Thermal Contact Resistance of Non-Conforming Rough ...

1 Thermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 1 Thermal Contact Resistance ofNon- conforming Rough Surfaces Part 2: Thermal Model M. BahramiJ. R. CulhamM. M. YovanovichG. E. Schneider36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 Department of Mechanical EngineeringMicroelectronics Heat Transfer LaboratoryUniversity of WaterlooWaterloo, ON, Canada Thermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 2 CONTENTS introduction objectives literature review present model numerical approach and results parametric study alternative approach (correlations) comparison with experimental data summary and conclusionsThermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 3 INTRODUCTION conduction (microcontacts) conduction (interstitial fluid) radiation across the gap two sets of resistances in series represent TCR in a vacuum many researchers assumed Bahrami et al.

2 (2003) reviewed existing Non-Conforming Rough modelsTZ'7T1T2temperature profilemicrocontacts constriction body 1body 2macro constriction resistanceQQFFaLQiQ = 6 QiRj Rmic RmacThermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 4 Thermal Resistance NETWORKRj RL,1 Rs,1 Rs,2 RL,21Rs1,2 i 1ns 1Rs,i1,2body 1body 2macrocontact constriction resistancemacrocontactspreading resistancemicrocontacts constriction resistancesjoint resistanceRRQmicrocontacts spreadingresistancesRR=RS,1S,2jL,2L,1con tact planethermal Resistance is defined as,R T/QThermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 5 TCR PROBLEM STATEMENTG eometrical AnalysisMacro-Geometry Micro-Geometry Macro- Contact (Bulk Deformations)Mechanical Analysis Micro-Contacts(Asperity Deformations) CoupledMacro-ConstrictionThermal AnalysisMicro-Constriction Thermal Joint ResistanceSuperpositionResistanceResista nceThermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 6 OBJECTIVES develop analytical TCR model for entire range of contacts.

3 conforming Rough elastoconstriction transition region study effects of input parameters on TCR derive simple correlations for determining TCR Thermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 7 GEOMETRICAL MODELING a) Contact of Non-Conforming Rough surfacesb) Contact of two Rough spherical segmentsc) Rough sphere-flat Contact , effective radius of curvature effective radius and roughness LK12 12 Lb bL22 Thermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 8 FLUX TUBE SOLUTION inside macrocontact area a number of parallel cylindrical heat channels exist basic element for macro and micro Thermal analysis Cooper et al. (1969)a2kbQQk1isothermalor isoflux heat Contact areaadiabaticRflux tube 1 Rflux tube 2 2ksa 1 a/bks 2k1k2k1 k2 Thermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 9 PRESENT MODEL (ASSUMPTIONS) solids are isotropic radiation heat transfer is negligible microcontacts are circular and steady-state heat transfer isothermal microcontacts microcontacts are flat surfaces are cleandrraLFP(r) bQvacuumLRL 1 aL/bL 3/22ksaLRj RL RsThermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 10 MICROCONTACTS Resistance surface elementsmicrocontactsflux tubes2aLdr2b (r)2a (r)Odr=n (r)R (r)dR (r)rrA (r)assssscontact planeOrReffective microcontactthermal resistancedraLbody 1body 2surface element=dR (r)

4 SsRs r r 2ksas r r Ar r Aa r 12erfc r ns 116 m 2exp 2 r 2erfc r AadRs r Rs r ns r Rs 1 1/dRs r Thermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 11 NUMERICAL RESULTSr/aHzR*s=2bLksRs0123103104105r/aH z = 25 mm F 50 N 1. 41 m E 112. 1 GPa m 0. 107 c1/c2 6. 27 GPa / 0. 15 bL 25 mm ks 16 W/mK Thermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 12 EFFECT OF ROUGHNESS ( m)R*=2bLksR03691215050100150R*sR*LR*jR*H zR*jminThermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 13 EFFECT OF LOADF(N)R*=2bLksR10010110210310410010110 2103R*LR*HzR*sR*jThermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 14 EFFECT OF RADIUS OF CURVATURE (m)R*=2bLksR10-210-110010110210-210-1100 101102103R*jR*sR*LR*HzThermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 15 ALTERNATIVE APPROACH conforming Rough conductance, Yovanovich (1982) heat transfer in Non-Conforming Rough Contact .

5 Using pressure distribution, Part I andQ Contact plane hs r TsdAahs 1. 25ks m 1 s mksaL2H P0sR 1/ hAa Thermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 16 PROCEDURE FOR UTILIZING THE MODEL cFF 0cF=cFF>If an estimate of microhardness is available, set 12,0miccH c== m, may be estimated from: = []m Start Input12,,,,,,,sLFmkEb cc ' , ==+()''02'3'002'' == = ()*20*21, += = 3/2(1/)2 LLLsLabRka =jLsRRR=+ End []()()()221222121121212122121211211smmmk kkkkEEE =+=+=+=+ =+ ()*0,21,ssccsLLLcHRsPbHabFF =+ += 2*Flat surfacesLsLLHbRFab = = ()()22* / 1 =+ = []*0m = 2,HzHzaa == () = 20, = (){}()3224max 0, = Thermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 17 EXPERIMENTAL DATAP arameter7.

6 15 bL 14. 28 mm 25. 64 E 114. 0 GPa 7. 72 F 16763. 9 N 16. 6 ks 227. 2 W/mK 0. 04 m 0. 34 0. 12 13. 94 m 0. 013 120 m (s)AAntonettiNi200Ni200-AgBBurdeSPS 245, CSCCC lausing-ChaoAl2024 T4 Brass AnacondaMg AZ 31 BSS303 FFisherNi 200-Carbon NbKKitschaSteel 1020-CSMM McMillan-Mikic SS303 MRMikic-Rohsenow SS305 MMilanez et Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 18 COMPARISON WITH DATA **+++++++++++++++++++++++ xxxxxxxxxxxxxxxxxxxxxxx ---------:::::: Rj*10-210-110010110210-210-1100101102A, P3435, Ni200A, P2627, Ni200A, P1011, Ni200A, P0809, Ni200A, P1617, Ni-AgA, P3233, Ni-AgB, A1, SPS245-CSB, A2, SPS245-CSB, A3, SPS245-CSB, A4, SPS245-CSB, A5, SPS245-CSB, A6, SPS245-CSCC, 2A, Al2024T4CC, 8A, Al2024T4CC, 1B, BrassCC, 2B, BrassCC, 3B, BrassCC, 4B, BrassCC, 2M, MgAZ31 BCC, 3S, SS303F, 11A, Ni-CSF, 11B, Ni-CSF, 13A, Ni-CSH, PNI0102, Ni200H, PNI0304, Ni200H, PNI0506, Ni200H, PNI0708, Ni200H, PNI0910, Ni200H, PSS0102, SS304H, PSS0304, SS304H, PSS0506, SS304H, PSS0708, SS304H, PZ40102-Zircaloy4H, PZ40304-Zircaloy4H, PZ40506-Zircaloy4H, PZ40708-Zircaloy4H, , , , , T1, S1020-CSK, T2, S1020-CSMM, T1, SS303MM, T2, SS303MR, T1, SS305MR, T2, SS305M, T1, SS304 The Present Model *+ x -:Rj ksbLRj /m 1 s bLB2H P0s 1 B aLbL 1.

7 80aHzbL loadThermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 19 SUMMARY AND CONCLUSIONS superposition of macro and micro Thermal Resistance effects of major parameters, , roughness, load, and radius of curvature on TCR were investigated for Non-Conforming Rough Contact , there is a value of surface roughness that minimizes TCR at relatively large loads effect of roughness on TCR becomes negligible simple correlations were derived that cover entire range of TCRT hermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 20 SUMMARY AND CONCLUSIONS 2 model was compared with more than 700 experimental data points, collected by many researchers comparison includes all three regions of TCR and wide range of mechanical, Thermal , and surfaces characteristics data include Contact between dissimilar metals such as Ni200-Ag and SS-CS RMS relative difference between the model and the data was estimated to be approximately Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 21 Natural Sciences and Engineering Research Council of Canada (NSERC) The Center for Microelectronics Assembly and Packaging (CMAP)ACKNOWLEDGEMENTST hermal Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 22 conforming Rough mc1-c2ksbLA,P3435.

8 34 .26 ,P2627 .14 .26 ,P1011 .24 .26 ,P0809 .24 .26 , .25 .390100 , .35 .390100 , .11 .26 , .19 .26 , .19 .26 , .23 .26 ,NI910 .23 .26 , .07 .23 , .12 .23 , .15 .23 , .19 .23 , .05 .15 , .15 .15 , .13 .15 , .21 .15 , .08 .27 , .16 .27 , .18 .27 , .20 .27 , .04 .23 Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 23 Rough SPHERE-FLAT /m c1/ c2ksbLB, . , . , . , . , . , . , , , , , , , ,2M , , , , , ,T1 ,T2 ,T1 ,T2 Contact Resistance of Non-Conforming Rough Surfaces, Part II36th AIAA Thermophysics Conference - Orlando, Florida, June 23 - 26, 2003 24 CORRELATIONSP0 P0P0,Hz 11 aLaHz 1.

9 80 4E 3 max 0, bL2 2. 25 3/2Rs 1. 25 bL2ks m/ Rss 0. 95/ 1 0. 071c2 H c1 1. 62 /m c2