HEAT TRANSFER ENHANCEMENT OF A HEATED BLOCK IN THE CHANNEL WITH CAVITY BY USING UNSTEADY FLOW PULSATION

Transcription

1 HEAT TRANSFER ENHANCEMENT OF A HEATED BLOCK IN THE CHANNEL WITH CAVIT B USING UNSTEAD FLOW PULSATION Jn-Chih Chng Dpartmnt of Aronautical Enginring, National Formosa Univrsity 64 Wun-Hua Road, Huwi, unlin 68, Taiwan R.O.C. Fax: , jcchng@nfu.du.tw Kywords: Cavity channl, Block hat sourc, Unstady, Pulsating flow, Enhancmnt ABSTRACT In this study, th ffcts of flow pulsation on mixd convction of channl flow ovr cavity mountd with a hatd block hav bn dtaild xplord. Attntion is particularly focusd on th influncs of th pulsation frquncy and amplitud on th flow structur and thrmal fild. In addition, hat transfr nhancmnt of th hatd block through pulsation flow is discussd. Rsults show that, an imposd pulsation flow could caus a significant altrnation in th flow structur and tmpratur distributions. Th hat transfr nhancmnt incrass monotonically with R and pulsation amplitud A. Th maximum hat transfr nhancmnt occurs at a crtain pulsation frquncy St which can b considrd to b th natural frquncy of th physical systm. Comparing th rsults of th cass with or without flow pulsation, th maximum augmntation of avrag Nusslt numbr is about % for th hatd block, as. St.,. A.8, R. INTRODUCTION Convctiv hat transfr in ducts with th abrupt chang in gomtry is widly ncountrd in many applications, such as in th cooling of lctronic quipmnts, cooling passags of turbin blads and hat xchangrs. Th application in lctronic quipmnt cooling is to blow th air through th plug-in PCBs to cool larg racks and cabints. Th backsid of PCBs and th IC componnts form a channl with numrous opn cavitis. Owing to th abrupt chang in channl gomtry, th phnomna of sparation, rattachmnt and rcirculation of th flow structur may occur and rsult in poor hat transfr. If thr ar hatd blocks mountd in th rgion of th cavity wall, multipl rcirculation clls gnrat and intract. Thn hat transfr prformanc bcom wors. Bcaus of its frqunt occurrnc in th industrial situations, th convctiv hat transfr from hatd blocks hav bn studid by numrous rsarchrs in th past fw dcads. Lhmann and Wirtz [], and Agonafr and Moffatt [] xprimntally and numrically invstigatd th charactristics of flows ovr an array of two-dimnsional, rctangular componnts mountd on channl wall. Hat was applid to th top surfac of on componnt. It was found that th variation of hat transfr cofficint along th hatd surfac is rathr diffrnt to that for smooth wall channl. Exprimnts hav bn carrid out by Kang t al. [], and Nakayama and Park [4] to xamin th ffcts of block hight and wall conduction on th hat convction for air flow ovr an isolatd block hat sourc mountd on plat. Davalath and Bayazitoglu [] numrically prdictd th bhaviors of forcd convction btwn paralll plats mountd with two-dimnsional multipl blocks. Rsults indicatd that th hat flux distributions at th rar surfacs of blocks ar much smallr than thos at th front and top surfacs. For th studis of channl flow ovr cavitis, th prvious rsults [6-7] showd that th sparation of stramlin and th intnsity of closd stram flow within th cavity ar a

2 function of cavity aspct ratio, rlativ channl siz to cavity siz, and paralll vlocity within th channl. Fang t al. [8-9] hav prsntd a numrical and xprimntal study of th tim-dpndnt hydrodynamics rmoval of contaminant from a cavity on th floor of th cavity with forcd and mixd convction. It was shown that th claning of contaminant in th channl is mor pronouncd during th unstady start-up of channl flow and th rat of claning dcrass as th flow rach a stady stat. Bsids, th chang in Grashof numbr causs a dramatic diffrnc in th obsrvd flow pattrn and claning fficincy. Papanicolaou and Jaluria [] numrically invstigat th mixd convction of multipl hatd blocks mountd on th cornr of rctangular cavity. It was found that th arrangmnt of hatd blocks affctd th flow structur and inducd unstadinss. For th studis of th hat transfr nhancmnt with flow pulsation, Azar [] utilizd a mchanical shakr at th inlt of a vrtical channl to nhanc th hat transfr of lctric componnts. Whn th xtrnal forcd air was supplid, th tmpratur of lctric componnt would b significantly rducd and thus ffct could act both on th upstram and down stram componnts. Kim t al. [] numrically studid th forcd convction hat transfr from two hatd blocks in a horizontal channl with a uniformly, oscillating vlocity at th channl inlt. Th rsults indicatd that natural shdding inducd by th upstram block would incras th hat transfr of th downstram block. Thr is dominant pak of hat transfr nhancmnt whn th pulsating frquncy changd. Th main objctiv of this study is to xamin th hat transfr nhancmnt of hatd block mountd on th cavity in a channl with pulsating flow imposd at th inlt of th channl. Grat attntion is paid to invstigat th ffcts of flow pulsation frquncy and amplitud on hat transfr augmntation for mixd convction of channl flow ovr cavity mountd with a hatd block. ANALASIS Th physical systm undr considration, as shown in Figur, is a two-dimnsional channl flow ovr a rctangular cavity. A hatd block mountd on th floor of th cavity, and th surfacs of th block ar subjctd to uniform hat flux. Bsids, th othr portions of th bottom plat and th wall of th up plat ar wll insulatd. A pulsating flow ntrs th channl with uniform vlocity U (τ) and uniform tmpratur T at th channl inlt. By introducing th Boussinsq approximation, th basic quations in dimnsionlss form dscribing th stady laminar mixd convction in a horizontal plat channl ar as follows Continuity quation U V + = () -momntum quation U U U P + U + V = + U () τ R -momntum quation V V V P Gr + U + V = + V + θ () τ R R and Enrgy quation θ τ θ θ + U + V = θ (4) R Pr Th govrning quations ar subjctd to th following boundary conditions: For H c < <, at = -L, U ( τ) = [ + Asin(Stτ)], V = θ = () for < <, at, U V θ = = = (6) θ =, U=V=, on th surfac of wall (7) n θ =, U=V=, on th front, top and rar n surfacs of a hatd block (8 Equations () (8) rfr to th usual no-slip conditions on all th solid walls, and th assumption of thrmal insulation for th channl plats. Th stram is with pulsating vlocity and uniform tmpratur at th channl inlt, and with hydrodynamic and thrmal fully dvlopd conditions at th xit far downstram to th cavity. With n rprsnting th outward normal dirction, quation (8) imposs th uniform hat flux along th surfacs of a hatd block

3 xposd to th stram. Th local Nusslt numbr along th front, top and rar surfacs of th hatd block is of intrst to thrmal systm dsign. It is dfind as hb q sb Nu = = = (9) k k(ts T ) θs In addition, th spacal avrag Nusslt numbr for front, top and rar surfacs of th hatd block is calculatd by L h Nu = Nu d h () L o h whr h is th dimnsionlss coordinat along th block surfac and L h is th total lngth of th front, top and rar sids of ach block. Sinc th unstady natural of th prsnt problm, th tim avrag of local and spacal avrag Nusslt numbr for on priod ar dfind as τ+ /St [Nu] = St Nud τ () τ and o τ+/st τ [Nu ] = St Nu d τ. () SOLUTION METHOD Th govrning quations () - (4) and boundary conditions () (8) wr solvd by a numrical schm drivd from th SIMPLER algorithm. Th proposd numrical algorithm was validatd in two ways. First, diffrnt numbrs of grid lins in both th and dirction wr mployd to nsur that th solution is grid indpndnt. Th diffrncs in U, V and θ at all grid points obtaind from th and 4 grid systms wr lss than % for a typical cas with R =, St =. and A =.. Thrfor th grid systm was st in th computation of th various cass to b prsntd. In addition, to nsur that th rsults ar not affctd by th longitudinal lngth of computation domain, tsts ar prformd by varying th computation lngth downstram of th cavity. Scondly, th rsults for th limiting cas without th apparanc of cavity is compard to th rlvant litraturs. Good agrmnt was found btwn th prsnt prdictions and th rsults prsntd by Davalath and Bayazitoglu []. Bsids, for numrical invstigation for th prsnt problm, a stady solution is computd firstly and as th initial condition. Thn a boundary condition of pulsation flow is imposd at th inlt of channl for th transint computation until th flow and thrmal fild appard priodically. In this study, th diffrncs in u, v and θ at all grid points obtaind from th and 48 tim stps pr priod wr lss than % for a typical cas for R =, St =. and A =.. Thrfor th tim stps pr priod was st in th transint computation of th various cass to b prsntd. Through ths program tsts th proposd numrical schm is considrd to b appropriat for th problm undr invstigation. RESULTS AND DISCUSSIONS Inspction of th forgoing analysis indicats that th flow and hat transfr charactristics in th prsnt systm dpnd on 9 paramtrs. Ths ar th Rynolds numbr R, ratio of th Grashof numbr to th squar of Rynolds numbr Gr/R, th Prandtl numbr Pr, th dimnsionlss hight of cavity H c, th dimnsionlss width of rctangular cavity L c, th dimnsionlss distanc btwn th channl inlt and th lft dg of cavity L, th dimnsionlss hight of hatd block H h, th Strouhal numbr St and dimnsionlss pulsation amplitud A. Sinc a vast numbr of th govrning dimnsionlss paramtrs ar rquird to charactriz th systm, a comprhnsiv analysis of all combinations of problms is not practical. Whil computations can b prformd by any combination of ths paramtrs, th objctiv hr is to prsnt a sampl of rsults that would illustrat th ffcts of St, A, and R on th convctiv hat transfr in a horizontal channl flow ovr a cavity. In particular, air (Pr =.7) flowing through th channl for L =, L c =, H c =., H h =., and Gr/R = is considrd. Th rsults ar prsntd for th cass with St varying from. to., A from. to.8, and R from to. Initially, th ffcts of th pulsating flow on th flow structur and thrmal distributions ar invstigatd. For th cas without flow pulsation

4 at th inlt of channl, i.. stady stat condition, th stramlins and isothrms of a typical cas for R = ar shown in Fig.. Figur (a) show that a strong primary rcirculation zon occupis in th cavity which obstructs th main flow into th rgion vicinity to th hatd block. In addition, a scondary rcirculation zon appars in th lft cornr of cavity du to th xistnc of th hatd block. Figur (b) show that th isothrms adjacnt to th cavity ar rathr spars and paralll distribution xcpt at th rgion clos to th top cornr. This implis that th hat transfr in th cavity is dominatd through th mchanism of hat conduction owing to th occurrnc of main flow sparation at th top cornr of cavity. Nxt, th stramlins and isothrms plots in on priod ar plottd to illustrat th ffct of pulsation flow in Fig. and Fig. 4 for R =, St =. and A =.. Eight plots with qual tim intrval ar drawn to show a complt cycl. Considring th oscillation mannr of inlt vlocity, th tim intrval btwn positions to 7 can b calld as th dclrating phas and th rst of th cycl as acclrating phas. During th dclrating phas, th inlt vlocity gradually dcrass. Thrfor, th original rcirculation clls in th cavity for stady stat ar dividd into two main rcirculation clls on th lft and right sids of th hatd block and grow gradually as shown in Fig.. Bsids, on rcirculation cll appars on th uppr plat of channl. This rcirculation cll dflcts th stramlin toward th hatd block as th main flow passs through th cavity, and th stramlins ar dnsly packd in th rgion nar th top sid of hatd block. On th othr hand, during th acclrating phas, th inlt vlocity gradually incrass from th minimum to th maximum (tim positions 7 to 8 and to ), ths rcirculation clls gradually shrink and disappar. Anothr rcirculation clls form on th lft sid cornr of cavity and rar sid of hatd block. Ths two rcirculation clls grow gradually with tim and push th original rcirculation clls comprssd. It is notd that th mor rcirculation clls ar gnratd and grown bsid th hatd block during th dclrating phas thn dstroyd during th acclrating phas. This kind of variation and movmnt of rcirculation clls will incras th intractions btwn main stram and rcirculation clls in th cavity, and nhanc th convctiv ffct in th vicinity of th hatd block. Figur 4 illustrats th influncs of pulsating flow on th tmpratur distributions. Th isothrms appar complicatdly du to th formation, growth, movmnt and shrinkag of ths rcirculation clls within th cavity. For th top sid of th block, th thrmal boundary layr is comprssd gradually during th dclrating phas. But it incrass during th acclrating phas bcaus th lft rcirculation cll is pushd across th hat block. For th front and rar sids, th thrmal boundary layr is affct significantly du to th distribution of th rcirculation clls. Howvr, an ovrall inspction on th isothrms in ths plots rvals that, th isothrms ar vidntly comprssd toward th hatd block as comparing to th rsults plottd in Figur (b). Thrfor, it is rasonably xpctd that th hat transfr charactristics can b ffctivly promotd by th pulsating flow imposd in th inlt of channl. Th rsults in Figurs and 4 illustrat that imposd pulsating flow could caus significant chang in th distributions of stramlins and isothrms. Now attntion is paid to invstigat th ffcts of pulsation flow on th hat transfr charactristics. Figur illustrat th priodic variation of spatial avrag of Nusslt numbr for R =, St =. and A =.. Aftr a transint stag, th variations of Nusslt numbr for all front, top and rar sids of hatd block ar with th sam oscillating frquncy qualing to th imposd inlt vlocity frquncy. Thrfor only a complt cycl is prsntd in Fig.. Howvr, th bhaviors on ach sid ar diffrnt and appar asymmtrically. For xampl, th spatial avrag Nusslt numbr of th top sid is out of phas with imposd pulsating flow at th tim position to, but almost in phas at th tim position to. In gnral, th hat transfr on th top sid is bttr than th othr sids owing to th main stram dflct toward to th top sid. Th Nusslt numbr of rar sid is th worst du to th flow stram is obstructd by th hatd block. Howvr, th avrag Nusslt numbr on ach sid of th hatd block is lagr than th rsults 4

5 of without imposd pulsating flow at th inlt. Figur 6 dpicts th hat transfr charactristics of th hatd block for R =, St =. and A =.. In Figur 6, th curv for th cas without imposd flow pulsation at th inlt, i.. A =, th local Nusslt numbr qual to th tim avrag of local Nusslt numbr [Nu] is rathr uniform along th front and rar surfacs of th hatd block. Howvr, th [Nu] slightly incrass with h along th top surfac of th hatd block. An ovrall inspction on th rsults in th Figur rvals that th tim avrag of local Nusslt numbr [Nu] distribution for th cas without flow pulsation is vry small and is du to th fact that conduction plays an important rol of hat transfr mchanism in th rgion vicinity to th hatd block. Whn a pulsating flow with A =. and St =. impos at th inlt, th hat transfr cofficint for th front and top surfacs of hatd block is gratly augmntd du to th intraction btwn th main stram and th rcirculation clls. Evn in th rar sid of hatd block th tim avrag of local Nusslt numbr [Nu] can also b improvd. Now, th attntion is turnd to th variation of tim and spacial avrag Nusslt numbr [ Nu] with pulsation amplitud A as shown in Fig. 7 for R = and St =.. Th incras th amplitud of imposd pulsating flow may nforc th flow fild intraction btwn th main stram and rcirculation clls in th cavity, which would nhanc th hat transfr charactristics in th vicinity of th hatd block. Thrfor, th hat transfr nhancmnt is monotonically incrasd with A. Th nhancmnt is about and for A =. and.8, rspctivly. Th variation of [ Nu ] with pulsation frquncy St is show in Fig. 8 for A =., R = and. Figur 8 shows that th tim and spacial avrag Nusslt numbr [ Nu] has local maximum at St =. in spit of R = or. Thrfor, St =. can b considrd to th natural frquncy of this systm undr th paramtr sttings, which sms indpndnt on R. Finally, th influncs of flow pulsation on th ovrall charactristics of hat transfr for th hatd block ar invstigatd. Figur 9 plots th variations of [ Nu] / Nu w vrsus R. Hr, th [ Nu] rprsnts th tim and avrag Nusslt numbrs for th hatd block, whn a flow pulsation with St =. and A =. is introducd at th inlt of th channl. Whil th Nu w is thos for th situation without flow pulsation. It is sn that, [ Nu] / Nu w riss with th incras in R in th rang of R. In addition, th maximum valu of [ Nu] / Nu w is about.. This rprsnts that, with a flow pulsation at th inlt of th channl, th nhancmnt on hat transfr cofficint for th hatd block is % of that without flow pulsation. CONCLUSIONS In this study, th hat transfr nhancmnts of a hatd block mountd in th cavity channl through th flow pulsation imposd at th inlt of th channl hav bn dtaild xplord. Attntion is particularly focusd on th ffcts of th dimnsionlss amplitud A and frquncy St on th flow structur, tmpratur distribution and Nusslt numbr variation for th systm at various Rynolds numbr R. Th major rsults ar drawn as follows.. Comparing th rsults of th cass with or without imposd flow pulsation at th inlt, th maximum augmntation of avrag Nusslt numbr is about % for th hatd block, as. St.,. A.8, R.. An imposd pulsation flow could caus a significant altrnation in th flow structur and tmpratur distributions. Th hat transfr nhancmnt is monotonically incrasd with R and pulsation amplitud A.. Th largst [ Nu] occurs at a crtain imposd pulsation frquncy, which sms indpndnt on R. This dimnsionlss pulsation frquncy can b considrd to b th natural frquncy of th physical systm. ACKNOWLEDGEMENT Th financial support of this study by th Enginring Division of National Scinc Council, R.O.C., through th contract NSC-9--E--9 is gratly apprciatd. NOMENCLATURE A dimnsionlss amplitud of pulsating flow b channl hight

6 H c dimnsionlss hight of rctangular cavity, h c/ b H h dimnsionlss hight of hatd block, h h/ b L dimnsionlss distanc btwn th channl inlt and lft sid wall of cavity, l /b L c dimnsionlss width of rctangular cavity, l c /b R Rynolds numbr, u h c /ν St dimnsionlss frquncy of pulsating flow, Strouhal numbr, f b/ u T s surfac tmpratur of hatd block U dimnsionlss longitudinal vlocity, u/ u u avrag inlt vlocity dimnsionlss longitudinal coordinat, x/b h dimnsionlss coordinat along hatd block surfac, x h / h h dimnsionlss transvrs coordinat, y/b θ dimnsionlss tmpratur, (T-T )/( q s b/k) θ s dimnsionlss surfac tmpratur at hatd block, (T s -T )/( q s b/k) REFERENCE [] Lhmann, G. L., and Wirtz, R. A., Th Effct of Variations in Stram-Wis Spacing and Lngth on Convction from Surfac Mountd Rctangular Componnts, ASME Wintr Annual Mting, Dnvr, HTD, Vol. 48, pp. 9-47, 98. [] Agonafr, D., and Moffatt, D. F., Numrical Modling of Forcd Convctiv Hat Transfr for Moduls Mountd on Circuit Boards, ASME J. Elctronic Packaging, Vol., pp. -7, 99. [] Kang, B. H., Jaluria,., and Twari, S. S., Mixd Convction Transport from an Isolatd Hat Sourc Modul on a Horizontal Plat, ASME J. Hat Transfr, Vol., pp. 6-66, 99. [4] Nakayama, W., and Park, S. H., Conjugat Hat Transfr from a Singl Surfac-Mountd Block to Forcd Convctiv Air Flow in a Channl, ASME J. Hat Transfr, Vol. 8, pp. -9, 996. [] Davalath, J. and Bayazitoglu,., Forcd Convction Cooling Across Rctangular Blocks, ASME J. Hat Transfr, Vol. 9, pp. -8, 987. [6] Higdon, J. L., Stoks flow in an arbitrary two-dimnsional domains: shar flow ovr ridgs and cavitis, J. Fluid Mch., Vol. 9, pp. 9-6, 99. [7] O Brin, V., Closd stramlins associat with channl flow ovr a cavity, Phys. Fluids, Vol., pp , 97. [8] Fang, L. C., Clavr, J. W. and Nicolaou, D., Transint rmoval of contaminatd fluid from a cavity, Int. J. Hat Fluid Flow, Vol., pp. 6-6, 999. [9] Fang, L. C., Effct of mixd convction on transint hydrodynamic rmoval of a contaminant from a cavity, Int. J. of Hat and Mass Transfr, Vol. 46, pp.9-49,. [] Papanicolaou, E., and Jaluria,., Mixd Convction from Simulatd Elctronic Componnts at Varying Rlativ Positions in a Cavity, ASME J. Hat Transfr, Vol. 6, pp.96-97, 994. [] Azar, K., Enhancd cooling of lctric componnts by flow oscillation, Int. J. Thrmophysics and Hat Transfr, Vol. 6, pp. 7-76, 99. [] Kim, S.., Kang, J. M., and Hyun, J. M., Forcd convction hat transfr from two hatd blocks in pulsating channl flow, Int. J. Hat and Transfr, Vol. 4, pp. 6-64, 998. T U(t) b h c l s q s hw h lc g hh Insulatd Figur Schmatic diagram of physical systm (a) (b) Fig. (a)stramlins and (b) isothrms of channl flow ovr cavity mountd a hatd block for R =, A =, i.. without flow pulsation. oo 6

7 () () () () () (4) () (4) () () () () (4). 4 (8) Figur Unstady distribution of stramlins in on priod of channl flow ovr cavity mountd a hatd block with flow pulsation for R =, St =. and A = (6) (7) Figur Unstady distribution of isothrms in on priod of channl flow ovr cavity mountd a hatd block with flow pulsation for R =, St =. and A =.. 7

8 without flow pulsation Avrag F.S. T.S. R.S. F.S. T.S. R.S. R= R= 9 Nu [Nu] Tim Position Figur Th priodic variation of spacial avrag of Nusslt numbr on th surfac of th hatd block for R =, St =. and A = St Figur 8 Th variation of tim and spacial avrag Nusslt numbr [ Nu] with pulsation frquncy St for R = and A = without flow pulsation with flow pulsation. [Nu] 4 8 F.S. T.S. R.S. [Nu] / [Nu,w ]. 6 4 F.S T.S. R.S. h Figur 6 Th tim avrag of hat transfr charactristics on th hatd block for R =, St =. and A = R Figur 9 Variation of Nu / Nu w vrsus R for A = and St =.. [Nu] A Figur 7 Th variation of tim and spacial avrag Nusslt numbr [ Nu] on th hatd block with pulsation magnitud A for R = and St =.. 8