fig.8(a)), and translate into a higher heat transfer coefficient (Fig.8(b)). Once observed the dry spot remains stable and gradually grows to cover up to about 10% of the heater area. Further increase in heat flux causes the dry spot to spread dramati-cally and blanket the whole surface of the wick with vapor. We deem this as the dryout heat flux and observe a sudden increase in average superheat. At this point the wick can no longer be Fig. 6 Temperature contours (inC) from finite element
analy-sis for an imposed heat flux of 100 W/cm2and evaporation
coef-ficient of 12 W/cm2-K. Here one end of wafer is assumed to be
at the saturation temperature of water Tsat5100C. Black
dashed line indicates relative size of the 1 3 1 cm2 heater
centered on a 2 3 2 cm2 wick. These contours represent the
measured substrate temperature field Tsubstrate.
Fig. 7 Sketch of the wick and liquid level based on experimen-tal observations at low to moderate and high heat fluxes
1The overall heat loss due to spreading estimated by Eq.(3)and supported by the
finite element models are accounted for in all presented data. In this way, we are able to isolate the total heat flux that is dissipated by evaporation/boiling within some uncertainty. Therefore, even though we cannot determine quantitatively the total area over which the bulk of the evaporation/boiling occurs, we can estimate the tem-peratureTwallat the pin fin array base using Eq.(5). This way of defining the heat
transfer coefficient includes the lateral heat spreading in the samples dissipated by evaporation/boiling.
considered operational. In most samples, we observe the dry spot to occur and be stable within 10–15% of the dryout heat flux. The dryout condition corresponds to the last data point for each sample plotted in Figs.8(a)and8(b). From these experiments we observe
that in the predominantly evaporative regime of heat transfer, dry-out occurs at larger values of applied heat flux as the pin fin height is increased from 56 lm to 145 lm, presumably due to the increased cross-sectional area available for flow through the taller microchannels.
4.2 Effect of Wick Depth on Performance: Predominantly Boiling Regime. As the wick depth H is increased beyond 145 lm, the conductance of the pin arraygpinsdecreases (see Eq.(6)) and is lower than the liquid film conductancegfilm. The initial slope of the heat transfer curve becomes a function of the pin fin height, as seen in Fig.8(a)forH¼ 207 lm and H ¼ 243 lm. Consequently, high values of superheat are observed at relatively low heat fluxes (50 W/cm2
). Here, nucleate boiling is visually observed at sev-eral locations on the wick as indicated by the dotted lines in Figs.8(a)and8(b). For samples that demonstrate nucleate boiling, the heat transfer curve has two distinct slopes: one corresponding to predominantly evaporation at low to moderate heat fluxes, and another corresponding to predominantly nucleate boiling at high heat fluxes. The slope of the heat transfer curve in the nucleate boiling regime is increased due to enhanced thin film area caused by ebullition of the generated bubbles. Escaping bubbles are con-strained in the lateral direction and elongated along the pores of the wick. This creates a thin film along the height of the pin fin instead of only near the meniscus as in evaporation. The thickness of the film on the sides of the pins depends on the bubble velocity and the pore size [20,21]. While it is generally observed that boil-ing in microchannel based heat pipes causes flow blockage and stops heat pipe operation, in the present study, a steady boiling re-gime could be maintained for heat flux increases up to 185 W/cm2 beyond nucleation incipience for 1 cm2heaters. The occurrence of nucleate boiling in biporous particle structures and layered meshes has been previously shown to yield high-performance wicks [12–15]. The structure and dynamics of the flow have remained a matter of conjecture. In this study, we supplement the heat transfer measurements with flow visualization of a stable nu-cleate boiling regime that is observed.
The visualization of boiling in wick structures is performed out-side the test chamber using a Fastec Imaging (IN100M2GB) CCD camera. Images are taken at 250 frames per second. Figure 9 shows the boiling process for a wick of depthH¼ 207 lm, with d¼ 13.5 lm pin fins, p ¼ 16.5 lm pore size, and w ¼ 31 lm microchannels. At a heat flux of 52 W/cm2, bubble nucleation occurs in the microchannels (Fig.9(a)), with the bubbles typically growing to a diameter equaling the combined width of two pin fin arrays (350 lm) before collapsing. As the heat flux is increased to 107 W/cm2, the superheat increases. Bubbles nucleating in microchannels collapse at smaller sizes, while nucleation also Fig. 8 (a) Heat transfer data for pin fin arrays of variable depth
H, for constant pin fin size d 5 13.5 lm, pore size p 5 16.5 lm, pin array width w 5 144 lm, and microchannel width w 5 31 lm. (b) Heat transfer coefficient variation with wick depth H. Only error bars at dryout heat fluxes are shown for each data set.
Fig. 9 Images of nucleate boiling at various heat fluxes in a wick sample for d 5 13.5 lm, p 5 16.5 lm, H 5 207 lm, and w 5 30 lm
occurs in the smaller pores formed by the pin fins (Fig.9(b)). In actual experiments, these bubbles appear and disappear very rap-idly (0.01 s). As the heat flux is further increased to 136 W/cm2
, the frequency of bubble generation increases. Bubbles are inter-mittently formed at discrete nucleation sites on the wick surface, and collapse when they grow beyond the wick height. In addition to these discrete locations, large areas in the pin fin array are seen to nucleate simultaneously (large dark spots in Fig.9(c)), resulting in audible loud bursting and violent ejection of liquid droplets. This bursting phenomenon causes the slope of the data to increase abruptly or even become negative giving a significant increase in heat transfer coefficient that causes a reduction in average super-heat. This is evident in Fig.8(a)for the wicks of depthH¼ 207 lm andH¼ 243 lm, at average values of superheat of 13 K and 18 K, respectively, where this bursting phenomenon is initially observed. This phenomenon commences at a larger average super-heat than that corresponding to the isolated bubble nucleation indicated by the dashed lines in Fig.8.
Figures10(a)–10(f)shows one such cycle of bursting and reced-ing of the wettreced-ing front followed by advancement of the wettreced-ing front back towards the nucleation zone. Immediately after droplet ejection, a large dry area is formed as seen in Fig.10(a). In subse-quent frames (Figs.10(b)–10(e)) motion of the liquid–vapor–solid contact line can be discerned, indicating liquid flow towards the nucleation area and rewetting of the surface, until the next burst occurs (Fig.10(f)). This process of rewetting shows that capillary pumping continues to be active even after the onset of nucleate boiling, and indicates that this regime of bubble nucleation is not an operating limit in such biporous structures. To the best of our knowledge, this regime of stable boiling has not yet been visually observed in other thin liquid film wick structures. As the heat flux is increased, the ejection frequency increases and the motion of the front can no longer be seen. At this point, the bubble ejection fre-quency is very high and the area where the nucleation occurs is so large that the wick can no longer supply the liquid to the surface. Here, the boiling limit is reached and the wick dries out.
4.3 Effect of Wick/Heater Area Ratio on Performance. As the applied heat flux is increased, the capillary pressure increases
in order to accommodate for the increased rate of evaporation [5]. This process induces entrainment of liquid towards the area directly above the heater, where the surrounding region acts as a liquid reservoir. Therefore, for a given wick structure, the ratio of the total wick area to the heater area influences the dryout heat flux. The area over which evaporation occurs is difficult to deter-mine visually; investigators usually resort to rough approxima-tions for the evaporation area [10] or report the applied heat flux based on the heater area [22,23]. Figure11shows a sketch of the general arrangement of the heater area (on the back of the wafer) within the wick. In one case, the wick dimensions above the reser-voir liquid level are 1.9 2 cm2
, with the 1 cm2 heater aligned centrally within the wick and with the reservoir level 5 mm below the heater edge. In another case, the wick area is 1 1.5 cm2
, and is aligned on three sides with the 1 cm2heater. Figure12shows the effect of this difference in wick and heater area on the wick performance. All data presented in Fig.12are for a single wick geometry with pin fin sized¼ 7.1 lm, pore size p ¼ 9.0 lm, chan-nel widthw¼ 30 lm, and wick depth H 149 lm. The larger area of the wick in the second case yields an improved dryout flux of 119.6 (64.2) W/cm2compared to 73.6 (62.6) W/cm2for the first case. The heat transfer coefficient also increases from 9.8 (60.7) W/cm2-K to 13.4 (61.5) W/cm2-K at a heat flux of approximately 60 W/cm2due to an increase in the effective con-tact line length for evaporation in the larger wick. The data Fig. 10 Burst sequence at an imposed heat flux of230 W/cm2: (a) Bubble bursting and violent ejection of liquid droplets.
(b) Formation of dry area around nucleation site. (c) and (d) Advancing wetting front. (e) Liquid almost fully rewetting the wick. (f) Start of next burst cycle.
Fig. 11 Sketch of arrangement of wick and heater surfaces with respect to the liquid reservoir: (a) Awick53.8 cm2,
Aheater51 cm 2 (b) Awick51.5 cm 2 , Aheater51 cm 2 and (c) Awick51.1 cm2, Aheater50.0625 cm2
suggests that larger wick-to-heater area ratios ought to allow for higher heat fluxes to be dissipated, since cooler liquid from the surrounding areas can penetrate deeper into the central hotspot before evaporating. This has particular relevance to the cooling of local hotspots within a microprocessor, where high heat fluxes on the order of hundreds of W/cm2may be generated [1–3]. In order to simulate a single hot spot on a chip, we fabricated a 2.4 mm 2.6 mm heater on a 1.1 cm2
wick for an area ratio of about 18:1 (filled red circles in Fig.12). For this heater size, evaporation predominates for heat fluxes as high as 160 W/cm2
beyond which nucleate boiling occurs until the dryout flux of 733.1 (6 103.4) W/cm2is reached. With this performance, thermal non-uniformities that may arise over small areas (on the order 1 mm2
or less) of a microprocessor chip [1,2] can be managed. This effect may also explain the high dryout fluxes (600 W/cm2
) observed by other investigators [22,23] for area ratios of approxi-mately 25:1 and 16:1, respectively.
4.4 Effect of Pin/Pore Size on Performance. Wayner and co-workers [24,25] have shown that in the microscale region of the liquid film near the wall consists of: (a) a nonevaporating film where long range intermolecular forces suppress evaporation, (b) a region of constant curvature where surface tension is dominant, and (c) an interline region where both surface tension and inter-molecular forces are important. In the interline region (length-several hundred nm) high mass (heat) fluxes occur due to enhanced fluid flow towards the contact line, modifying the film profile and the apparent contact angle [26]. However, this region occupies a small fraction of the total film length for large menisci (radius > few lm). Therefore, the major portion of the heat trans-fer occurs through conduction in the microscale liquid film (thick-nessfew lm) of constant curvature [18,27,28]. In order to increase total heat flux, one needs to increase the number of such regions by reducing pore size.
Figures 13(a)and13(b)show the effect of varying the pin fin sized and spacing p on the heat transfer curve, for channel depths H in the range between 135 lm and 158 lm as summarized in Table1, and channel widthsw of 30 lm and 60 lm. Expectedly, from Fig.13(b)it is evident that for samples withw 60 lm, the heat transfer coefficient increases as pore sizep decreases from 28 lm to 8.5 lm because in this manner the number of pins and thus available area for evaporation of thin liquid film near the con-tact line is increased. In samples withw 30 lm, there is an increase in heat transfer coefficient as pore size p is decreased
from 16.5 lm to 9.2 lm. Forp¼ 9.2 lm, the heat transfer coeffi-cient reaches a maximum of 20.7 ( 62.4) W/cm2-K at a dryout heat flux of 119.6 ( 64.2) W/cm2. For large (1cm2
) heaters, this represents both the highest heat flux and the highest heat transfer coefficient reported in literature for the predominantly evaporative heat transfer attesting to the benefits of using biporous wick struc-tures. The heat transfer coefficient drops significantly for the smallest pore size of p¼ 4.9 lm which might entail a different physical explanation deviant from expectation as detailed below.
For a scaling analysis valid to leading order, we neglect spatial variations in curvature, all convective effects, and approximate the region of dominant thermal resistance as a thin liquid film of heightLfilmand average thickness d near the top of each pin (Fig.14). The dominance of conduction over convection in the pores of the wick is verified by considering the Peclet number vd=a. Here v is the velocity of liquid required to maintain a fixed liquid/vapor interface undergoing evaporation,d is the character-istic length scale which in this case is the pin size, and a is the liq-uid thermal diffusivity. The velocity is calculated by
v¼ q qlhfg
(7)
Fig. 12 Effect of the ratio of wick surface area to heater area, for d 5 7.1 lm, p 5 9.0 lm, w 5 30 lm, and H 5 149 lm. Only the error bar at dryout heat flux is shown for each data set, where the two sets with lower attained heat fluxes have error bars that are smaller than the marker size.
Fig. 13 (a) Heat transfer data for various pin fin and pore size with channel size w 5 30 lm, nominal array width D 5 150 lm, and nominal wick depth H 5 145 lm. (b) Heat transfer data for varied pin fin size with channel size w 5 60 lm, nominal array width D 5 260 lm, and nominal depth H 5 150 lm. Only error bars at dryout heat fluxes are shown for each data set.
For the highest levels of heat flux considered of approximately q¼ 200 W/cm2
, this velocity scale is on the order ofv 1 mm/s which yields Peclet numbers that range from 1.7 102 for the smallest pin size testedd¼ 3.1 lm to 1.59 101ford¼ 29 lm. This implies that even at such high heat fluxes, conduction heat trans-fer is still the dominant mode by at least one order of magnitude.
In the wick structures considered here composed of pin fins with square cross section and side lengthd and pin spacing p, the length Lfilmof the thin liquid film near the contact line is truncated by the assumed constraint that the meniscus takes on a spherical shape away from the solid surface and perfectly wets the solid surface (Fig. 14). The number of pins N protruding out of an area A is N¼ ð1 /ÞA=d2. Thus, the conductance (W/cm2
-K) of the liquid film is gfilm¼ ð1 /Þ d2 klð4dÞLfilm d (8)
where (4d)Lfilmis the surface area of the thin liquid film surround-ing the pin of size d. Considering a two-dimensional situation (Fig.14), the scalesLfilmand d are related through the relation
Lfilm
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðp=2Þ2 ðp=2 dÞ2 q
(9) Under this assumption, the conductance can be determined in terms of all measurable quantities with the film thickness d being the only fitting parameter.
gfilm¼ 4klð1 /Þ d ffiffiffiffiffiffiffiffiffiffiffi p d 1 r (10) We observe that at low to moderate heat fluxes, the slopes of the heat transfer curve are nearly independent of applied heat flux for all pore sizes. This indicates that the liquid level in the wick is high, the base of the wick structure is not activated, and the assumptions used in deriving Eq.(10)are satisfied. For compari-son of the observed film conductance with the predictions of Eq.(10), we extract heat transfer coefficients from Fig.13(a)for various pore sizes at a moderate heat flux of60 W/cm2
where evaporation is the dominant mode of heat transfer. A 1-D conduc-tion model is used to extract the film conductance. This analysis assumes a heat transfer area of 1cm2at the base of the pins, which translates into varied thin film area as p and d are varied as indi-cated by (4d)Lfilm term in Eq.(8). A potentially larger area for evaporation due to thermal spreading is captured in the
uncer-tainty and will not affect the trend with p significantly. Eq.(10)is plotted in Fig.15as a solid line for a film thickness d¼ 4 lm. The data for samples with channelsffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w 60 lm appear to follow the
p=d 1 p
trend predicted by Eq.(10). A similar trend can be dis-cerned for the samples with channelsw 30 lm (dashed line in Fig.15, d¼ 4 lm), for which the values of conductance are higher for the 9.2 lm and 16.5 lm pores. The higher values of conduct-ance for the samples with 30 lm channels are attributed to a greater wicking area around the heater of 4.2 cm2compared to a value of 3.8 cm2for those with 60 lm channels which is a conse-quence of the fabrication. This reduces the number of pins by roughly 10% when the larger channels are used. The only anom-aly to the trend is the film conductance for the sample with p¼ 4.9 lm pores and w ¼ 30 lm channel. Here the conductance dips sharply below the estimated trend. We attribute this to the suppression of evaporation caused by interface curvature and reduced liquid pressure.
To better interpret these results, we letTlbe the temperature of bulk liquid, while the curved liquid–vapor phase interface is at Tlv. For the two-dimensional geometry considered here, the super-heat required for phase equilibrium is given by combining the Kelvin and Clapeyron effects to yield
Tlv¼ TsatðPlÞ 1 þ
r ðp=2Þqvhfg
(11)
As pore sizep is reduced from 16.5 down to 4.9 lm, Eq.(11) pre-dicts the required superheat to be of the order of 1–6 K, respec-tively. In a situation far from equilibrium with high interfacial mass fluxes, the required superheat may be considerably larger. Consequently, as pin sized and pore size p decrease in order to increase the surface area for evaporation, a larger fraction of the heat flux from the pin fin is used to superheat the liquid flowing towards the meniscus resulting in low observed overall heat trans-fer coefficient forp¼ 4.9 lm. Numerical calculations by Ranjan et al. [29] indicate that increases in superheat of even 2–4 K can reduce interfacial evaporation coefficients by as much as an order of magnitude.
5
Conclusions
Experimental data are presented for evaporation from a bipo-rous medium consisting of pin fin arrays periodically separated by larger microchannels.
1. Heat fluxes of up to 119.6 (64.2) W/cm2can be dissipated in predominantly evaporation heat transfer, accompanied by heat transfer coefficients of 20.7 (62.4) W/cm2-K. While Fig. 14 Sketch of a thin liquid film and meniscus around a
micro pin fin. Here Lfilmis the liquid film length along the pin
that forms at the meniscus, p is the pore size spanning the pins, d is the side length of a square cross section pin, and d is the thickness of the thin liquid film.
Fig. 15 Variation of the thermal conductance of the thin liquid film as a function of pore size at moderate evaporative heat fluxes of60 W/cm2
the mechanism and the interplay between evaporation and boiling are not completely understood to the best of our knowledge, for heater size considered here, these values rep-resent some of the higher heat flux dissipated in a predomi-nantly evaporative mode of heat transfer from porous structures.
2. For larger pores and deeper wicks (p > 16 lm and H > 145 lm respectively), a nucleate boiling regime is observed with high dryout heat fluxes up to 277.0 (69.7) W/cm2for large heaters (1 cm2
), and high heat transfer coefficients up to 19.6 (60.8) W/cm2-K. A stable regime of boiling is observed for up to 185 W/cm2beyond the heat flux of boil-ing incipience in these samples.
3. For small heaters of area 0.0625 cm2, high heat fluxes of up to 733.1 (6103.4) W/cm2can be dissipated, making these wick structures attractive for hotspot thermal management. 4. The overall heat transfer coefficient is increased with a
reduction in pore size and accompanying increase in surface area. A simple model is proposed that captures the trends in the observed data.
Acknowledgment
This research was supported by the University of California Discovery Grant Ele07-10298, DARPA Grant N66001-08-2060 and Intel Corporation Grant 20070104. The authors would like to gratefully acknowledge several useful discussions with Dr. Van Carey at UC Berkeley. Test samples were prepared at the UC Berkeley Microfabrication Laboratory.
Dusˇan Coso, Vinod Srinivasan, and Ming-Chang Lu contrib-uted equally to this work.
Nomenclature
d¼ pin fin diameter, m D¼ width of pin fin array, m
gfilm¼ conductance of liquid film, W/m2-K h¼ heat transfer coefficient, W/m2
-K
hconv¼ free convection heat transfer coefficient, W/m2-K H¼ height of pin fins/microchannels, m
kepoxy¼ thermal conductivity of the thermal epoxy, W/m-K kSi¼ thermal conductivity of silicon, W/m-K
Lfilm¼ length of thin film surrounding each pin fin, m P¼ pressure, N/m2
p¼ pore size–pin fin spacing, m q¼ heat flux, W/m2
Q¼ heat flow corrected for heat losses, W Qinp¼ heat generated via power supply, W
Qloss¼ total measured heat loss by any means other than phase change heat transfer, W
Rconv¼ convective thermal resistance, m2-K/W Rfilm¼ thermal resistance of the liquid film, m2-K/W
Rint¼ thermal resistance of the liquid/vapor interface, m2-K/W
RL¼ thermal resistance of the liquid filling the wick, m2-K/W
Rmatrix¼ thermal resistance of the solid liquid matrix, m2-K/W
Rpins¼ thermal resistance of the solid pin fins of the wick, m2-K/W
Rsubstrate¼ thermal resistance of the substrate, m2-K/W twafer¼ thickness of the silicon wafer, m
T¼ temperature, K
Tsubstrate¼ temperature of the substrate, K
Tvap¼ temperature of the vapor at saturation pressure, K Twall¼ temperature of the pin array base in contact with the
liquid, K U¼ uncertainty
v¼ velocity scale, m/s w¼ width of microchannel, m
Greek Symbols
d¼ liquid film thickness surrounding a pin fin, m /¼ porosity q¼ density, kg/m3 r¼ surface tension, N/m
Subscripts
lv¼ liquid–vapor interface l¼ liquidsat¼ saturation conditions
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