Numerical Optimization of Pin-Fin Heat Sink with Forced Cooling

Transcription

1 Numerical Opimizaion of Pin-Fin Hea Sink wih Forced Cooling Y. T. Yang, H. S. Peng, and H. T. Hsu Absrac This sudy presens he numerical simulaion of opimum pin-fin hea sink wih air impinging cooling by using 4 Taguchi mehod. L 9 ( 3 ) orhogonal array is seleced as a plan for he four design-parameers wih hree levels. The governing equaions are discreized by using he conrol-volume-based-finie-difference mehod wih a power-law scheme on he non-uniform saggered grid. We solved he coupling of he velociy and he pressure erms of momenum equaions using SIMPLEC algorihm. We employ he k ε wo-equaions urbulence model o describe he urbulen behavior. The parameers sudied include fin heigh H (35mm-45mm), iner-fin spacing a, b, and c (2 mm-6.4 mm), and Reynolds number ( Re = ). The obecive of his sudy is o examine he effecs of he fin spacings and fin heigh on he hermal resisance and o find he opimum group by using he Taguchi mehod. We found ha he fin spacings from he cener o he edge of he hea sink gradually exended, and he longer he fin s heigh he beer he resuls. The opimum group is H3a1b 2c 3. In addiion, he effecs of parameers are ranked by imporance as a, H, c, and b. T Keywords Hea sink, Opimum, Elecronics cooling, CFD. I. INTRODUCTION HE rapid developmen of elecronic echnology causes he sizes of elecronic componens o shrink. The hea flux per uni area has increased dramaically over he pas decade. Thus, he effecive removal of hea has played an imporan role in ensuring a reliable operaion of elecronic componens. Convenional elecronics cooling normally used forced air cooling wih hea sink showing superioriy in erms of uni price, weigh and reliabiliy. A number of research scholars have examined he hermal and hydraulic characerisics of various hea sinks exensively. The seady-sae forced-convecive cooling of a horizonally based pin-fin assembly has been invesigaed experimenally by Haq e al. [1]. The overall pressure drop and he effec of he shroud clearance were examined. Ledezma e al. [2] performed an experimenal, numerical and heoreical sudy of he hea ransfer on a pin-finned plae. They demonsraed he opimizaion principle experimenally by comparing several spacing designs in he same air sream in a wind unnel. Moreover, he correlaion equaions for opimal fin-o-fin Y. T. Yang is wih he Naional Cheng Kung Universiy, Tainan, Taiwan, (phone: ~62172; fax: ; yyang@mail.ncku.edu.w) H. S. Peng was PhD suden, graduaed from Naional Cheng Kung Universiy; currenly he works in he indusry. H. T. Hsu was MSc suden, graduaed from Naional Cheng Kung Universiy; currenly he works in he indusry. spacing and he maximum hermal conducance were developed. Ledezma and Bean [3] performed he experimenal and numerical sudy of hea sinks wih sloped plae fins. This sudy discussed he hermal performance on he orienaion of he fin array and he iling of he cress of he plae fins. Li e al. [4] and Li and Chen [5] invesigaed he hermal performance of pin-fin and plae-fin hea sinks wih confined impingemen cooling by using infrared hermography. The resuls show ha he hermal resisance of he hea sinks decreases wih he increased Reynolds number of he impinging e. However, he reducion of he hermal resisance decreases gradually as he Reynolds number increases. Moreover, i revealed ha he influence of fin widh is more obvious han he fin heigh. In addiion, he opimal impinging disance increases wih he increasing Reynolds number. Finally, hey concluded ha he hermal performance of he pin-fin hea sinks is superior o ha of he plae-fin hea ones. Furhermore, he hermal performance of pin-fin hea sinks wih air impingemen cooling was performed numerically and experimenally by Li and Chen [6]. The effecs of he fin geomery and he Reynolds number on he hea ransfer of he hea sinks were also discussed. Brignoni and Garimella [7] demonsraed he experimenal opimizaion of confined impinging air es used in conuncion wih a pin-fin hea sink. Enhancemen facors for he hea sink relaive o a bare surface were evaluaed, and were in he range of 2.8 ~ 9.7, wih he larges value being obained for he larges single nozzle. Boh he average hea ransfer coefficiens and he hermal resisance were expressed for he hea sink as a funcion of a Reynolds number, an air flow rae, a pumping power, and a pressure drop, o assis in opimizing he e impingemen configuraion for given design consrains. Maveey and Hendricks [8] invesigaed he performance sudy of pin-fin hea sinks wih impingemen cooling which considered he effecs of geomery, nozzle-o-hea sink verical placemen, maerial, and Reynolds number. The resuls revealed ha here is an opimal nozzle-o-sink heigh and Reynolds number for which he hea dissipaion is maximized. The bes performance occurred when he dimensionless impingemen disance was beween 8 and 12, and when he Reynolds number was beween and The resuls also presened ha due o he higher spreading resisance efficiency of he carbon composie maerial, i led o more uniform cooling of he hea sink. Moreover, he influence of he nozzle-o-hea sink verical placemen on he hermal performance was reduced as he Reynolds number increased. The comparisons beween numerical and experimenal resuls for he cooling performance from a pin-fin hea sink wih an 884

2 impinging air flow have been sudied by Maveey and Jung [9]. The opimizaion sudies were also discussed o quanify he effecs of changing he fin shapes on he cooling performance. The numerical resuls illusraed a complex pressure gradien inside he fin array and a greaer pressure gradien improved mixing and hea ransfer. I also revealed ha a complicaed fluid moion wih large pressure gradiens generaed voriciy, circulaion and flow reversals. The enhancemen of hea ransfer from a discree hea source in a confined air e impingemen was experimenally sudied by El-Sheikh and Garimella [10]. A variey of pin-fin hea sinks were mouned on he hea source and he resuling enhancemen was discussed. Relaive o an unpinned hea sink, he hea ransfer from he pinned ones was improved by 2.4 o 9.2 imes. Due o he inroducion of he hea sinks, he enhancemen facors relaive o he bare hea source varied from 7.5 o 72. Resuls for he average hea ransfer coefficien were correlaed as a funcion of he Reynolds number, fluid properies and geomeric parameers of he hea sinks. The hermal performance of a pin-fin hea sink was sudied heoreically and experimenally by Kobus and Oshio [11]. They carried ou a heoreical model ha has he capabiliy of predicing he influence of various physical, hermal and flow parameers on he effecive hermal resisance of a pin-fin array hea sink. Besides, he predicive capabiliy of he heoreical model was verified by comparing wih experimenal daa and was shown o be excepionally good over he range of parameers. Kobus and Oshio [12] invesigae he influence of hermal radiaion on he hermal performance of a pin fin array hea sink heoreically and experimenally. A heoreical hermal radiaion model was developed for predicing he effecive hermal resisance of a fin array hea sink. The hermal and hydraulic behavior due o e impingemen on pin fin hea sinks was experimenally invesigaed by Issa and Orega [13]. This sudy showed ha he pressure loss coefficien increased wih increasing pin densiy and pin diameer, and decreased wih increasing pin heigh and clearance raio. Moreover, he overall base-o-ambien hermal resisance decreased wih he increasing Reynolds number, pin densiy and pin diameer. Duan and Muzychka [14] performed he experimenal invesigaion of he hermal performance wih four hea sinks of various impingemen inle widhs, fin spacings, fin heighs and airflow velociies. They developed a hea ransfer model o predic he hermal performance of impingemen air cooled plae fin hea sinks for design purposes. An experimenal sudy was conduced o invesigae he hea ransfer from a parallel fla plae hea sink under a urbulen air e impingemen by Sansoucy e al. [15]. The forced convecion hea ransfer raes from a fla plae and from a fla plaed hea sink under an impinging confined e have been obained. In addiion, he experimenal resuls were compared wih he numerical predicions obained in an earlier sudy. They concluded ha he numerical analysis in a previous sudy was adequae for appraising he mean hea ransfer rae in e impingemen for siuaions of hermal managemen of elecronics. Excluding numerical simulaion or experimenal sudies, he enropy generaion mehod was also uilized o evaluae or opimize he hermal performance of he hea sink [16-20]. The procedure is based on he minimizaion of enropy generaion resuling from hea ransfer and pressure drop. The model demonsraes a rapid and sable procedure for obaining opimum design/operaional condiions wihou resoring o parameric analyses by using repeaed ieraions wih a hermal analysis ool. Moreover, several scholars have aemped o modify he fin shape o improve he hermal and hydraulic performance. The sudy of pin fin hea sink wih differen fin shape designs was performed by Yang and Peng [21], [22]. They designed he fins wih un-uniform fin heigh and widh o improve he hermal performance. The resuls demonsraed ha he adequae fin shape design could enlarge he hea ransfer area and decrease he flow resisance in he cenral region. I decreases he uncion emperaure and increases he enhancemen of he hermal performance simulaneously. Sahe and Sammakia [23] and Shah e al. [24] conduced a sudy of a new and unique high-performance air-cooled impingemen hea sink. The influences of he fin shape, paricularly near he cener of he hea sink were examined. The sudy revealed ha he pressure drop can be reduced by cuing he fins in he cenral impingemen zone wihou sacrificing hea ransfer raes. I enhances no only he hermal performance bu also he hydraulic performance of he sink. Shah e al. [25] exended he previous work by discussing he effec of he removal of a fin maerial from he end fins and he oal number of fins, and he reducion in he size of he hub fan. They developed a new opimal hea sink design by using acual fan operaing characerisics. Lorenzini and Morei [26] analyzed he Y-shape fins and examined he geomeries by varying he angle beween he wo arms of he Y and proposed new shape for he fins. Naphon and Sookkasem [27] invesigaed he hea ransfer characerisics of apered cylinder pin fin hea sinks experimenally and numerically. Ji e al. [28] sudied he cooling performance of riangular folded fin hea sink. They discussed he influence of he fin pich, he Reynolds number, and he fin heigh. The resuls showed ha he cooling performance of riangular folded fin hea sinks depended significanly on he fin heigh, he fin pich, and he Reynolds number. Moreover, he empirical correlaions were developed o predic he hea ransfer coefficien and pressure drop. The numerical predicions of hea ransfer and flow characerisics of hea sinks wih ribbed and dimpled surface have been done by Wee e al. [29]. The resuls showed ha he hea ransfer augmenaion produced by he ribs is abou 104% higher han ha produced by he smooh-surface hea sink. Bu he ribs also produce higher saic pressure variaions, higher velociy gradiens, and higher sreamwise voriciy magniudes. Applying dimples o hea sink surface gives a spaially averaged Nussel number increase of 63%, wih a pressure drop penaly which is much lower han he one produced by ribbed surfaces. In he presen sudy, he numerical simulaions of pin-fin hea sinks wih impingemen cooling in hermal-fluid characerisics are invesigaed. The purpose of his sudy is o 885

3 examine he effecs of he fin heigh and iner-fin spacing on he hermal performance of he hea sink. Energy equaion of fluid T µ l µ T ρu = + x x σ l σ T x Energy equaion of solid (3) T k s = 0 xi xi (4) Transpor equaion for k Fig. 1 Physical domain II. MATHEMATICAL MODEL AND NUMERICAL METHOD The schemaic diagram of he geomery and he compuaional domain is shown in Fig. 1. The dimensions of he compuaional domain were based on he work by Li and Chen [6]. Taking advanage of he symmery, he numerical simulaions have been performed by considering only a one-quarer model of he physical domain. The boundary condiions for his problem are saed as follows. A he flow inle, he air was uniformly induced downward wih a consan emperaure. The enrainmen boundary condiions are used a he oule. No slip condiions wih hermally insulaed are provided on all he oher walls. A he boom of he hea sink, a uniform consan hea flux is applied o he heaing area. The adiabaic hermal boundary condiions are uilized a he ouer perimeer of he boom of hea sink excep for he heaing area. The urbulen hree dimensional Navier-Sokes and energy equaions are solved numerically (using a finie difference scheme) combined wih he coninuiy equaion o simulae he hermal and urbulen flow fields. An eddy viscosiy model is used o accoun for he effecs of urbulence. The flow is assumed o be seady, incompressible, and hree dimensional. The buoyancy and radiaion hea ransfer effecs are negleced. In addiion, he hermophysical properies of he fluid are assumed o be consan. The hree dimensional governing equaions of mass, momenum, urbulen kineic energy, urbulen energy dissipaion rae, and energy in he seady urbulen main flow using he sandard k ε model are as follows: Coninuiy equaion ρui = 0 (1) x Momenum equaion u p u i ( ) u i i ρ u = + µ + µ + (2) x xi x x x i k µ k u u i ui ρ u = µ + + µ + ρε x x k x x x σ i x Transpor equaion for ε 2 ε µ ε ε u u i ui ε ρ u = µ + + C1µ + C2ρ x x x k x x σ ε i x k The Reynolds number of he impinging e is defined as (5) (6) Win d Re = (7) ν where d denoes he diameer of nozzle. As far as evaluaing he efficiency of hea dissipaion, hermal resisance is ofen used o rae he performances of he hea sink. The hermal resisance of he hea sink, R h, can be defined by R T T Q ave in h = (8) where T ave and T in are he average emperaure of he base of he hea sink and he emperaure of he inle fluid, respecively. Q is he heaing power applied on he base of hea sink. The coefficien of enhancemen (COE) is defined o quanify he improvemen in hea ransfer raes due o he differen ypes of he hea sink fins. This is expressed as COE Nu Nu new = (9) origin where he average Nussel number Nu is calculaed by hd Nu = (1) (10) k a and he average convecion hea ransfer coefficien h is calculaed by 886

4 h = T base q T in (11) Numerical approach We employ a non-uniform and saggered grid sysem. A saggered grid arrangemen is used in which he velociies are sored a a locaion on he conrol-volume faces. All oher variables including pressure are calculaed a he grid poins. The numerical mehod used in he presen sudy is based on he SIMPLEC algorihm [30]. Pressure and velociy correcion schemes are implemened in he model algorihm o arrive a a converged soluion when boh he pressure and velociy saisfy he momenum and coninuiy equaions. For non-linear problems, we employ he under-relaxaion o avoid divergence in he ieraive soluions. The resuling ses of discreized equaions for each variable are solved by he line-by-line procedure which is he combinaion of he Tri-Diagonal Marix Algorihm (TDMA) and he Gauss-Seidal ieraion echnique. The soluion is considered o be converged when he normalized residual of he algebraic equaion is less han a 3 prescribed value of10. Taguchi mehod In he presen sudy, all parameers influencing he hermal resisance and he pressure drop have no been invesigaed in deails as i requires a large number of simulaions and ime aken. The Taguchi mehod developed by Genichi Taguchi is a useful mehod for sysemaically opimized designs. The number of simulaions required for a whole analysis in he case of four hree-level parameers can be reduced from 81 ( 3 4 ) o 9. The L 9 ( 3 4 ) orhogonal array can be adoped for furher analyses of he sensiiviy of each parameer. Table I and Table II lis he values of four facors hree levels and nine cases for L 9 ( 3 4 ) orhogonal array. The parameers affecing hermal resisance, namely fin heigh H, iner-fin spacing a, iner-fin spacing b, iner-fin spacing c (denoe in Fig. 2) are insered in columns A, B, C, and D. The purpose is o obain he minimum hermal resisance. The performance saisics were chosen as he opimizaion crierion. I was used for he smaller he beer siuaions, evaluaed using he following equaion: n 2 yi i= 1 S N = 10log = log y + S n 2 2 ( ) (12) TABLE I L 9(3 4 ) ORTHOGONAL ARRAY OF THE TAGUCHI METHOD Case no. Parameers and heir levels A B C D TABLE II FACTORS USED IN THE TAGUCHI METHOD Parameers Levels A: Fin heigh (H) (mm) B: Iner-fin spacing (a) (mm) C: Iner-fin spacing (b) (mm) D: Iner-fin spacing (c) (mm) Fig. 2 Denoaions of he pin fin hea sink Fig. 3 Grid refinemen 887

5 Fig. 4 The mesh disribuion of compuaional domain (original design, mesh-95175) Fig. 5 The effec of each parameer on he hermal resisance ( Re = 15000) Fig. 6 The effec of each parameer on he hermal resisance ( Re = 25000) Fig. 7 Simulaions of Nussel number of hree hea sinks as a funcion of Reynolds number Fig. 8 Effecs of he Reynolds number and he fin design (beer han he original design) on COE (a) 888

6 (b) Fig. 9 Velociy field (opimum design, z = 0.045m) (a) Re = 15000, (b) Re = row3 row2 row1 c b a b c (a) (b) y channel3 channel2 channel1 Fig. 10 (a) Differen locaions in he physical domain, (b) fin emperaure disribuion (Re= 15000, a row-1) III. RESULTS AND DISCUSSION The dimensions of he hea sink in his sudy were based on he work by Li and Chen [6]. Boh he lengh and widh of he x base of he hea sink are 80mm. The area of he heaer is 40mm 40mm, which is in he cener of he hea sink. The heaing area is heaed wih heaing power 20 W. The parameers used in he grid refinemen es were based on he uniform iner-fin spacing design and H = 40mm. A oal number of meshes, 70602, and were employed o assess he grid independence. As shown in Fig. 3, he resuls of he grid sensiiviy sudy showed ha he simulaions based on he meshes provide saisfacory numerical accuracy. A non-uniform and saggered grid sysem wih a large concenraion of nodes in regions of seep gradiens, such as hose close o he walls is employed. As seen in Fig. 4, he non-uniform grid sysem is chosen as a compromise beween compuaional effor and accuracy. From Table III and Fig. 5, i can be seen ha he mos effecive parameers on he hermal resisance are found as follows: he iner-fin spacing (a), he fin heigh (H), he iner-fin spacing (c), and he iner-fin spacing (b). The hermal resisance decreases wih increasing he fin heigh. Increasing he fin heigh enlarges he hea ransfer area of he hea sink, which enhances he hea ransfer rae. Hence, he hermal performance improved. The hermal resisance increases by increasing he iner-fin spacing a. The hermal resisance decreases when he iner-fin spacing b changes from 2mm o 4.2mm, and hen increases when iner-fin spacing b changes from 4.2mm o 6.4mm. The effec of iner-fin spacing c is conrary o iner-fin spacing a. The hermal resisance decreases when increasing he iner-fin spacing c. I is imporan o enlarge he hea ransfer area for efficien hea dissipaion in he cenral region of he hea sink. Therefore, he iner-fin spacing a should be decreased in he cener of he hea sink in order o increase he hea ransfer area in he cenral region. The momenum of working fluid is weak around he rim of he hea sink. Hence, he iner-fin spacing c should be increased o reduce he flow resisance and allow more working fluid o flow ou. Fig. 6 depics he effec of each parameer on he hermal resisance a Re = As shown in he figure, he rends of he S/N raio are similar o he previous case. Fig. 7 shows he simulaions of he Nussel number of hree hea sinks as a funcion of he Reynolds number. From Fig. 7, i is seen ha increasing he Reynolds number increases he Nussel number. However, he incremen of he Nussel number decreases gradually as he Reynolds number increases. The figure also shows he comparison of he Nussel number beween he original and opimal designs. The resul of opimum condiion of he Nussel number is much higher han he original designs. The effecs of he Reynolds number and he fin design (beer han he original design) on COE is shown in Fig. 8. Alhough he fin heigh of case 9 is higher han cases 2 and 4, he COE of case 9 is lower. This is because he flow peneraion ino he hea sink becomes weaker due o he increased flow resisance. Hence, he iner-fin spacing should be designed for more working fluid o flow ino he hea sink. Moreover, i can be seen ha COE decreases when he Reynolds number increases. The enhancemen of he hea 889

7 ransfer by increasing he Reynolds number may have a limiaion. Table IV shows he emperaure comparison beween he original and opimum designs a differen heaing power. When he heaing power is 20 W, he emperaure difference beween original and opimum design is abou 4K a Re = and 1.4K a Re = When he heaing power increased from 20 W o 40 W, he emperaure difference beween original and opimum design is more obvious. As shown in Fig. 9, he working fluid flows direcly ino he hea sink and acceleraes as i eners he iner-fin spacing as a resul of he area conracion. Then, he fluid is deceleraed giving rise o increased saic pressure and flow resisance. The fluid flow changes direcion o flow along he base plae of he hea sink. The velociy field decreases from op o boom and from inner o ouer. Fig. 10 shows he emperaure disribuion a row-1. The main influence of impinging e on he hea sink is a he cenral region. Hence, as shown in he figure, he emperaure of he ip of fin-1 is lower han oher fins. Besides, he hea dissipaions are cenrally concenraed on he fin base. The flow peneraion ino he cener of he hea sink becomes weaker due o he flow resisance. Therefore, he emperaure of he boom of fin-1 is much higher han fin-2 and fin-3. In addiion, he velociy of fluids in channel-2 and channel-3 are abou he same. The emperaure difference beween fin-2 and fin-3 appeared o be minimal. Heaing power TABLE III THE S/N VALUES AND EFFECTS OF EACH PARAMETER A B C D Level Level Level Effec Rank Bes TABLE IV THE AVERAGED TEMPERATURE OF BASE PLATE Fin shape T ave (K) Re=10000 Re=15000 Re=20000 Re=25000 Q = 20 W Origin Opimum Q = 60 W Origin Opimum IV. CONCLUSION The presen sudy provides valuable informaion on he pin-fin hea sink wih air impinging cooling by numerical simulaions wih he Taguchi mehod. The parameers affecing hermal performance have been sysemaically 4 invesigaed by using L 9 ( 3 ) orhogonal array. The governing equaions are discreized by using he conrol-volume-based-finie-difference mehod wih a power-law scheme on an orhogonal non-uniform saggered grid. The coupling of he velociy and he pressure erms of momenum equaions are solved by he SIMPLEC algorihm. The k ε wo-equaions urbulence model is employed o describe he urbulen srucure and behavior. The parameers sudied include fin heigh H (35mm, 40mm, 45mm), iner-fin spacing a (2mm, 4.2mm, 6.4mm), iner-fin spacing b (2mm, 4.2mm, 6.4mm), and iner-fin spacing c (2mm, 4.2mm, 6.4mm). The resuls of he presen sudy are described as follows. 1) The opimum group is H3a1b 2c 3, i.e. H = 45mm, a = 2mm, b = 4.2mm, c = 6.4mm. 2) The effecs of parameers are ranked by imporance as a, H, c, and b. 3) I is found ha an adequae arrangemen of iner-fin spacing could increase he Nussel number and COE. The incremens of he Nussel number and COE decrease gradually as he Reynolds number increases. A high Reynolds numbers, he effecs of geomeries are decayed. ACKNOWLEDGMENT We would like o hank he Naional Science Council of he Republic of China for supporing his proec under conrac No. NSC E MY2. REFERENCES [1] R. F. B. Haq, K. Akinunde, and S. D. Prober, Thermal Performance of a Pin-Fin Assembly, In. J. Hea Fluid Flow, vol. 16, pp , [2] G. Ledezma, A. M. Morega, and A. Bean, Opimal Spacing beween Pin Fins wih Impinging Flow, J. Hea Transfer, vol. 118, pp , [3] G. Ledezma, and A. Bean, Hea Sinks wih Sloped Plae Fins in Naural and Forced Convecion, In. J. Hea Mass Transfer, vol. 39, no. 9, pp , [4] H. Y. Li, S. M Chao, and G. L. Tsai, Thermal Performance Measuremen of Hea Sinks wih Confined Impinging Je by Infrared Thermography, In. J. Hea Mass Transfer, vol. 48, pp , [5] H. Y. Li, and K. Y. Chen, Thermal Performance of Plae-Fin Hea Sinks under Confined Impinging Je Condiions, In. J. Hea Mass Transfer, vol. 50, pp , [6] H. Y. Li, and K. Y. Chen, Thermal-Fluid Characerisics of Pin-Fin Hea Sinks Cooled by Impinging Je, J. 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