05286856 (1).pdf

148 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGY, VOL. 33, NO. 1, MARCH 2010

Comparison of Micro-Pin-Fin and MicrochannelHeat Sinks Considering Thermal-Hydraulic

Performance and ManufacturabilityBenjamin A. Jasperson, Yongho Jeon, Kevin T. Turner, Frank E. Pfefferkorn, and Weilin Qu

Abstract This paper explores the potential of micro-pin-fin heat sinks as an effective alternative to microchannel heatsinks for dissipating high heat fluxes from small areas. Theoverall goal is to compare microchannel and micro-pin-fin heatsinks based on three metrics: thermal performance, hydraulicperformance, and cost of manufacturing. The channels and pinsof the microchannel and micro-pin-fin heat sinks, respectively,have a width of 200m and a height of 670m. A comparison ofthe thermal-hydraulic performance shows that the micro-pin-finheat sink has a lower convection thermal resistance at liquid flowrates above approximately 60 g/min, though this is accompaniedby a higher pressure drop. Methods that could feasibly fabricatethe two heat sinks are reviewed, with references outlining currentcapabilities and limitations. A case study on micro-end-millingof the heat sinks is included. This paper includes equations thatseparate the fabrication cost into the independent variables thatcontribute to material cost, machining cost, and machining time.It is concluded that, with micro-end-milling, the machining timeis the primary factor in determining cost, and, due to theadditional machining time required, the micro-pin-fin heat sinksare roughly three times as expensive to make. It is also notedthat improvements in the fabrication process, including spindlespeed and tool coatings, will decrease the difference in cost.

Index Terms Micro heat sink, micro-manufacturing, micro-machining, pin-fin heat sink.

NOMENCLATUREManufacturing VariablesCtotal Total cost of heat sink [$].CT Total cost of tools [$].CM Total cost of materials [$].fr Feedrate [mm/min].t Time to fabricate heat sink [min].Manuscript received November 25, 2008; revised February 19, 2009. First

version published October 13, 2009; current version published March 10,2010. This work was supported by the National Science Foundation, GrantCBET-0729693 at the University of Wisconsin-Madison, and Grant CBET-0730315 at the University of Hawaii at Manoa. Recommended for publicationby Associate Editor A. Bhattacharya upon evaluation of the reviewerscomments.

Y. Jeon was with the Department of Mechanical Engineering, University ofWisconsin-Madison, Madison, WI 53706 USA. He is now with the HyundaiMotors, Seoul, South Korea (e-mail: [email protected]).

K. T. Turner, B. A. Jasperson, and F. E. Pfefferkorn are with the Depart-ment of Mechanical Engineering, University of Wisconsin-Madison, Madi-son, WI 53706 USA (e-mail: [email protected]; [email protected];[email protected]).

W. Qu is with the Department of Mechanical Engineering, University ofHawaii at Manoa, Honolulu, HI 96822 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCAPT.2009.2023980

tc Chipload [mm].R Operator rate [$/hr].CT Cost per tool [$].w Width of heat sink for case study [mm].l Length of heat sink for case study [mm].Ns Spindle speed [rpm].Ntools Number of tools required for fabrication of one

heat sink.n f Number of flutes.tchange Time to change one tool [min].tcleaning Time to clean up after machining [min].tmachining Machining time [min].tsetup Setup time before machining [min].ttoolchange Total time to change tools [min].dstraight Tool path to machine straight channel heat sink

[mm].dstgpin Tool path to machine staggered pin fin heat sink

[mm].

Thermal-Hydraulic Performance VariablesAt Area of heat sink base surface [m2].Aht Total heat transfer area of microscale enhancement

structure [m2].Aht, eff Total effective heat transfer area of microscale

enhancement structure [m2].h Heat transfer coefficient [W/m2 C].Hfin Height of fin [m].Lhs Length of heat sink [m].P Pressure drop across heat sink [bar].Pdh Pressure drop in developing region [bar].Pfh Pressure drop in fully-developed region [bar].q eff Heat flux based on heat sink base area [W/cm2].Rconv Average convection thermal resistance [C/m].T f Water bulk temperature [C].Tw Fin base temperature [C].Whs Width of heat sink [m].Wch Width of flow channel [m].Wfin Width of fin [m].Wt Mass flow rate [g/min].

Greek Symbols Aspect ratio of microchannel.b Viscosity evaluated at coolant bulk temperature,

[Ns/m2].1521-3331/$26.00 2010 IEEE

JASPERSON et al.: COMPARISON OF MICRO-PIN-FIN AND MICROCHANNEL HEAT SINKS 149

Whs = 1.0 cm, Lhs = 3.38 cm

Hfin = 670 m

Wfin = 200 m Wch = 200 m

Flow

(a)

Flow

Wfin = 200 m Wch = 200 m

Hfin = 670 m

Lfin = 200 m

SL = 400 m

Whs = 1.0 cm, Lhs = 3.38 cm

(b)

Fig. 1. Structure and dimension of (a) microchannel heat sink and (b) micro-pin-fin heat sink.

w Viscosity evaluated at fin base temperature, [N.s/m2]. Density, [kg/m3].

Subscriptsave Average.f Liquid (water).in Inlet.mc Microchannel heat sink.mpf Micro-pin-fin heat sink.out Outlet.W Wall.

I. INTRODUCTION

THE CEASELESS pursuit of improved performance withsimultaneous reduction in volume leads to ever-increasingdissipative heat loads in a wide range of modern micro-electronic devices. It has been shown that the performanceand reliability of these devices are strongly affected by theirtemperature as well as immediate thermal environment. Asa result, there is an increasing demand for highly efficientthermal management techniques capable of dissipating highheat fluxes from small areas.

Single-phase liquid-cooled miniature heat sinks, whichhave internal heat transfer enhancement structures and flowpassages that are tens to hundreds of micrometers in size,have emerged as one solution to the aforementioned thermalmanagement challenges. Among the large variety of possiblemicroscale enhancement structures, parallel-plate fins havereceived the most attention so far [1][5]. These miniature

heat sinks consist of parallel channels aligned with the flow[Fig. 1(a)]. Key technical merits of microchannel heat sinks,as demonstrated by the previous studies, include low thermalresistance to dissipative heat flux, high heat transfer areato volume ratio, compact dimensions, and small coolantinventory requirement [1][5].

Recent advances in microfabrication technologies, however,allows more complex microscale geometries to be fabricateddirectly into high-thermal-conductivity solid substrates (e.g.,metals) at low cost. This makes it possible to explore morecomplex and 3-D enhancement structures that may be moreeffective in transferring heat than the aforementioned parallel-plate fins. A possible configuration is staggered [Fig. 1(b)] oraligned micro-pin-fin arrays [6][14].

Staggered micro-pin-fin heat sinks have the potential toremove a high heat flux for a given volume of the heatsink and flow rate of working fluid, and hence improve theperformance of the heat-generating component. Despite thepotential for improved heat transfer from micro-pin-fin heatsinks, economics and realistic microfabrication options willcontinue to play an important role in whether these devicesare a viable choice over the nearest alternative (e.g., straightmicrochannel heat sinks). Unlike microchannel heat sinks,whose thermal-hydraulic performance can be fairly accuratelydescribed by conventional macrochannel analytical models [3],[4], reliable analytical or numerical models for micro-pin-finheat sinks have not been developed yet due to the complexnature of fluid flow and heat transfer. Existing studies on liquidsingle-phase heat transfer and pressure drop in micro-pin-finarrays are mostly empirical. In these previous studies, specific


TABLE IPOTENTIAL MANUFACTURING METHODS FOR MICRO HEAT SINKS

Mfg Method Can Mfg Mass ProductionSuitability*PrototypingSuitability*

Cost Comparisonof Designs

EDMWire Channel Poor Average NAPlunge Both Poor Average Pin Channel

EtchingLIGA/Electroforming Both Good Good Pin Channel

Casting Both Very Good Poor Pin Channel

Extrusion Channel Very Good Poor NA

MachiningEnd Mill Both Average Very Good Pin > ChannelSlot/Form Mill Channel Good Very Good NA

Sintering Both Very Good Poor Pin Channel

micro-pin-fin configurations were tested and new heat transferand pressure drop correlations proposed [6][14].

The objective of the present paper is to simultaneouslycompare the thermo-hydraulic performance and manufactura-bility of the aforementioned two types of miniature heatsinks. Material is presented in four sections: 1) a review ofmanufacturing techniques that can be used to make these microheat sinks out of metals; 2) a thermal-hydraulic analysis ofsingle-phase water cooled copper heat sinks to explore whetherthe micro-pin-fin design has the potential to outperform themicrochannel design; 3) a case study of micro-end-milling todetermine the difference in manufacturing cost of the two heatsink designs; and 4) a discussion of the results.

II. REVIEW OF MANUFACTURING TECHNIQUES

A. Scope of AnalysisBecause it is a highly specialized and emerging area, there is

a need to review the different manufacturing methods that canbe used to fabricate microscale heat sinks. Due to the higherthermal conductivity and mechanical performance of metalalloys as compared to nonmetallic (i.e., silicon) materials,this review focuses on the fabrication of micro heat sinksout of metal alloys. This paper does not attempt to predictwhich technique is best suited for making micro heat sinks,because there are too many production variables that mustbe considered when making that decision (material, design,tolerances, quantity, existing equipment, etc.). Instead, the goalis to critically review a variety of methods that may be wellsuited for prototyping, low-volume production, or high-volumeproduction of heat sinks.

An excellent source on the fabrication of heat sinks withfeatures similar in size to those discussed in this paper is thepaper by Eugene et al. [15], which discusses the fabricationof micro-meso heat sinks embedded in turbine blades. Eugeneet al. conclude that the three most viable candidates formass manufacturing microscale features inside turbine blades

are micro electrical discharge machining (micro-EDM), microlaser machining, and micro casting.

B. Potential Fabrication MethodsTable I summarizes the potential fabrication methods

discussed below, their ability to make the two heat sinkgeometries, their suitability for mass production and prototypefabrication, and a comparison of the manufacturing cost foreach heat sink design.

1) Electrical Discharge Machining: EDM erodes/removesmaterial when a spark discharges between an electrode (tool)and a workpiece. Material is removed from the workpiecebecause of the rapid temperature rise and explosive phasechange resulting from the concentrated energy released by theelectric arcs [16]. The electrode does not experience the samerate of material removal because its high thermal diffusivitydissipates the heat more rapidly. Repeatedly discharging aspark at high frequencies under controlled conditions allowsfor bulk material removal around the tool. Hence, the cavitythat is created takes the inverse shape of the tool (or wire)that is used as the electrode. Intricate and microscale designscan be created in electrically conductive materials withoutimparting large forces or a significant heat-affected zone [17].The heat-affected zone is minimal because of the localizednature of the repeated material removal events and the EDMtool and workpiece are immersed in a dielectric fluid thatremoves heat and debris while also controlling the arcs [16].

EDM uses either a thin wire or a shaped electrode asthe tool [17]. Wire EDM [Fig. 2(a)] uses wires down to adiameter of 20m and can create straight through-thicknessslots or cuts [18]. Electrodes are also commonly machined intocylindrical or square cross-section bars and plunged straightinto the material to drill a hole or moved laterally to mill outshapes [Fig. 2(b)]. Very complicated geometries that need tobe created repeatedly (high-volume production) often use ashaped electrode that is plunged into the workpiece once in aprocess called die sinking [Fig. 2(c)] [19]. Micro-EDM milling


Workpiece Direction

Wire Direction

(a)

(b)

(c)

Fig. 2. Illustrations of three electrodischarge machining techniques: (a) wireEDM, (b) die sinking, and (c) EDM milling.

and drilling can utilize electrodes as small as 5 to 10m indiameter [16], [20], [21] and aspect ratios as large as 20 havebeen obtained [22], [23]. These tools are more than adequatefor all features in the micro heat sinks being considered.

The cost of EDM is primarily a function of the timerequired to shape each part due to the relatively low materialremoval rate. Die sinking is the fastest method of creating theheat sinks; however, it requires the most complicated (henceexpensive) die to be manufactured. Dies and all other types ofEDM electrodes wear out after repeated use [24]. Hence theselection of an EDM method is a function of the part geometryand volume. There are examples in the literature of heat sinksthat have been fabricated through these methods [25].

2) Photolithographic-Based Techniques: Photolithographyis a core fabrication technique utilized in the manufacturingof integrated circuits and microelectromechanical systems.Photolithography uses a transparent mask containing a desireddevice pattern and an exposure source (e.g., a UV light source)to transfer patterns onto a photodefinable polymer resist. Thepatterned resist can be used as a mask for etching a substrateor serve as a mold that can be filled with a metal [26]. Becauseof the multiple process steps involved and significant overheadassociated with the facilities and equipment, photolithography

(a) (b)

(c) (d)

(e) (f)

Fig. 3. Schematic of LIGA process: (a) deposit a conductive seed layer, (b)spin on a thick layer of photoresist, (c) expose photoresist to high-energyX-rays through a mask, (d) develop photoresist removing X-ray exposedmaterial, (e) deposit metal into photoresist mold, and (f) dissolve photoresistmold.

is best suited to batch production and most economical forhigh-volume production.

Etching methods, such as deep reactive ion etching [27],[28], can be employed to create heat sinks out of silicon,but they cannot generally be used to create high-aspect-ratiostructures in metals and will not be discussed here. However,lithography can be used to form metal heat sinks usingelectrodeposition-based techniques such as the lithographie,galvanoformung, und abformung (LIGA) process. The originalLIGA process has three main steps (Fig. 3): 1) A thick layerof X-ray resist, typically poly(methyl methacrylate) (PMMA),is deposited on a carrier substrate coated with a conductiveseed layer [Fig. 3(a) and (b)], 2) The resist is exposed tohigh-energy X-rays through a mask [Fig. 3(c)] and thendeveloped [Fig. 3(d)], yielding a 3-D mold; 3) A method ofmetal deposition, most commonly electroplating, is used tofill the mold [Fig. 3(e)]; and 4) The resist mold is dissolved(i.e., expendable), resulting in the final free-standing metalcomponent [Fig. 3(f)] [26]. Similar processes that use thickphotosensitive resists, such as SU-8 and PMMA, eliminate theneed for an X-ray source and provide the ability to producesimilar structures with reduced cost [29][31]. SU-8 processescan also be incorporated to create positive molds, which thencan be used for subsequent metallic device creation [32].

LIGA processes are able to produce structures with aspectratios as large as 60:1 [33] with tolerances on the order ofmicrometers. This method can make the smallest features ofany technique described in this paper; however, one mustsacrifice some resolution (i.e., tolerance) for increased aspectratio [34]. Common metals used in LIGA and LIGA-likeprocesses include nickel [30], copper [35], and gold [33].


Heating/Cooling Passages

(a) (b) (c)

Fig. 4. Schematic of die casting: (a) metal molds with runner and cooling passages, (b) molds pressed together with molten metal being inserted, and(c) separation of molds and removal of part.

In addition, LIGA-like fabrication has been utilized to makeheat sinks or cooling plates in the past [36], [37]. The abilityto create complex 2-D shapes, as shown in [30], provides theoption for creating nonstandard pin shapes and optimizing theheat sinks for thermal and hydraulic performance.

3) Casting: The process of casting, in its most basic form,involves pouring a molten metal into a pre-fabricated mold,allowing the metal to solidify, and then removing the part fromthe mold [17]. Of the numerous casting methods, only the twothat produce the finest features and, hence, are most likely tomake microscale heat sinks will be described here: die castingand investment casting.

Investment casting utilizes a wax (typically for macroscale)or plastic (microscale) pattern that defines the shape of thefinal part. Ceramic powder is poured around the pattern, dried,and then sintered to increase the strength of the ceramic moldand melt out the pattern. The mold is filled with molten metalby vacuum die casting (evacuate the mold and pressurized gasforces metal into it) or centrifugal casting (forces generated byspinning are utilized), and after solidification the expendablemold is removed [38].

Important considerations that determine the quality ofa microcasting include the preheating temperature of themold and the filling pressure of the mold. Baumeister et al.[38] showed, for a particle-hardened gold-based alloy andAlbronze microcastings, that flowlength increases with anincrease in preheating temperature and filling pressure. Like-wise, grain size increases with increasing preheating temper-ature due to the slower cooling rates.

In comparison to investment casting, metal-mold-basedmicrocasting (Fig. 4) offers the ability to reuse molds, increaseefficiency in production, and greater repeatability in partproduction [39]. Aspect ratios of 8 or 9 can be achieved withmicrocasting [40], and casting of features as small as 200min size is feasible [38][42]. Die casting does have somegeometric limitations; notably, undercuts cannot be included

in the permanent die as it would be impossible to remove thesolidified part.

Cast parts only approach the theoretical density of the metaland, hence, may have a slightly lower thermal conductivitythan the same part milled out of a forged or extruded billet.Casting has been the mainstay of high-volume production ofcomplex metal parts. The cost of the permanent mold wouldnot make this method suitable for prototyping or low-volumeproduction.

4) Extrusion: Extrusion is a method of producing constantcross-sectional area parts through the plastic deformation ofbillets through a die (Fig. 5) [17]. Hence, this method couldmake straight channel heat sinks [Fig. 1(a)] but not thestaggered micro-pin-fin design [Fig. 1(b)]. Most macroscalemetal heat sinks used for cooling computer chips are madevia extrusion. However, before extrusion can be applied tothe mass production of micro heat sinks, further research anddevelopment is required. Microextrusion is an area of activeresearch [43], [44] with the promise of industrial application inthe not too distant future. Microextrusion processes encountertwo problems that are not found in their macroscale counter-parts. Current process limitations include the precision of thetools used in creation of the dies and the precision (i.e., back-lash) present in forming machinery [45]. In addition, the sizeof the final extruded part relative to the grain size of the billetmaterial has a significant effect on manufacturing. Krishnanet al. [46] showed that 568m diameter extruded pins withgrains 211m in size tended to curl due to inhomogeneousdeformation, while pins with 32m grain size did not.

5) Sintering: Sintering in the microfabrication realm maytake the form of micro powder injection molding (PIM). Inthis process, a metal powder combined with a binder systemis injected into a mold of the final part shape (Fig. 6). Afterinjection, the binder is removed (through thermal means orother methods) and the part is sintered [47]. Fu et al. [48]demonstrated the ability to create 316L stainless steel pillars


Die

Billet

Fig. 5. Schematic of extrusion process.

(a)

(b) (c) (d)

Fig. 6. Schematic of micro powder injection molding, (a) inject metal-binder mix into mold, (b) heat to remove binder, (c) sinter metal powder, and(d) remove part.

through PIM that were 100m in diameter, 200m inheight, and had a 200m pitch. A silicon master was createdto serve as the expendable mold. This process differs fromcasting because the powderbinder mixture does not have to beinjected at elevated temperature, allowing for a wider varietyof mold materials to be used. The part can be sintered inthe mold or after it is removed from the mold. Similar tocasting, the near-net-shape part shrinks upon cooling, whichcan induce distortion and stresses in the part, and a smallamount of porosity must be taken into account.

Other sintering fabrication methods include selective lasersintering (SLS), where powder is deposited and then selec-tively sintered layer by layer to form a bulk part. Macroscalesystems may have a powder-feed cylinder which suppliesthe powder to the machine, and a part-build cylinder, whichis incrementally lowered to create each layer. The powderis typically transferred using a roller [17]. In micro-SLS,a powder deposition device replaces the roller and selectivelyplaces the powder for the micro features [49], [50]. Using thisconcept, feature sizes as small as 100m are reported [49].

(a) (b)

Fig. 7. Schematics of milling: (a) slot milling and (b) end milling.

6) Machining: a) Slot/form milling: Slot milling is a poten-tial method of manufacturing the straight channel heat sinks.A single circular cutter with teeth on the outer portion of thebit or a cluster of cutters [Fig. 7(a)] can be used. Slotting sawsas thin as 150m are commercially available, sufficient for thefeature sizes on the micro heat sinks being compared in thispaper.

b) End milling: Micro-end-milling [Fig. 7(b)] refers to anend-milling process that uses cutting tools between 5 and1000m in diameter to create microscale features on micro-,meso-, and macroscale parts [51]. It is a direct method ofcreating true 3-D shapes in myriad materials, frequently ina single process step. The fact that the geometry of interestis created by a part program that controls the movementof the end mill makes this method flexible. Therefore, it isclearly suited for prototyping metal heat sinks and low-volumeproduction.

To maintain the same cutting speed as the diameter ofan end mill decreases, the spindle speed must be increasedproportionally. For example, to achieve the recommendedcutting speed for wrought aluminum alloys being end-milledwith a tungsten carbide tool (3.15 m/s [52]) a 200m-diameterend mill requires a spindle speed of 300 000 rpm. Currently,there are 200 000 rpm spindles commercially available, andongoing research aims to develop spindles that can achievemore than 1 million rpm [53]. However, most micro-end-milling is done with spindles between 50 000 and 100 000 rpm,because it is not yet known if the cutting speeds that decadesof empirical data have shown to work well at the macroscaleare optimal for micromachining [54], [55]. Micro-end-millsremove small amounts of material with each rotation, thushigh-speed spindles do not need to be powerful with costsranging from approximately $5,000 for a 50 000 rpm air-drivespindle (fixed rpm) to $25 000 for a 200 000 rpm electric-drivespindle with variable rpm.

As will be shown in the case study, the cost of machininga heat sink is inversely proportional to the time it takes tomachine a part (productivity), which is mainly a function of thefeed rate (mm/min) at which a micro-end-mill can be movedthrough the material. The feedrate fr is the product of thechipload tc number of flutes (cutting edges) n f , and spindlespeed Ns

fr = tc n f Ns . (1)Hence, doubling the spindle speed or number of flutes

will double the feedrate and cut the time to machine a


CutterRotation

MaterialFeed

Chip Load[ft/tooth]

Fig. 8. Schematic of chip load.

part in half. The third variable that influences the feedrate(hence, productivity) is the chipload tc (Fig. 8): the depth ofengagement of a flute in the direction of travel. The mag-nitude of the chipload for a micro-end-mill is fundamentallylimited by the strength and flexibility of these small diametertools [51]. Decreasing the diameter of an end mill decreasesthe flexural stiffness and the cutting forces it can withstandwithout bending and/or breaking. The force acting on the toolis a function of the chipload, depth of cut, and material beingmachined. Decreasing the depth of cut will enable an increasein the chipload but requires more passes of the tool to createa feature of the desired depth.

Micro-end-milling is a viable option for prototyping andlow-volume production.

III. THERMAL-HYDRAULIC PERFORMANCEThermal-hydraulic performance of the micro-pin-fin heat

sink was determined experimentally with details provided inprevious papers [13], [14]. Only a brief overview is presentedhere. Made of 110 copper, the micro-pin-fin heat sink had aplatform area of 1.0 cm in width (Whs) by 3.38 cm in length(Lhs). An array of 1950 staggered micro-pins with 200 200m2 cross section and 670m height were milled out ofthe top surface (Fig. 9).

Thermal performance of the micro-pin-fin heat sink isrepresented by an average convection thermal resistance Rconv

Rconv = Tw,ave Tf ,aveq eff At(2)

where At is the total base area of the heat sink

At = Whs Lhs = 1.0 3.38cm2. (3)q eff is the effective input heat flux, Tw,ave is the average

pin-fin base (wall) temperature, and Tf ,ave is the average water(fluid) bulk temperature. Hydraulic performance is representedby the measured pressure drop across the heat sink P .Details on how to determine q eff , Tw,ave, Tf ,ave, and Pfor the micro-pin-fin heat sink can be found in previouspapers [13], [14].

As heat transfer and pressure drop in microchannel heatsinks can be adequately described by available analytical mod-els developed for macrochannels [3], [4], a pseudo microchan-nel heat sink is proposed. Thermal-hydraulic performance of

the microchannel heat sink is determined using the heat trans-fer and pressure drop models summarized in Table II [56],[57].

The performance of the two micro heat sink geometriesare compared assuming identical heat sink substrate material,single-phase liquid coolant, overall dimensions, microscalestructure dimensions, and operating conditions. Fig. 1(a) illus-trates the structure and key characteristic dimensions of themicrochannel heat sink along side those of the micro-pin-finheat sink. In particular, the (Wfin, Wch, Hfin) combination forthe microchannel heat sink is chosen to be (200m, 200m,670m), which is the same as that for the micro-pin-fin heatsink. Average convection thermal resistance for the microchan-nel heat sink is similarly evaluated from (2) using the heattransfer models provided in Table II. Pressure drop across themicrochannel heat sink P is the sum of the pressure dropacross the upstream hydrodynamically developing entranceregion Pdh and the pressure drop across the downstreamfully developed region Pfh. Analytical models for evaluatingthe two pressure drop components are provided in Table II.

Fig. 10(a) and (b) compare the average convection thermalresistance for the micro-pin-fin heat sink and microchannelheat sink for Tin = 30 and 60 C, respectively. The solidline and dashed line in these figures are power-law curvesto best-fit the micro-pin-fin heat sink and microchannel heatsink data, respectively, and are used to indicate the overalldata trend. It can be seen from Fig. 10(a) and (b) that Rconvfor the microchannel heat sink is fairly constant throughout thetotal flow rate Wt range, while Rconv for the micro-pin-fin heatsink is more sensitive to Wt and decreases significantly withincreasing Wt . In the low Wt range, Rconv for the micro-pin-finheat sink is higher than that for the microchannel heat sink,but becomes lower at a higher Wt . The comparison indicatesa better micro-pin-fin heat sink thermal performance at anelevated cooling water flow rate.

Fig. 11(a) and (b) compare the pressure drop across themicro-pin-fin heat sink and microchannel heat sink for Tin =30 and 60 C, respectively. It can be seen from Fig. 11(a)and (b) that P in the micro-pin-fin heat sink is significantlyhigher than that in the microchannel heat sink at all flow ratestested.

IV. CASE STUDY: MICRO-END-MILLINGThe authors have the most experience with micro-end-

milling [Fig. 7(b)] and have used it to manufacture coppermicro heat sinks (Fig. 9). In this section, the cost of micro-end-milling two different heat sink geometries, pin-fin and straightchannel (Fig. 1), is compared. Only relative differences willbe highlighted since any productivity improvements that wouldbe applied to machining of one design would also be appliedto the other. The goal of this case study is to determine whichheat sink is more expensive to manufacture by micro-end-milling and why.

In order to compare the geometries directly, the same basematerial (110 copper), and hence material cost and overallheat sink geometry (width = 1.0 cm, length = 3.38 cm) areassumed. Likewise, the pin width and gap (200m) is con-sistent between heat sinks, and hence the same tool diameter


(a) (b)

Fig. 9. Photographs of (a) copper heat sink and (b) pin fin geometry created by micro-end-milling.

TABLE IIANALYTICAL MODELS FOR MICROCHANNEL HEAT SINK [16], [17]

Heat transfer coefficient

h

For L 0.2 (thermally fully-developed flow),h =

(Nu3

k fdh

) (wb

)0.14

Nu3 = 8.235(1 1.883 + 3.7672 5.8143 + 5.3614 2.05); = ST WfinHfinL = zRedh Pr fFor L 0.2 (thermally developing flow),h =

{Nu4 + 8.68(103 L)0.506 exp

[(9.9776 ln () 26.379) L]} ( Nu3Nu4

) ( k fdh

) (wb

)0.14

Nu4 = 8.235(1 2.042 + 3.0852 2.4773 + 1.0584 0.1865)

Pressure loss components

Pdh

Pdh =2 fapp,dh f u2f Ldh

dh ; Ldh = (0.06 + 0.07 0.042)Reindh

fapp,dh = 1Re

3.44 (L+dh)0.5 + K ()

/(4L+dh

)+ ffh Re3.44

(L+dh

)0.5

1+C(

L+dh)2

(wb)0.58

ffh Re = 24(1 1.355 + 1.9472 1.7013 + 0.9564 0.2545)L+dh = LdhRedh ; K () = 0.6740 + 1.2501 + 0.3417

2 0.83583

C = (0.1811 + 4.3488 1.60272) 104

Pfh Pfh =2[

ffh(w

/b

)0.58] f u2f Lfh

dh ; Lfh = L Ldh

is used for both geometries. Assuming the same tool materialresults in a constant tool cost. Furthermore, if the same feedrate is used in both cases, the tool life should be the same.Machining both parts on the same machine with the sameoperator running means that the tool change time is constant.Since the heat sinks have the same geometric envelope andsimilar features sizes, it is assumed that setup and cleaningtimes are the same for both designs. The remaining variablesthat determine the cost difference between the two heat sink

geometries are tool path, which dictates the machining time t ,and cost rate R.

The overall cost of the heat sink can be broken down intothe cost of tools CT , the cost of materials CM , as well asthe product of manufacturing time t and cost rate R (4). Thechange in Ctotal between the heat sinks can be calculatedby taking the difference of each subcomponent of the totalcost

Ctotal = CT + CM + t R. (4)


Micro-pin-fin heat sinkMicrochannel heat sink

WaterTin = 30 C

wt[g/min]

R conv[

C/W

]

30 40 50 60 70 80 90

0.16

0.14

0.12

0.10

0.08

0.06

0.04

0.02

(a)


WaterTin = 60 C

wt[g/min]

R conv[

C/W

]

30 40 50 60 70 80 90

0.16

0.14

0.12

0.10

0.08

0.06

0.04

0.02

(b)

Fig. 10. Comparison of micro-pin-fin heat sink and microchannel heat sink average convection thermal resistance for (a) Tin = 30 C and (b) Tin = 60 C.


WaterTin = 30 C

wt[g/min]

P [b

ar]

30 40 50 60 70 80 90

0.12

0.10

0.08

0.06

0.04

0.02

0.00

(a)


WaterTin = 60 C

wt[g/min]

P [b

ar]

30 40 50 60 70 80 90

0.12

0.10

0.08

0.06

0.04

0.02

0.00

(b)

Fig. 11. Comparison of micro-pin-fin heat sink and microchannel heat sink pressure drop for (a) Tin = 30 C and (b) Tin = 60 C.

The cost of the tools CT is a function of the number of toolsrequired Ntools and the cost per tool CT . The number of toolsrequired to manufacture one heat sink is a function of tool lifeand final part geometry, because it dictates the total tool pathand, along with feed rate, determines the machining time. Inthis analysis, we are assuming that only one tool design isused. However, in reality tools with shorter flute lengths willbe used where possible because they last longer

CT = Ntools CT . (5)Since the cost per tool does not change between heat sinks, thetotal tool cost only varies with the number of tools. The toollife and tool geometry are assumed constant between heatsinks, meaning that the number of tools varies solely withthe final part geometry of the heat sinks.

The material costs CM are dependent on the volume ofmaterial required and the per unit cost. The heat sinks

have the same overall dimensions and are made out of thesame material, so CM does not vary between the two heatsinks.

The final term in (4) is the cost of the processing time.The cost rate R includes the capital cost of machinery, anyoverhead and utilities required for operation, additional train-ing required for machining/setup of process, labor, etc. Thesefactors do not change, regardless of fabrication geometry, andas such can be excluded from the current comparison.

The total time t required to manufacture the heat sink is afunction of the machining time, the amount of time requiredfor tool changes, setup time, and cleaning time (6). Theamount of time spent machining is a function of the feedrateand geometry of the final design. More complex designsrequire more passes with the tool, resulting in longer machin-ing time (7). Feedrate is a complex function of multiple para-meters, including material properties, tool strength/geometry,


2(wfin)

wfinl

Fig. 12. Illustration of tool path for milling channel heat sink.

tool coating, and metal working fluids (8)t = tmachining + ttoolchange + tsetup + tcleaning (6)

tmachining = f (feed rate, part geometry, tool geometry) (7)Feed rate = f (material, tool strength, tool geometry,

tool coating, metalworking fluid). (8)None of the variables that feed rate is a function of changesbetween heat sinks, meaning that the feed rate can be assumedto be constant. Likewise, the tools used to machine bothgeometries can be 180m in diameter (allowing for runout)because both designs have the same characteristic dimension(spacing between pin/wall). Therefore, machining time isbased solely on geometry.

The time required for tool changes is also related to the workpiece material. Shaping a material that is harder to machineresults in shorter tool life, more tool changes, and longermachining time due to the increased tool changes. The timeper tool change is a function of the machine being used, and,when automated, takes less than 1 min.

Since setup time, cleaning time, feed rate, machine used,and operator are the same, the time to manufacture the heatsinks varies only with the geometry of the part. The costequation (4) for comparing the two geometries simplifies to (9)

Ctotal = Ntools CT + (tmachining + ttoolchange) R. (9)The remainder of this section will focus on the geometric

differences between straight channel and staggered-pin-fin heatsinks and how to calculate the tool path length. The methodfor machining a straight channel heat sink in a piece of copperwith length l and width w is shown in Fig. 12. For analysispurposes, assume that w and l are multiples of wfin, whichis the width of one fin. The machining length dstraight that isrequired to fabricate one layer for a straight channel for thisgeometry is given by (10)

dstraight = w wfin2(wfin) (l) + w 3(wfin). (10)The tool path for machining one layer of a staggered pin-finheat sink dstgpin is more complicated (Fig. 13) and longer sincemore material must be removed in order to create the extrasurface area that benefits heat transfer (11)

dstgpin = l wfin2wfin[

2w + 6wfin + 2wfin(

w wfin2wfin

)]. (11)

w

l

(a)

wfin

2(wfin)(b)

(c) (d)

(e) (f)

Fig. 13. Illustration of tool path for milling staggered pin heat sink: (a) firstpass, illustrating the effect of tool radius on the corners of the pins, (b) secondpass, which finishes the first column of pins and makes the first cut on thesecond column, and (c) through (f) repeating the process to make multiplecolumns of pins.

Substituting typical numerical values (l = 3 cm, w = 1 cm,w f in = 200m) into (10) and (11) and comparing themshow that the tool distance for the staggered-pin heat sinkdesign used in this paper is approximately three times greaterthan for the straight channel. Experience has shown that for a200m diameter tool, a depth of cut of approximately 50mis appropriate. Therefore, each heat sink would require 12layers, each of length d, to machine the 600m-deep pins.Fig. 14 shows the total machining distance as a function ofthe pin/wall width.

V. DISCUSSION

When comparing the manufacturability of pin-fin versusstraight channel heat sinks, the geometries shown in Fig. 1are assumed. The width of and distance between the pinsor channel walls [Fig. 1(a)] are 200m and the aspect ratiois 3:1, making the height of the pins/walls 600m. For thestaggered pins [Fig. 1(b)], the distance between rows of pins is200m with alternating patterns. This geometry was also usedin the thermal-hydraulic performance analysis as well as themicro-end-milling case study, to allow for a direct comparisonbetween all the different aspects of the study.


Mac

hini

ng D

istan

ce [m

]

140

Staggered PinsStraigth Pins

120

100

80

60

40

20

00

Pin/Wall Width, wfin [microns]100 200 300 400 500 600

Fig. 14. Total machining distance (tool path as a function of pin/wall widthfor a 1 cm 3.38 cm area).

The tool path for one layer of a straight channel andstaggered-pin-fin heat sink with 200m feature size (wfin)is approximately 830 and 2600 mm, respectively. The totalmachining distances for micro-pin-fin and microchannel heatsinks of this size (12 layers) are approximately 10 and 31.25 m,respectively. With a feedrate of approximately 100 mm/minfor 200m diameter end mills shaping pure copper, totalmachining times of 100 and 312.5 min result. If the tool lifeis approximately 2 meters, and each tool change takes 1 min,then the straight channel can be made with 5 tools and the pinfin requires 16. As a first-order estimation, the cost of eachtool is approximately the same as the hourly rate. Examiningthese numbers in (9) shows that tmachining R is an orderof magnitude greater than any other costs that differ betweenthe two heat sink designs being considered. Therefore, thecost of machining the heat sinks will scale with the machin-ing distance (Fig. 14). Hence, the pin-fin heat sink will beapproximately three times as expensive to make if the materialcosts, setup time, and cleaning time are much smaller than themachining time. As improvements in productivity (i.e., feedrate) are made by developing new tool coatings and usinghigher speed spindles, the percentage of the part cost related tomachining time will decrease. This also means that the differ-ence in cost between the two heat sink designs will decrease.

An appealing option that would minimize the differencein manufacturing cost between the two miniature heat sinkswould be to fabricate a mold with micro-end-milling tofacilitate casting of the final part. If casting were used forhigh-volume production of micro heat sinks, the difference inunit cost between microchannel and micro-pin-fin heat sinkswould be small. Approximately the same amount of materialis used, and the tolerances and dimensions are similar. Theonly significant cost difference would be in the mold, whichwould be more complex for the micro-pin-fin heat sink.

Returning to the discussion on the thermal-hydraulicperformance, the average convection thermal resistance Rconvfor the two heat sinks can be written as

Rconv = 1have Aht, eff (12)

where have represents the average heat transfer coefficient, andAht,eff represents the total effective heat transfer area of themicroscale enhancement structures. Equation (12) indicates

that an improved thermal performance (low Rconv) can beachieved by either enhancing heat transfer (increasing have)or increasing total effective heat transfer area Aht,eff .

Total heat transfer area Aht for the micro-pin-fin heat sinkis approximately 13.3 cm2, and for the microchannel heat sink13.0 cm2. Total effective heat transfer area Aht,eff assumesvalues lower than those of Aht due to the fin effect. Aht,effranges from 12.0 to 12.9 cm2 for the micro-pin-fin heat sink,and is 12.5 cm2 for the microchannel heat sink. This showsthat the pin-fin geometry that was chosen does not have asignificant area advantage over the chosen microchannel heatsink geometry.

The better thermal performance for the micro-pin-fin heatsink at high flow rate can therefore be attributed to enhancedheat transfer. The data trend as shown in Fig. 10(a) and (b)may be explained by the nature of water flow in the micro-pin-fin array. At low flow rate, flow in the micro-pin-fin arrayis dominated by laminar flow, and vortices in the wake arerelatively weak. As a result, the downstream faces as well asa substantial portion of the side faces of the square micro-pin-fins are not exposed to the main flow, which leads to aless efficient use of the total heat transfer area. As flow rateincreases, flow in the micro-pin-fin array is more tortuous,and vortices in the wake become stronger, which enhancesheat transfer through reducing boundary layer thickness andactivating a larger portion of pin-fin surface areas.

The higher pressure drop across the micro-pin-fin heat sinkas shown in Fig. 11(a) and (b) is a result of the drag forcepresented by each and every pin-fin. Because a staggeredmicro-pin-fin configuration was used, every pin-fin sees a flowimpinging on its upstream face. The pressure drop may bedecreased, while maintaining the same surface area, by usingmicro-pin-fins with airfoil cross sections [6].

VI. CONCLUSION

After comparing copper microchannel and micro-pin-finheat sinks (same characteristic dimensions; single-phase waterflow) using thermal performance, hydraulic performance, andcost of manufacturing as metrics, it is concluded that neitherdesign is better for all applications.

The average convection thermal resistance decreases withincreasing flow rate for the micro-pin-fin, but it does not varysignificantly with flow rate for the microchannel heat sink.Below a flow rate of approximately 60 g/min, the micro-pin-finheat sink has a higher thermal resistance than the microchannelheat sink. Above 60 g/min, the micro-pin-fin heat sink has alower thermal resistance. This variation in thermal resistanceis attributed to the more tortuous flow and strong vortices inthe wake at high flow rate. Therefore, the micro-pin-fin heatsink would be chosen for its better thermal performance atflow rates above 60 g/min.

The pressure drop across the micro-pin-fin heat sink isapproximately twice as large as that across the microchannelheat sink at low rates. The difference in pressure drop increaseswith increasing flow rate for the range of flow rates evaluatedin this paper. Therefore, the improved thermal performance athigh flow rates comes with a significant increase in pressure


drop. Other pin designs (diamond, circular, airfoil, etc.) thatare being studied have the potential to provide the same ther-mal performance without the same increase in pressure drop.

Multiple manufacturing methods exist for creating heatsinks out of metal. Casting and extrusion are the most eco-nomical choices for mass production; micro-end-milling andmicro-EDM are ideal for prototyping. If casting a significantvolume of heat sinks, the cost per unit would be similar forboth heat sink designs. The tool path needed to end-mill themicro-pin-fin heat sinks is approximately three times greaterthan for the microchannel heat sinks. The machining time isdirectly related to the length of the tool path, and becauseof the limited feed rates available at this time, the cost tomicromachine heat sinks is primarily a function of machiningtime. Therefore, the cost to micro-end-mill a micro-pin-finheat sink is approximately three times greater than that for amicrochannel heat sink. As ongoing research enables increasesin spindle speeds and feedrates, the total cost to machine theseheat sinks will decrease and the difference in cost between thetwo designs will decrease.

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Benjamin A. Jasperson received the B.S. degreein mechanical engineering from the University ofWisconsin, Madison in May 2008. He is currentlypursuing masters degree in mechanical engineeringat the University of Wisconsin, under the supervisionof Professors Pfefferkorn and Turner.

His research areas include micro heat flux sensors,micro end milling and micro fabrication.

Mr. Jasperson is a member of Tau Beta Pi(Wisconsin Alpha).

Yongho Jeon received the B.S. degree in mechanicalengineering from Ajou University, South Korea,and the Illinois Institute of Technology, in 2003.He received the M.S.M.E. and Ph.D. degrees fromthe University of Wisconsin, Madison, in 2005 and2008, respectively.

He is currently the Manager of fundamental manu-facturing engineering development team at HyundaiMotors, Seoul, South Korea.

Kevin T. Turner received the B.S. degree inmechanical engineering from Johns Hopkins Uni-versity, Baltimore, MD, in 1999, and the S.M. andPh.D. degrees in mechanical engineering from theMassachusetts Institute of Technology, Cambridge,in 2001 and 2004, respectively.

Since 2005, he has been a Faculty Member in theDepartment of Mechanical Engineering, Universityof Wisconsin, Madison. His primary research inter-ests are the mechanics and design of MEMS andsemiconductor manufacturing processes.

Dr. Turner is a member of American Society of Mechanical Engineers andthe Materials Research Society. In 2008, he received the ASEE FerdinandP. Beer and E. Russell Johnston, Jr. Outstanding New Mechanics EducatorAward.

Frank E. Pfefferkorn received the B.S.M.E. degreefrom the University of Illinois, Urbana-Champaign,in 1994, and the M.S.M.E. and Ph.D. degreesin mechanical engineering from Purdue University,West Lafayette, IN, in 1997 and 2002, respectively.

He has been a Faculty Member in the Departmentof Mechanical Engineering, University of Wiscon-sin, Madison, since 2003. His primary research inter-est is in developing a science-based understandingof manufacturing processes, including heat transferproblems, micro end milling, friction stir welding,

thermally-assisted manufacturing, and laser micro-polishing.Dr. Pfefferkorn is a member of the American Society of Mechanical

Engineers and the Society of Manufacturing Engineers. He is the recipient ofa Research Initiation Award and the 2007 Kuo K. Wang Outstanding YoungManufacturing Engineer Award from the Society of Manufacturing Engineers.

Weilin Qu received the B.E. and M.S. degreesin engineering thermophysics in 1994 and 1997,respectively, both from Tsinghua University, Beijing,China, and the Ph.D. degree in mechanicalengineering in 2004 from Purdue University,West Lafayette, IN.

He joined the Department of Mechanical Engineer-ing, University of Hawaii at Manoa, Honolulu as anAssistant Professor in 2004, where he established theMicroScale Thermal/Fluid Laboratory. His researchhas been focused on microscale thermal/fluid trans-

port processes, boiling and two-phase flow, high-heat-flux thermal manage-ment, and electronic cooling. His doctoral research involved experimentalstudy, theoretical modeling, and numerical analysis of the various transportphenomena associated with single-phase liquid flow and forced convectiveboiling in microchannels.

Dr. Qu is a member of the American Society of Mechanical Engineers.

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