Increasing Heat Transfer in Microchannels with Surface Acoustic Waves*

Transcription

1 Increasing Heat Transfer in Micrchannels with Surface Acustic Waves* Shaun Berry 0/9/04 *This wrk was spnsred by the Department f the Air Frce under Air Frce Cntract #FA87-05-C-000. Opinins, interpretatins, cnclusins and recmmendatins are thse f the authr are nt necessarily endrsed the United Stated Gvernment.

2 Study Mtivatin As the trend in electrnics cntinues twards higher integratin density and higher pwer devices current remte cling technlgy will nt be able t handle the predicted levels f heat remval Increased integratin density f electrnics, including 3D chip stack will push lcalized heat fluxes >kw/cm and package-level vlumetric heat generatin > kw/cm 3 New paradigm fr embedded cling required Micrfluidic cling hlds ptential prmise and a large amunt f research and technlgy develpment has been ging n (multiple DARPA prgrams since 000) Single-phase flw perfrmance in micrchannels limited t high flw rates due t laminar flw cnditins and fixed thermal bundary layer In this numerical study surface acustic waves (SAWs) are evaluated as a disruptive flw technlgy SAWs cupled with single-phase micrchannel flw Gal is t drive circulating/chatic flw t disrupt thermal bundary layers Example f remte cling fr chips w/heat spreaders and thermal interface materials (TIMs) Thermal management needs be embedded clse t heat surces t handle the envisined heat lads Micrfluidic embedded cling IC r high pwer RF A.B. Chen et. al. CS MANTECH Cnf. 03. Cmsl Cnference Bstn- SRB 0/9/4 DARPA Defense Advanced Research Prjects Agency

3 Surface Acustic Waves (SAWs) and Acustic Streaming SAWs are generated by sinusidal electrical ptential applied t an interdigitated transducer (IDT) n piezelectric substrate and prpagate alng the surface Used extensively in telecmmunicatin Signal prcessing and filtering When a SAW traveling alng the surface cmes in cntact with a fluid medium sme f SAW s energy is refracted int the liquid Acustic streaming ( Leaky SAW ) Nn-linear acustic interactin ccurs within a thin viscus bundary layer (<µm fr MHz frequencies) Bulk fluid mtin arises frm viscus interactins with the bundary layer Frequency ranges: t 00 s MHz Substrate amplitude ranges: 0. nm t 0 nm Gaining attentin in micrfluidics Fluid mixing and particle and cell srting Metal IDT X. Ding. et. al. Lab Chip, 3, , 03. Circulating flw X. Ding. et. al. Lab Chip, 3, , 03. Cmsl Cnference Bstn- 3 SRB 0/9/4

4 Numerical Mdeling f Acustic Streaming Numerical simulatin challenges: SAW perate in MHz range and behave with harmnic time dependences e iωt Viscus effects in a fluid ccur n msec r larger time scales This requires a time-averaged respnse f the acustic scillatins Perturbatin expansin is emplyed n dependent variables u, p, and ρ t slve cnservatin f mass and mmentum Acustic velcity is f first-rder (u ) Streaming velcity is assumed t be f secnd-rder (u ) Cmputatinal methdlgy: Slve the first-rder acustic mtin (u, p, ρ ) Use first-rder slutin as inputs fr secnd rder cnservatin equatins Time averaged equatins need t be slved Cntinuity: Mmentum: ρ u t + µ u ρ + µ B u = ρ u µ + 3 Mass surce term (kg/m s) u ( u ) p = ρ + ρ ( u ) u t Vlume frce Surce terms (N/m 3 ) Cmsl Cnference Bstn- 4 SRB 0/9/4

5 COMSOL Mdeling COMSOL ver. 4.3b Step : slving first rder equatins using Thermacustics interface Study : Frequency Dmain SAW intrduced as velcity n channel walls Step : Slving secnd rder equatins using Cnjugate Heat transfer interface Study : Statinary (steady state) Surce terms (first-rder results) added t mass and mmentum equatins Mmentum equatin Vlume frce, F directly added Mass Cnstitutive equatin needs t be altered Use weak cntributin N cupling f first-rder terms t Energy equatin Time-averaged respnse f cmplexvalues Ex: Mass surce term = ρ u ρ u x = Re[ cnj( ρ) ux ] u bc x ( x, L) = ωd e α sin nπ x L Cmsl Cnference Bstn- 5 SRB 0/9/4

6 Mdel Simulatin Results: Laminar Flw Only Mdel parameters: L = 000 µm w = 50 µm f = 5 MHz d = 0. nm U in = n inlet flw SAW velcity B.C. Water filled channel Cntur Plts f First-Order Fields Time-averaged Secnd-rder Results Pressure Velcity cntur plt Temperature Hrizntal velcity Streamlines Vertical velcity Rayleigh streaming vrtices Cmsl Cnference Bstn- 6 SRB 0/9/4

7 Mdel : Effect f Inlet Velcity Inlet flw included in nd rder simulatins st rder results the same fr all cases U in <= Max acustic streaming velcity Circulating flw in the micrchannel is created U in > Max acustic streaming velcity Advectin dminates flw and vrtices are nt generated Need t increase acustic streaming velcity t have higher Reynlds number flws Time-averaged nd Order Results: Streamlines fr <u > ) U in = µm/s (Re << ) ) U in = 0 µm/s (Re << ) 3) U in = 00 µm/s (Re << ) U in < u streaming (max) U in u streaming (max) U in > u streaming (max) L = 000 µm w = 50 µm f = 5 MHz d = 0. nm U in = varied Cmsl Cnference Bstn- 7 SRB 0/9/4

8 Effects n Acustic Streaming Velcity Maximum acustic streaming velcity ccurs when: Channel width w = λ/ Wave length determined frm fluid prperties Acustic streaming velcity dependent n SAW amplitude d Streaming velcity is quadratic in SAW amplitude fr all frequencies Cmsl Cnference Bstn- 8 SRB 0/9/4

9 Heat Transfer Results Mdel parameters: L = 000 µm w = 00 µm f = 7.5 MHz d = 0 nm U in = 0.0 m/s (Re = ) T w = 00 C T w = 5 C '' w q = 54 W/cm '' w q = 7 W/cm Results shw under the right cnditin there is an increase in heat transfer due t SAWs Stream velcity < Acustic streaming velcity ρul µ Cmsl Cnference Bstn- 9 SRB 0/9/4

10 Summary Develped the framewrk t numerically simulate Acustic Streaming in micrchannels frm surface acustic waves Cupled three physics tgether Acustics, fluid flw and heat transfer Results indicate that SAW can enhance heat transfer Bulk stream velcity < Acustic streaming velcity Cnsiderably mre analysis wrk needs t be dne Need t increase vrticity strength in rder fr cncept t be useful in micrfluidic cling Identified ptential ways t achieve this cnditin Pulse the SAW and frequency r amplitude mdulate Pulse the inlet velcity Explre different frequencies and gemetries Launch SAW frm different lcatins in channel Perpendicular t the flw Cmsl Cnference Bstn- 0 SRB 0/9/4

11 Thank yu! Questins? Cmsl Cnference Bstn- SRB 0/9/4

12 Cmsl Cnference Bstn- SRB 0/9/4 Backup Material

13 Mdel Material Parameters C Density ρ f 998 kg/m 3 Speed f sund c f 495 m/s Dynamic viscsity µ 8.90e-4 Ps s Thermal diffusivity D.43e-7 m /s Slid * Density ρ s 4650 kg/m 3 Speed f sund c s 3990 m/s *Single crystal Lithium Nibate Cmsl Cnference Bstn- 3 SRB 0/9/4

14 Physics First-rder equatins Secnd-rder equatins a) Thermdynamic heat transfer equatin fr T T αt0 p = D T + t ρ C t b) Kinematic cntinuity equatin in terms f p p t T = α γκ t p u c) Mmentum equatin fr velcity field u a) Cntinuity equatin ρ u = ρu b) Mmentum equatin µ µ u + µ B + u p 3 u = ρ + ρ t u c) Energy equatin ( u ) ρ u µ = p + µ u + µ B + t 3 ( u ) ( K T ) Q ρ C p u T = + Equatins slved with Thermacustics Physics interface in COMSOL <x> = time average quantity ver full scillatin perid Equatins slved with Cnjugate Heat Transfer interface in COMSOL Cmsl Cnference Bstn- 4 SRB 0/9/4

15 Time Averaging f Cmplex Variables Fr cmplex-valued fields A(t) and B(t) with harmnic time dependence, the time average is the real part: A ( t) B( t) = Re[ cnj( A( 0) ) B( 0) ] Ex: Mass surce term: = = ρ u ρ u ρ u + x y x y ρ u ρ u x y = = Re [ cnj( ρ ) u ] x [ ( ρ ) u ] Re cnj y Cmsl Cnference Bstn- 5 SRB 0/9/4

16 SAW Streaming Analysis SAW can be generalized as peridic i.e. harmnic The fluid mtin induced by harmnic frcing in general has tw cmpnents Harmnic cmpnent This is the mtin f the fluid frm the acustic respnse Steady cmpnent This is the streaming respnse The cmputatinal challenge is hw t separate the tw cmpnents T slve fr the cnservatin f mass and mmentum a perturbatin expansin is dne n dependent variables u, p, ρ u = u p = p + εu + εp + ε u + Ο ε 3 ( ) 3 ( ) 3 ( ) + Ο ε ρ = ρ + ερ + ε ρ + Ο ε + ε p ε = U c ε << Smallness factr (acustic Mach #) Cmsl Cnference Bstn- 6 SRB 0/9/4