Coupled-Physics Modeling of Electrostatic Fluid Accelerators for Forced Convection Cooling

Transcription

1 Coupld-Physics Modling of Elctrostatic Fluid Acclrators for Forcd Convction Cooling N. E. Jwll-Larsn *, P. Q. Zhang., and C. P. Hsu Univrsity of Washington, Sattl, WA, I. A. Krichtafovitch Kronos Air Tchnologis, Rdmond, WA, 9825 and A. V. Mamishv Univrsity of Washington, Sattl, WA, Classic thrmal managmnt solutions ar bcoming inadquat and thr is an incrasing nd for fundamntally nw approachs. Elctrohydrodynamic ionic wind pumps, also known as lctrostatic fluid acclrators (EFA), hav th potntial for bcoming a critical lmnt in lctronics thrmal managmnt solutions. As th EFA fild continus to volv, dvloping nw EFA-basd tchnologis will rquir accurat modls that can hlp prdict pump prformanc mtrics, such as air vlocity profil, back prssur, and cooling fficincy. Many prvious modling fforts only account for lctrostatic intractions. For truly accurat modling, howvr, it is important to includ ffcts of fluid dynamics and spac charg diffusion. Th modling problm bcoms spcially challnging for th dsign and optimization of EFA dvics with gratr complxity and smallr dimnsions. This papr prsnts a coupld-physics finit lmnt modl (FEM) that accounts for spac charg gnration from a corona discharg, as wll as spac charg diffusion and fluid dynamic ffcts in EFAs. A cantilvr EFA structur is modld and analyzd for forcd convction cooling. Numrical modling prdicts maximum air vlocitis of approximatly 7 m/s and a maximum convction hat transfr cofficint of 282 W/(m 2 K) for th cantilvr EFA structur invstigatd. Prliminary xprimntal rsults for a microfabriactd cantilvr EFA dvic for forcd convction cooling ar also discussd. Nomnclatur A s C p D E E E h av I c J k = ara of surfac S = spcific hat capacity = diffusivity of air ions = lctric fild intnsity = lctric fild strngth at th surfac of corona lctrod = brakdown lctric fild strngth of air = avrag convction hat transfr cofficint = ion currnt laving th ionization zon = currnt dnsity = thrmal conductivity * Graduat rsarch assistant, Dpartmnt of Elctrical Enginring, Box 3525, non mmbr Undrgraduat rsarch assistant, Dpartmnt of Elctrical Enginring, Box 3525, non mmbr Graduat rsarch assistant, Dpartmnt of Elctrical Enginring, Box 3525, non mmbr Chif Tchnical Officr, NE 9th, non mmbr Associat Profssor, Dpartmnt of Elctrical Enginring, Box 3525, non mmbr 1

2 p = air prssur q = spac charg dnsity Q = hat flux in watts R = distanc from th cntr of th corona lctrod tip to th ionization zon R = radius of corona lctrod tip S = an arbitrary surfac T = tmpratur in dgrs Klvin T sa = substrat to ambint tmpratur diffrntial in dgrs Klvin U = Vlocity vctor V = lctric potntial at th xtrnal boundary of th ionization zon V = lctric potntial at th surfac of th corona lctrod ε = dilctric prmittivity of fr spac µ E = ion mobility in air µ = dynamic viscosity ρ = air dnsity I. Introduction h problm of thrmal managmnt in microlctronics is at th cntr of attntion of acadmia, govrnmnt Tagncis, and industry worldwid. Rapid dvlopmnt of microlctronics has ld to an immns componnt dnsity. Within this dcad th siz of a singl componnt will dcras to narly 25 nm. This in turn will amplify th alrady xisting problm, which is that ach smiconductor componnt mits hat associatd with th lctrical rsistanc, lading to a larg hat flux from a shrinking surfac ara. Manwhil, th progrss in MEMS and powr lctronics is also affctd by th bottlnck of hat rmoval. In high-spd MEMS applications, nw issus includ th mchanical hat gnration du to friction and th introduction of combustion procsss in microdvics. In powr lctronics, high currnt applications crat high hat fluxs that rquir dramatic improvmnt in hat dissipation mthods. Existing cooling dvics ar no longr fficint in trms of nrgy consumption and hat rmoval. Th dcrasing siz of microlctronics componnts and th incrasing thrmal output dnsity rquirs a dramatic incras of thrmal xchang surfac from classic hatsink/rotary fan assmblis. Howvr, simpl growth of hatsink ara is no longr a viabl option for most applications. Elaborat cooling systms ar bing dvlopd, including thos using phas chang hat pips, liquid cooling, rfrigration, novl thrmal intrfac matrials (TIM), and Pltir dvics to sprad th hat from high hat flux aras, 1 but th last stp of hat xchang with th ambint nvironmnt always rmains ncssary. Classic rotary fans hav bn usd for forcd convction ovr th last fw dcads and ar still usd to nabl th final hat xchang with th ambint. Th classical rotary structural gomtry, although usd in numrous applications, is limitd in both scal and dsign flxibility, du to th ncssity of high-spd rotating parts. Turbulnt flow, vibration, and gyroscopic forcs introduc inhrnt infficincy and nois to a rotary systm. Evn in th applications for which acoustic nois and vibrations do not prsnt a significant problm, rotary fans ar difficult to optimiz for mor than a singl air flow circulation pattrn, du to thir narly static cross-sctional air vlocity profil. Elctrostatic fluid acclrators (EFAs) offr narly laminar air propulsion with dynamic airflow profils, controllabl air vlocitis, and a possibility to dcras th ffctiv boundary layr at th solid-fluid intrfac. 2,3 In addition, EFA propulsion is achivd without moving mchanical parts, thus nabling flxibl dsign and possibl intgration at th MEMS lvl. 4,5 As th EFA fild continus to volv, thr is a growing nd for accurat modls that can hlp prdict pump prformanc mtrics, such as air vlocity profil, back prssur, and cooling fficincy. Many prvious modling fforts only account for lctrostatic intractions. 6-8 For accurat modling, howvr, it is important to includ ffcts of fluid dynamics and spac charg diffusion. Prliminary coupld-physics modling has bn conducd in on-dimnsional spac without accounting for charg gnration, 4,9 showing good agrmnt with analytical modls for a simpl on-dimnsional spac. 1 Th modling problm bcoms spcially challnging for dsign and optimization of EFA dvics with high gomtric complxity and small scal. Th hat transfr and EFA flow charactristics ar analyzd using a two-dimnsional coupld-physics finit lmnt mthod modl that accounts for charg gnration, spac charg diffusion, and fluid dynamic ffcts. Prliminary rsults from a proof of concpt microfabricatd EFA dvic ar also analyzd. 2

3 II. Background Th mchanism of corona-inducd ionic wind propulsion is illustratd in Figur 1. Gas molculs nar th corona discharg rgion bcom ionizd whn a high intnsity lctric fild is applid btwn a high tip curvatur corona lctrod and a low tip curvatur collctor lctrod. In th cas of a wir or rod lctrod, th diamtr of th lctrod is quivalnt to th tip curvatur of a ndl lctrod. Th ionizd gas molculs travl towards th collctor lctrod, colliding with nutral air molculs. During ths collisions, momntum is transfrrd from th ionizd gas into th nutral air molculs, rsulting in th movmnt of gas towards th collctor lctrod. Th oprating voltag rang for corona discharg lis btwn th corona onst and th air gap brakdown voltag. 11 Corona inducd airflow is possibl with both positiv and ngativ voltags. It has bn rportd that highr stram vlocity can b achivd by using positiv polarity. 12 In gnral, th slction of polarity dpnds on a larg numbr of factors, which includ lctrod matrial, dvic gomtry, ozon gnration constraints, and othrs. Th govrning quations dscribing th intraction of lctric chargs with moving mdia in an lctrostatic fluid acclrator hav bn known for a long tim. Comprhnsiv rviws and tutorials on this subjct ar radily availabl. 11,13-18 III. Modling of EFA A. Govrning quations for lctrohydrodynamic flow Elctrohydrodynamic flow inducd by corona discharg and th rsulting hat transfr is dscribd by th following quations. Th lctric potntial V is govrnd by th P oisson s quation 2 V (1) whr q is th spac charg dnsity and is th dilctric prmittivity of fr spac. Th lctric potntial is dfind from lctric fild intnsity E as 3 q E V (2) Elctric currnt in th drifting zon is a combination of thr ffcts: conduction (motion of ions undr lctric fild rlativ to ntir airflow), convction (transport of chargs with airflow), and diffusion. Thrfor, currnt dnsity J is givn by J m Eq Uq D q (3) E whr m is th air ions mobility in an lctric fild, U is vlocity vctor of airflow, and D is th diffusivity E cofficint of ions. Currnt continuity condition givs quation for currnt dnsity J (4) Th hydrodynamic part of th problm is dscribd by th Navir-Stoks quations and momntum continuity quation for stady stat incomprssibl air flow r 2 U U p m U q V (5) whr r is th air dnsity, p is th air prssur, and m is th air dynamic viscosity. Hat transfr thn can b dscribd by thrmal conduction and convntion Figur 1. Ion stram of a DC lctrostatic air pump, whr a high voltag is applid btwn th corona and collctor lctrods. U (6) Q k T rc U T (7) p whr Q is th hat flux, k is th thrmal conductivity of th mdium, T is th tmpratur, is th dnsity of th air, and C p is th spcific hat capacity of air. Th systm of quations (1), (4), (5), (6), and (7) is subjct to appropriat boundary conditions dscribd blow for th EFA forcd convction hat transfr modl invstigatd in this study.

4 B. Spac charg gnration Spac charg gnration by corona discharg in an EFA dvic can b modld by applying appropriat lctrostatic and charg transport boundary conditions at th surfac of th ionization zon. A dscription of th boundary conditions for spac charg gnration stimation is dscribd in this sction. Th gap btwn corona and collcting lctrods can b dividd into two rgions, th ionization and drift zons. Th ionization zon xists in clos proximity to th corona lctrod, in which air ionization occurs, and both positiv and ngativ ions xist. Th drift rgion, locatd btwn th ionization rgion and th collctor lctrod contains ions of a singl polarity that hav bn drivn out of th ionization rgion by th lctric fild. Whn th radius of th corona lctrod is much smallr than th distanc btwn corona and collcting lctrods, th ionization zon forms a uniform shath ovr th coronating rgion of th corona lctrod surfac. For th positiv corona, th lctric fild strngth E at th surfac of a smooth corona lctrod of radius R is givn by P k s mpirical formula for air at standard conditions 11 E E / R (8) whr th corona lctrod radius R is masurd in mtrs and E = V/m is th brakdown (ionizing) lctric strngth of air. In contrast with th drifting zon, th nt spac charg dnsity is ngligibl in th ionization zon sinc it contains chargs of both polaritis in similar magnituds. Thus, assuming th lctrod tip radius is much smallr than th distanc btwn corona and collcting lctrods, th lctric potntial and lctric fild intnsity insid th ionization zon ar V V E R ln r (9) R R E E r (1) whr V is th voltag at th lctrod surfac, and V is th voltag at a radius r from th cntr of th corona lctrod tip within th ionization rgion. At th boundary btwn th ionization and drifting zons, th lctric fild strngth is qual to th brakdown lctric fild strngth E. Using Eq (9) and Eq (1), th xtrnal radius of th ionization zon can b stimatd: 2 R R E / E R / R (11) Th voltag drop through th ionization zon can b found by intgrating th lctric fild strngth from R. As th rsult, th voltag on th xtrnal boundary of th ionization zon is givn by V V E R ln E E R to (12) At th xtrnal surfac of th ionization zon, K aptsov s assum ption is usd, 19 which stats that th ionization zon radius rmains approximatly constant with V onc a corona is formd. This nabls stimation of th surfac charg dnsity by spcifying th lctric fild strngth: E E at r R. Thrfor, spac charg gnration du to corona discharg can b stimatd by prscribing voltag V to th xtrnal surfac of th ionization zon at a radius R from th cntr of th corona lctrod tip to satisfy P oisson s quation. Th charg transport quation is similarly satisfid by applying a surfac charg dnsity at th xtrnal surfac of th ionization zon such that th rsulting lctric fild at that surfac locatd at a radius R is qual to th brakdown fild intnsity E. IV. Numrical modl and procdur A high tip curvatur cantilvr bam suspndd ovr a flat conductiv thrmal xchang surfac, shown in Figur 2, was usd as th basis for th EFA-inducd hat transfr modld in this study. A DC voltag is applid btwn th corona lctrod and conductiv thrmal xchang surfac crating ions at th tip Figur 2. Diagram of cantilvr EFA dvic structur and opration. 4

5 of th cantilvr. Th ions ar acclratd towards th thrmal xchang surfac crating an air jt along thir path, rsulting in forcd convctiv thrmal transfr from th substrat. Th cantilvr EFA dsign, although not ncssarily optimal for cooling, was chosn du to its rlativ as of modling as wll as as of fabrication and as of xprimntal analysis with IR imaging. Th thrdimnsional cantilvr EFA structur shown in Figur 2 can b approximatd by th two-dimnsional modl shown in Figur 3, whr th dvic is rducd to a singl crosssctional plan takn across th nd of th cantilvr as dpictd in Figur 3 (a) and (b). Th simplifid twodimnsional modl maks a numbr of assumptions, including rducing th cantilvr tip to a circular crosssction, and ffctivly ignoring th lctric fild and fluid dynamics contribution by th rst of th cantilvr structur. Howvr, ths approximations will lad mainly to scond ordr ffcts in IV charactristics and air jt shap. Th EFA-inducd hat transfr was numrically modld in FEMLAB, a finit lmnt modling suit, using th stady-stat coupld physics modling approach outlind prviously using Eq (1) through Eq (12). Th numric simulation spac, subdomains, and boundaris ar shown in Figur 4. Th simulation spac was brokn into two subdomains, th ionization and drift zons. Th ionization zon, shown in Figur 4, is th rgion btwn th surfac of th corona lctrod and th ionization zon boundary. Th drift zon thn is th rmaining ara btwn th ionization zon boundary and th substrat. Th substrat, although shown in Figur 4 for illustration, was not a subdomain but was accountd for by application of appropriat boundary conditions at its intrfac with th drift zon. Elctrical domain quations wr solvd only within th drift zon subdomain, whil th fluid dynamics and hat transfr quations wr solvd within both th drift and ionization zon subdomains. Although th nt charg within th ionization zon is ngligibl and thus no additional body forc is applid to th air within th ionization zon, th Navir-Stoks quations ar solvd thr in ordr to account for th actual lctrod tip gomtry rathr than th largr siz of th ionization zon. Th subdomain modling paramtr valus ar shown in Tabl 1. Boundary conditions applid to th numrical modl, ar shown in Tabl 2 and ar as follows. For 5 Figur 3. Two cross-sction viws of th EFA dvic ar shown in (a) and (b). Th dashd lin in (a) shows th location of th plan of crosssction that is displayd in (b). Th simulation spac usd to modl th EFA is shown in (b), whr th corona lctrod tip cross-sction is approximatd as a circl. Modl dimnsions not drawn to scal. Tabl 1. Sub-domain modling paramtr valus usd in FEM modling Modling paramtr Valu Rlativ dilctric prmittivity 1 of air Charg diffusion cofficint 2.66E-5 Ion mobility cofficint m 2 /(Vs) Dnsity of air 1.15 kg/m 3 Kinmatic viscosity of air m 2 /s Hat capacity of air 1.7 kj/(kgk) Thrmal conductivity of air W/(mK) Corona lctrod to substrat sparation 3mm Corona lctrod tip radius 5μm Tabl 2. Boundary conditions usd in FEM modling Boundary Elctrostatics Charg transport Fluid Hat transfr dynamics Substrat groundd Zro diffusiv flux No-slip Constant Tmpratur 6 C Corona lctrod Voltag applid only to ionization boundary (V ), which is basd on applid corona lctrod voltag, Eq(12), of 3.5 to 6.5 kv N/A No-slip Constant Tmpratur 26 C Air boundaris ABC Zro diffusiv flux Nutral prssur *Air boundary undr ABC Zro diffusiv flux Nutral EFA air jt (Sts prssur ambint air tmpratur) Ionization boundary Voltag V and lctric fild intnsity E Surfac charg dnsity solvd by simulation N/A Convctiv flux* Constant Tmp 25 C Figur 4. FEMLAB simulation spac, showing gomtry and location of corona lctrod tip and ionization zon boundary in rlation to substrat. Schmatic dimnsions not drawn to scal. N/A

6 lctrostatics, a constant positiv DC voltag V was applid to th ionization zon surfac, and zro volts wr applid to th substrat/thrmal xchang surfac. All othr boundaris wr st to an absorbing boundary condition (ABC). For charg transport, a spac charg surfac 4.3 kv 3 mm dnsity is applid to th surfac of th ionization zon, calculatd using Eq (8) to Eq (12). A zro 2.25 diffusiv flux condition is imposd on all boundaris xcpt for th xtrnal surfac of th ionization zon. Th validity of this assumption is justifid by th fact (a) 1 that th diffusion trm is vry small compard to th 3 mm conduction trm in Eq (4) and can b st to zro at th boundaris with ngligibl ffct. 22,23 For fluid.5 dynamics, a no-slip condition is applid to th surfac of th substrat and corona lctrod, and a nutral (b) prssur condition is assignd to all air boundaris. 7.5 m/s Th hat transfr problm was solvd by applying a 3 mm constant tmpratur to th substrat, corona lctrod surfac, and air boundaris which had a nt 4 influx of air into th modl. A convctiv flux boundary condition was applid to all othr xtrnal ( c ) air boundaris. 7 C V. Numrical Rsults Numrical simulations rsults for th cantilvr EFA dsign corrlatd wll with th xpctd lctric fild profil, charg distribution, air jt vlocity, jt shap, and th rsulting hat transfr. Surfac plots of a cantilvr EFA with a thr-millimtr sparation shown in Figur 5 display th solutions to th four coupld physical phnomna modld: lctrostatics, charg transport, fluid dynamics, and hat transfr in Figur 5 (a, b, c, and d). Th plots shown in Figur 5 wr gnratd using modling paramtrs in Tabl 1, Tabl 2, and a corona lctrod to substrat lctric potntial diffrnc of 5.5 kv. Th lctric potntial and corrsponding lctric fild, Figur 5 (a), match th xpctd shap and profil dcrasing in magnitud from th dg of th ionization zon to th substrat. Th light shadd half-circl ovr th corona lctrod rprsnts th ionization zon, which was not part of th solution spac for lctrostatic or charg transport calculations, as xplaind prviously. Th spac charg, gnratd within th ionization zon and acclratd through th drift zon, is distributd with high dnsity nar th ionization zon and dcrasing slowly towards th collctor, with th spac charg dnsity falling off fastr in th x dirction to th lft or right of th corona lctrod. Thus, th ion stram has its largst componnt in th y dirction dirctly abov th ionization rgion travling from corona to substrat, Figur 5 (b). Th travling ion stram inducs an air jt along its path that impings on th substrat surfac as sn in Figur 5 (c), with th gratst y-dirctional air vlocitis cntrd dirctly abov th ionization rgion in th ara of th highst 3 mm (d ) 25 1mm Figur 5. EFA simulation rsults: (a) lctric potntial as colord surfac map and lctric fild arrows, (b) normalizd spac charg dnsity as a colord surfac map and columbic forc as arrows, (c) air vlocity as a colord surfac map and air vlocity as arrows. (d) air tmpratur as a colord surfac map and air vlocity as arrows. Arrows in all figurs scald linarly. Figur 6. EFA simulatd ion currnt, I c, vs. applid corona lctrod voltag V. plottd on th lft vrtical axis. EFA powr vs. applid corona lctrod voltag V plottd on th right vrtical axis. 45 6

7 spac charg dnsity. Th impinging air jt dcrass th fluid and thrmal boundary layr thicknss, producing th thrmal boundary layr shown in Figur 5 (d), which is thinnst at ithr sid of th air jt and incrass moving away from th cntr. Th ion currnt, I c, laving th ionization zon can b calculatd by multiplying Eq (3) by th ara of th ionization zon surfac with th lctric fild at th boundary of th ionization zon qual to E. It was assumd for th cantilvr structur that approximatly on half hmisphr of th cantilvr tip would hav an activ corona rgion with an ara of 3.62x1-7 m 2. Th currnt-tovoltag charactristics of th cantilvr EFA follow th xpctd xponntial currnt dpndnc on th lctric potntial btwn corona lctrod V and substrat 6 as shown in Figur 6, with I c incrasing from 9.6x1-8 amprs to 4.6x1-6 amprs ovr a V rang of 3.5kV to 6.5kV. Th dvic powr riss xponntially with th applid voltag du to th xponntial incras in currnt. A linar positiv rlationship was obsrvd btwn EFA air jt vlocity and V, as shown in Figur 7. Simulatd air vlocitis fll within th rang of vlocity magnituds rportd from xprimntal analysis. 6 Th EFA air jt y- dirctional componnt vlocity was avragd ovr thr cross-sctions, ach cntrd ovr th corona lctrod and positiond on millimtr abov th bottom of th solution domain in Figur 5. Th thr cross-sction lngths chosn wr on, ight, and twnty millimtr(s). Th avrag air vlocity ovr th 1 mm cross-sction rangd from approximatly 1 m/s to 7.6 m/s with th highst vlocity at a V of 6.5 kv. Th EFA-inducd air jt is focusd around a 1 mm cross-sction, with th avrag airflow for a 2 mm cross-sction falling to.15 m/s and 1.14 m/s for and applid V of 3.5 kv and 6.5 kv rspctivly. Th avrag convctiv hat transfr cofficint h av can b calculatd by h Q / A T (13) av s sa Figur 7. Simulatd EFA air jt y componnt vlocity vs. applid voltag V avragd ovr thr crosssction distancs on millimtr abov th bottom of th numrical solution domain shown in Figur 5. Figur 8. Simulatd convctiv hat transfr cofficint h av vs. applid voltag V. h av calculatd ovr four circular disk shapd aras on th substrat cntrd abov th corona lctrod. Disk diamtrs of on, two, thr, and ight millimtr(s) wr usd. whr Q is th thrmal powr in watts rmovd from a surfac S, A s is th ara of surfac S, and Δ T sa is th tmpratur diffrnc in Klvin btwn S and th ambint air. Th avrag convctiv hat transfr cofficint along th substrat scald approximatly linar with incrasing applid voltag V as shown in Figur 8. Th avrag hat transfr cofficint was calculatd at th surfac of th substrat ovr four circular disk shapd aras, ach cntrd abov th corona lctrod. Disk shapd surfac aras with diamtrs of on, two, thr, and ight millimtr(s) wr usd for th calculation. Th highst h av of 282 W/(m 2 K) was ovr th on millimtr disk at th maximum applid voltag of 6.5 kv. Th valu of h av was rlativly constant at a disk siz of on to thr millimtr(s) but droppd off up to 38.5 prcnt ovr th ight millimtr disk at th highst V. Notably, ths Figur 9. Simulatd cooling fficincy in prcnt vs. applid voltag V. Cooling fficincy calculatd ovr four circular disk shapd aras on th substrat cntrd abov th corona lctrod. Disk diamtrs of on, two, thr, and ight millimtr(s) wr usd. 7

8 calculations assum a symmtric flow pattrn about th disk axis, which would only b approximatly tru for th cas of a cantilvr corona lctrod. Howvr, xprimntally it was shown that du to th lctrical and fluidic impact of th ntir cantilvr structur, th air jt is angld out from th corona tip, rathr than pointd dirctly down at th substrat. This crats a cooling zon ara that is approximatly circular and positiond out in front of th cantilvr as shown in Figur 1, making th disk assumption a fair approximation. Th EFA thrmal cooling fficincy can b calculatd by dividing th thrmal powr rmovd by th EFA dvic ovr a givn ara by th total powr input to th systm by EFA opration. Th calculation was don ovr th sam four discs dscribd in th convctiv hat transfr cofficint, and thir thrmal cooling fficincy prcnt ar shown in Figur 9. Cooling fficincy rangd from 3.27x1 5 % to 133 %, dcrasing with dcrasing thrmal xchang ara and incrasing applid voltag V. Although th vlocity and convctiv hat transfr cofficint incras linarly with incrasing voltag, th EFA currnt and thus powr incras xponntially with th incrasing voltag, giving th highst airflow and cooling fficincis at th lowst oprating voltags. Notably, hat gnration from th corona discharg was takn into account in this analysis by applying a constant tmpratur to th corona lctrod tip that was two dgrs highr than ambint, which was th largst tmpratur ris sn on th corona lctrod from xprimntal analysis with IR imaging. Howvr, hat gnration will occur throughout th ionization zon and from ion bombardmnt on th substrat that was not modld in this invstigation that would dcras th convction hat transfr cofficints and cooling fficincy valus prsntd hr. Ths hating ffcts ar likly only to hav a significant ffct whn th EFA is oprating at th dg of its brakdown lctric potntial. VI. A mso-scal cantilvr EFA shown in Figur 2 was microfabricatd in silicon and xamind for proof of concpt EFA-nhancd convction cooling. Figur 3(a) shows schmatically th cross-sction of th xprimntal stup, whr th ion collction and hat transfr surfac includs a fiv millimtr thick layr of conductiv foam on top of a hot plat. Conductiv foam was chosn du to its nonrflctiv proprty making it a good candidat for IR imaging. Th insulating layr abov th collctor lctrod was a four-millimtr-thick slab of high dnsity insulating foam. Th corona lctrod, locatd on top of th insulating foam, was a cantilvr bam protruding ovr th hatd surfac, and connctd to a portion of a silicon substrat. High voltag diffrnc was applid btwn th corona and th collctor lctrod. Figur 1 shows four stags of th Exprimntal Rsults (a) (c) xprimnt. All imags wr takn with a FLIR ThrmCAM S sris camra at approximatly 2 frams pr scond at a rsolution of 23x32. Th scal on th right of ach imag shows tmpratur in C and a corrsponding color (shad in th black and whit vrsion). Orang color (lightr shad in b/w) corrsponds to high tmpraturs, and blu color (darkr shad in b/w) corrsponds to low tmpraturs. Th orang (light) rctangular objct at th bottom is th hatd collctor lctrod, an quivalnt of a thrmal xchang surfac. Th blu (dark) objct abov it is a pic of a silicon wafr from which th cantilvr corona lctrod is protruding. Th corona lctrod is small and nar ambint tmpratur, and thrfor cannot b sn at this rsolution. Th position of th corona lctrod can b infrrd from th figurs that show cooling ffct. Th silicon wafr is connctd to th powr sourc with a standard alligator clip. Th outlin of th alligator clip can b sn by looking closly abov and to th right of th silicon wafr in vry imag. Figur 1 (a) shows th stup with a hot plat on and in stadystat rgim, and with th EFA turnd off. Figur 1 (b) shows how th spot dirctly undr th corona lctrod cools off slightly whn th EFA is partially on (voltag is blow nominal). Figur 1 (c) shows th maximum cooling ffct for this stup, undr nominal voltag. Figur 1 (d) is takn at th nd of xprimnt, whn th EFA was turnd off and th hat distribution rturnd to stady-stat. This xprimnt dmonstrats that vn an unoptimizd stup can produc a significant cooling ffct. Dsign, fabrication, and tsting dtails ar discussd in this rfrnc. 22 (b) (d) Figur 1. Exprimntal dmonstration of cooling ffct with a micro-fabricatd EFA. (a) Hatd surfac, EFA off, (b) V = 5 kv, Δ T 1 C, (c) V = 8.5 kv, Δ T 25 C, (d) r-hatd surfac, EFA off. 8

9 VII. Conclusions and Futur Work This papr prsnts a numrical coupld-physics modling approach for lctrostatic fluid acclrators (EFA) for forcd convction cooling that includs spac charg gnration and took into account th ffcts of fluid dynamics and spac charg diffusion. A cantilvr EFA structur was analyzd using th coupld physics modling approach, and prliminary xprimntal rsults of a cantilvr EFA dvic microfabricatd in silicon wr prsntd. Numrical simulation rsults agrd wll with xprimntal rsults prsntd in litratur for EFA prformanc charactristics including IV charactristic trnds, vlocity magnitud valus, vlocity vs. oprating voltag trnds, and cooling fficincy vs. oprating voltag. Avrag simulatd EFA air jt vlocitis rangd from 1 m/s to 7.6 m/s ovr a on millimtr cross-sction. Maximum convction hat transfr cofficint was found to b 282 W/(m 2 K) ovr a disk-shapd surfac ara with a radius of on millimtr. Proof of concpt microfabricatd EFA forcd convction cooling dvic dmonstratd a 25 o surfac tmpratur rduction whil oprating. Futur work will incorporat spac charg gnration modling with fild mission for micro- and nano-scal mittrs, as wll as modls with gomtris optimizd for hat transfr. Acknowldgmnts Financial support has bn providd by th Washington Tchnology Cntr Phas I RTD grant, Intl Corporation, and Kronos Air Tchnologis. Additional studnt support was providd by th Graingr Foundation. Undrgraduat rsarch scholarships wr fundd by th Univrsity of Washington Mary Gats Rsarch Training Grant, th Washington NASA Spac Grant Consortium, and th Elctrical Enrgy Industrial Consortium. Th IR quipmnt donation by th Intl PPAP group is gratly apprciatd. Rfrncs 1 Michal Ohadi and Jianwi Qi, "Thrmal Managmnt of Harsh-Environmnt Elctronics," 2th Annual IEEE Smiconductor Thrmal Masurmnt and Managmnt Symposium, 24, pp G. M. Colvr and S. El-Khabiry, "Modling of DC Corona Discharg Along an Elctrically Conductiv Flat Plat With Gas Flow," IEEE Transactions on Industry Applications, vol. 35, no. 2, pp , Mar L. Lgr, E. Morau, and G. G. Touchard, "Effct of a DC Corona Elctrical Discharg on th Airflow Along a Flat Plat," IEEE Transactions on Industry Applications, vol. 38, no. 6, pp , Nov D. Schilitz, S. Garimlla, and T. Fishr, "Numrical Simulation of Microscal Ion Drivn Air Flow," ASME IMECE, Articl 41316, Washington DC, F. Yang, "Corona-drivn air propulsion for cooling of microlctronics," Mastr Thsis, Dpartmnt of Elctrical Enginring, Univrsity of Washington, Sattl, WA, F. Yang, N. E. Jwll-Larsn, D. L. Brown, D. A. Parkr, K. A. Pndrgrass, I. A. Krichtafovitch, and A. V. Mamishv, "Corona Drivn Air Propulsion for Cooling of Elctronics," Intrnational Symposium on High Voltag Enginring, N. E. Jwll-Larsn, D. A. Parkr, I. A. Krichtafovitch, and A. V. Mamishv, "Numrical Simulation and Optimization of Elctrostatic Air Pumps," IEEE Confrnc on Elctrical Insulation and Dilctric Phnomna, 24, pp N. E. Jwll-Larsn, E. Tran, I. A. Krichtafovitch, and A. V. Mamishv, "Dsign and Optimization of Elctrostatic Air Pumps," IEEE Transactions on Dilctrics and Elctrical Insulation, vol. accptd, Danil J.Schlitz, Sursh V.Garimlla, and T.S.Fishr, "Microscal Ion-Drivn Air Flow Ovr a Flat Plat," Procdings of HT-FED4, 24, pp J. Syd-Yagoobi, J. E. Bryan, and J. A. Castanda, "Thortical-Analysis of Ion-Drag Pumping," IEEE Transactions on Industry Applications, vol. 31, no. 3, pp , May F. W. Pk, Dilctric Phnomna in High Voltag Enginring, Nw York:McGraw-Hill, E. Shr, G. Pinhasi, A. Pokryvailo, and R. Bar-on, "Extinction of Pool Flams by Mans of a DC Elctric Fild," Combustion and Flam, pp , Castllanos A, "Elctrohydrodynamics," Intrnational Journal of Hat and Mass Transfr, vol. 38, J. S. Chang and A. Watson, "Elctromagntic Hydrodynamics," IEEE Transactions on Dilctrics and Elctrical Insulation, vol. 1, no. 5, pp , F. Hauksb, Physico-Mchanical Exprimnts on Various Subjcts, London, England, 179, pp L. B. Lob, Fundamntal Procsss of Elctrical Discharg in Gass, Nw York, Wily & Sons Inc., M. Robinson, "Movmnt of Air in th Elctronic Wind of Corona Discharg," AIEE Transactions, vol. 8, pp , May O. M. Stutzr, "Ion Drag Prssur Gnration," Journal of Applid Physics, vol. 3, no. 7, pp , July N. A. Kaptsov, Elktrichski Yavlniya v Gazakh i Vakuum, Moscow, OGIZ, J. Q. Fng, "Application of Galrkin Finit-Elmnt Mthod With Nwton Itrations in Computing Stady-Stat Solutions of Unipolar Charg Currnts in Corona Dvics," Journal of Computational Physics, vol. 151, pp , J. Q. Fng, "Elctrohydrodynamic Flow Associatd With Unipolar Charg Currnt Du to Corona Discharg From a Wir Enclosd in a Rctangular Shild," Journal of Applid Physics, vol. 86, no. 5, pp ,

10 22 C. P. Hsu, N. E. Jwll-Larsn, A. C. Rollins, I. A. Krichtafovitch, S. W. Montgomry, J. T. Dibn II, and A. V. Mamishv, "Elctrostatic Fluid Acclrators Miniaturiation Using Microfabrication Tchnology," 26 ASME Intrnational Mchanical Enginring Congrss and Exposition, Chicago, Illinois, USA (unpublishd.) 1