UNSTEADY LAMINAR CONVECTION FLOW OVER PERIODIC GROOVES BY USING SIO 2 -WATER NANOFLUID

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1 UNSTEADY LAMINAR CONVECTION FLOW OVER PERIODIC GROOVES BY USING SIO -WATER NANOFLUID AMIRHOSSEIN HESHMATI, MOHAMMAD PARSAZADEH & FARSHID FATHINIA 3,&3 Department of Mechancal Engneerng, Unversty Technology Malaysa, Johor, Malaysa Abstract unsteady lamnar forced convecton flow n a -dmensonal channel over perodc grooves s numercally nvestgated. Fnte volume method s used and the equatons were dscretzed by second order upwnd method. The rbheght to channel-heght rato (B/H) s. The downstream wall s heated by a unform heat flux whle the upstream wall s nsulated. Quas steady pont was obtaned at τ=0. The heat transfer s analyzed wth dfferent nanopartcles volume fracton and dameter of 0-4% and 0nm-50nm for SO respectvely at Reynolds number of 400 and τ=0. Water s used as a base flud of nanopartcles. The results revealed 4% heat transfer enhancement compared to the water n a grooved channel by usng SO nanopartcle wth volume fracton and nanopartcle dameter of 4% and 0nm respectvely. Keywords Unsteady, Forced convecton, Perodc grooves, Nanofluds, Heat transfer I. INTRODUCTION The mprovement of heat transfer has been pad more attenton due to ncreasng the engneerng applcatons. One of the common passve ways to enhance the heat transfer s usng the roughen surfaces, grooves, baffles, and rbs to produce local turbulent flow or dsturbng the flow. Hgh performance of varous engneerng applcatons s owed to the effcent heat transfer enhancement. Grooved channels have a sgnfcant role n ths sort of heat transfer enhancement. Energy system equpment, electronc coolng, coolng of nuclear reactors, coolng of turbne blades, combuston chambers, envronmental control systems are the benefcal samples of ths method []. Analyzng the thermal and flow feld over groove channel has been expermentally and numercally done by nvestgators snce last two decades. Eamsa and Promvonge [] have nvestgated flow and thermal behavor of forced convecton of an ncompressble arflow n a -dmensonal channel wth 9 perodc transverse grooves on ts lower wall. They found that reverse re-crculaton flow can consderably ncrease heat transfer n a transverse grooves channel. Adach et al. [3] presented the effect of expanded grooves on pressure drop determned n a horzontal channel ncludng 54 grooves sets to measure the pressure drop even for small Reynolds numbers. Adach and Uehara [4] studed Correlaton between heat transfer and pressure drop n -dmensonal horzontal channels usng fully developed flow wth perodcally grooved parts. A consderable effect on heat transfer was seen by changng rb shapes. Rb-Trangular groove (RR- TG), Trangular rb-trangular groove (TR-TG) and Trangular rb-rectangular groove (TR-RG) were three shapes that havng mounted on the lower wall of channel and analyzed wth a turbulent flow by Eamsa and Promvonge [5]. They found that Rectangular rb-trangular groove (RR-TG) has hghest heat transfer. They also studed the effects of ptch rato on heat transfer rate for these three geometres. In a smlar effort Kamal and Bnesh [6] studed effects of square, trapezodal and trangular rb shapes wth decreasng heght, whle ncreasng heght was n trapezodal rb shape numercally, on characterstcs of turbulent ncompressble arflow n a -dmensonal horzontal rbbed channel, whle unform heat flux was mposed on lower wall and upper wall was mantaned n an adabatc condton. They concluded the hghest mean Nusselt number and enhancement factor were for trapezodal rb wth decreasng heght. Effects of Reynolds number and wall thermal conductvty rato to the flud and geometrc parameters on heat transfer for rectangular and arc-shaped grooves have been reported by Shokouhmand et al. [7]. Heat transfer n an ntermttently and symmetrcally grooved channel wth 7 contguous trangular grooves followed by a flat secton n the range of Reynolds number varyng between 600 and,800 was nvestgated by Grener et al. [8]. Ther results revealed that Nusselt number s went up wth ncreasng Reynolds number. As for flow characterstcs effects, modfyng the topology of grooved channel s another way to ncrease the heat transfer, havng been utlzed by researchers durng last decades. Herman and Kang [9] expermentally studed forced convecton coolng of electrcal components n grooved channels wth three dfferent topologes of basc grooved channel (BGC), grooved channel wth cylndrcal eddy promoters (GCC) and grooved channel wth curved vanes (GCV) n lamnar, transtonal and turbulent arflows n the range of 00 to 6,500 Reynolds

2 number. They reported BGC s the best for moderate to hgh Reynolds numbers whle GCV has the optmum performance. They also nvestgated the heat transfer performance of grooved channel by attachng curved vanes at downstream of each block. The goal of usng curved vanes n ths experment was to enhance heat transfer at flank regons and elmnate large recrculaton zone n grooves. Ortz et al. [0] have nvestgated the heat transfer enhancement n a -dmensonal horzontal grooved channel by attachng curved deflectors. They revealed that n basc grooved channels; flow after passng over a rb drectly hts the next rb, s heated, gets trapped and creates recrculaton flow. Some researchers have focused on utlzng nanofluds to ncrease heat transfer parameters. Oronzo et al. [] studed the effect of nanofluds on rbbed channel numercally and found that heat transfer s mproved. Al-aswad et al. [] nvestgated numercally forced convecton flow over backward facng step by usng nanofluds. In ther research water was base flud and Au, Ag, Cu, CuO, Al O 3, SO, TO, and damond were nanopartcles. They concluded SO have generally mproved the heat transfer. It s clear from above studes that conventonal fluds have been used to nvestgate the characterstcs of heat transfer and usng nanofluds flow was not analyzed on grooved channel n unsteady lamnar condton and t has motvated the current study. Alaswad et al. [] reported that SO provdes hghest heat transfer enhancement compared to some other nanopartcles. So, n the present study, - dmentonal numercal smulatons over perodc grooves n a horzontal channel are carred out wth SO as nanopartcle that volume fracton and nanopartcle dameter vared -4% and 0-50nm respectvely. Water was used as the base flud under study. The purpose of ths study s to obtan the Nusselt number and skn frcton coeffcent of the consdered Nanoflud wth dfferent nanopartcle dameter and nanopartcle concentraton along the channel for lamnar unsteady flow. II. MODEL DESCRIPTION AND GOVERNING EQUATIONS The schematc of nterested system s shown n Fg.. Ths channel was fxed by nne grooves and 8 rbs along the downstream channel wall. The channel length, rb land (s) s set to be 870 mm and 5H/4 respectvely. The channel heght s H=40mm, whle groove wdth (B) s fxed to 3H/4. The entry length of 0H s consdered to create a fully developed flow. The last groove s located to 0H upstream of the ext. The length of test secton and rb heght was 670 mm and H/ mm, respectvely. Ths geometry has been fxed by eght rbs wth the length of 50mm (s=5h/4). The groove wdth rato, (B/H), s located to be B/H=0.75. Foregong geometrcal dmensons and heat flux are the same as grooved channel of smth and Pongjet []. Fg. Grooved channel The governng equatons under consderaton of the steady -dmensonal ncompressble form of Contnuty equaton, Naver-Stokes equatons and Energy equaton are as [3]: Contnuty equaton: u 0 t x () Momentum equaton: u u u j p j g t x x x () Energy equaton: T ut R u q ( ) T x x C x c x v p (3) where u s the velocty vector n the x drecton, P s the pressure, ρ s the densty, R s the specfc gas constant, γ s the rato of heat capactes, c v and c p 3

3 are the specfc heat at constant volume and specfc heat at constant pressure respectvely. Vscous stress tensor and heat flux are presented respectvely as: u u j u k j j (4) x j x 3 xk and T q k (5) x where µ and k are dynamc vscosty and thermal conductvty respectvely. The densty of nanoflud can be obtaned from [4]: (6) nf f np where f and np are mass denstes of base flud and NPs, respectvely. The effectve heat capacty s gven as [4]: C C C (7) p p p nf f np Where (ρc p ) f and (ρc p ) np are heat capactes of base flud and Nanopartcles, respectvely. The effectve thermal conductvty equaton of nanoflud s wrten as [4]: k k k (8) k eff statc Brwnan statc kf k k k k np f f np k k np f k k f np (8.) 4 KT k 5 0 C f, T, Brwnan f p f (8.) R where K np and K f are the thermal conductvtes of nanopartcles and base flud respectvely. Boltzman Constant: 3 k J (8.3) K T f T, T (8.4) for % 4% and 300K, where T s the flud temperature, and T 0 s the reference temperature. The effectve vscosty can be obtaned usng followng mean emprcal correlatons [4]: (9) eff f d d d f 6M N f0 3 p f np np (9.) where M s the molecular weght of base flud, N s the Avogadro number, and f0 s the mass densty of the based flud calculated at temperature T 0 =93K. The effectve thermal expanson s expressed as [4]: (0) nf f np for dfferent partcle materals the equatons are lsted n Table II. TABLE II VALUES FOR DIFFERENT PARTICLES Type of partcles β Concentraton (%).4594 SO.956(00 ) % 0% III. NUMERICAL IMPLEMENTATION Governng equatons s solved by fnte volume method usng SIMPLE algorthm. The normalzed resdual values are converged at 0-3 for all varables. Second order upwnd method numercal approaches have been mplemented for convectve and dffusve terms, respectvely. Besdes, researchers have mplctly appled the dscretzed nonlnear equatons. The pressure velocty couplng algorthm SIMPLE (Sem Implct Method for Pressure-Lnked Equatons) was chosen to evaluate the pressure feld. At the nlet, unform velocty profle has been mposed. Impermeable boundary condton over the channel wall s mplemented whle a constant heat flux condton s appled to over lower wall to create a thermally developed condton []. In ths case three parameters have been presented, velocty profle, skn frcton coeffcent and Nusselt number. Skn frcton coeffcent s calculated by shear stress over the test secton as []: w c f (5) u where w s shear stress, and u are densty and velocty, respectvely. The local Nusselt number s defned by: h( x) D Nu( x) h (6) k and average Nusselt number can be calculated by: Nu Nu( x) dx (7) l IV. GRID TESTING AND CODE VALIDATION Grd testng s mplemented usng several mesh szng and denstes to guarantee a grd ndependent soluton. Ar s used as a grd testng flud wth four dfferent grds szes of 30,5 cells, 5,050 cells, 94,050 cells, and 04,800 cells are selected to 4

4 compare ther local Nusselt numbers wth the RNG k ε turbulence model. Fg. represents varous local Nusset numbers of dfferent grd szes. The results revealed that after 94,050 cells, the dfference between results s less than 4%. Therefore, mentoned grd sze s chosen whch separate the results dependence from grd sze. Fg. Effect of grd sze on local Nusselt number at Re=9000 Fg. 3 shows the accuracy of the selected grd sze. The devaton of ths study and referred study s slghtly ncreased wth the rase of Reynolds number. However, ths percentage of devaton s less than 5% whch can be evdenced that the results of the foregong grd sze are n accordance wth Smth and Pongjet study []. Fg. 4 Average Nusselt number of SO, =4% and dp=0nm Average Nusselt numbers and skn frcton coeffcents of lamnar forced convecton and unsteady flow for SO wth 4% nanopartcle concentraton and 0nm nanopartcle dameter n four dfferent tme (τ=,5,0,0) and Reynolds number of 400 n a grooved channel s llumnated n Fg Steady state flow s the tme that all dervatves of tme are totally dsappeared and no change observed wth changng the tme at a specfc pont. Accordng to such a defnton, the result ndcates that the average Nusselt number and skn frcton coeffcent are ndependent and slghtly vared snce τ=0. Furthermore, the velocty profle at mddle of the rb 4 and groove 5 are shown n Fg. 6(rb 4 and groove 5 s chosen to effects of rb and groove channel totally reflected to the workng flud). A huge varaton s seen when the τ vared from to 5 whch ths alteraton was seen for average Nusselt number and skn frcton coeffcent that ths change decreased as τ change from 5 to 0 whch proves the unsteady condton for workng flud. Eventually, ndependence of the velocty profle from tme varaton s seen for both rb and groove snce τ=0. So, ths tme can be called quas steady state that the flud propertes almost do not change over tme. Accordng to such a noton, quas steady state pont can be mplemented to further nvestgaton. Fg. 3 Valdaton of local Nusselt numbers at dfferent Reynolds number V. RESULTS AND DISCUSSION The unsteady flow smulaton s done for SO nanopartcle and nanopartcle concentraton of % to 4% and nanopartcle dameter vared from 0nm to 50nm. Water used as a base flud for Nanoflud mxture n a Reynolds number of 400. Fg. 5 Average skn frcton coeffcent of SO -water wth =4% and dp=0nm 5

5 Fg. 6 Dfferent tmes of velocty profle of groove 5 for SO -water wth =4% and dp=0nm rb 4 groove 5 Fg.7 depcts dfferent nanopartcle dameters vared from 0nm to 50nm for SO -water Nanoflud and ts effects on velocty profle of rb 4 and groove 5 at Reynolds number of 400. It would be emnent that velocty profle shapes for all nanopartcle dameters are smlar. It means that there s no recrculaton or vortex s produced by changng nanopartcle dameter However, velocty ncreases wth decreasng nanopartcle dameter. Moreover, a fluctuaton on groove velocty profle s observed due to the reversed flow havng produced on groove channel whch strongly affect on velocty profle. The results reveal that nanopartcle dameter of 0nm provdes more velocty than other nanopartcle dameters n both rb and groove sectons. Average Nusselt number of SO -water Nanoflud for nanopartcle dameter vared from 0nm to 50nm at nanopartcle concentraton of 4% and Reynolds number of 400 n a grooved channel s shown n Fg. 8.a. Obvously, Nusselt number decrease wth ncreasng nanopartcle dameter. A sgnfcant reason of such a Nusselt number reducton s due to the velocty reducton havng mentoned before. A part from that, thermal conductvty of Fg. 7 Effect of Dfferent nanopartcle dameters on velocty profle for SO -water wth =4% rb 4 groove 5 the Nanoflud mxture plays a sgnfcant role on heat transfer enhancement. In ths case, hgher thermal conductvty s provded by stronger Brownnan moton at smaller nanopartcle dameters [5]. Fg. 8.b llumnates average skn frcton coeffcent of the SO -water nanoflud at the same condton as Nusselt number. The fgure shows effectveness of the skn frcton coeffcent wth nanopartcle dameters that average skn frcton coeffcent ncrease wth decreasng nanopartcle dameter due to the ncreasng shear stress over the test secton by ncreasng nanopartcle dameter. Fg. 9 ndcates the effects of nanopartcle concentratons on velocty profle for SO -water nanoflud vared from 0% (pure water) to 4% at nanopartcle dameter of 0nm n a grooved channel. Accordng to the no changes on the velocty profle appearance s seen by changng the volume fracton; so, no dfference exsts on streamlnes of the workng flud flow. However, the velocty ncreases wth ncreasng nanopartcle concentraton. Hghest velocty s acheved at 6

6 Fg. 9 Effects volume fractons on velocty profle for SO - water wth =4% rb 4 groove 5 Fg. 8 Average Nusselt number Average skn frcton coeffcent of SO,for dfferent nanopartcle dameters wth =4% volume fracton of 4% for both rb and groove velocty profles. Varety volume fracton affect on average Nusselt number and skn frcton coeffcent at fxed Reynolds number havng shown n Fg It would be obvous that ncreasng volume fracton caused to heat transfer enhancement and hgher average skn frcton coeffcent. A man reason of such an augmentaton on heat transfer s that hgher volume fracton provdes hgher velocty whch strongly affect on heat transfer enhancement. Furthermore, hgher volume fracton has hgher dynamc and statc thermal conductvtes whch n turn ncrease average Nusselt number. Fg. 0 Average Nusselt number Average skn frcton coeffcent of SO, for dfferent nanopartcle volume fracton at dp=4% 7

7 VI. CONCLUSION Unsteady Lamnar Convecton Flow Over Perodc Grooves By Usng So -Water Nanoflud In the present nvestgaton, a numercal smulaton of -dmensonal unsteady lamnar forced convecton flow over perodc grooves n a horzontal channel heated by a unform heat flux on grooved wall and nsulated upper wall was conducted at B/H=0.75. Second order upwnd method was chosen to equatons dscretzaton. Quas steady pont was obtaned at τ=0. Varetes SO nanopartcles characterstcs wth water as base flud were chosen and compared wth pure water to dentfy the approprate nanopartcle characterstcs at τ=0. Snce skn frcton frcton coeffcent was reported for all nanopartcles characterstcs of SO. Eventually, the 4% volume fracton and 0nm nanopartcle dameter provded hghest heat transfer enhancement and skn frcton coeffcent n unsteady lamnar forced convecton flow. REFERENCES [] Ankt Kumar, A.K.D., Effect of a crcular cylnder on separated forced convecton at a backward-facng step. Internatonal Journal of Thermal Scences,Vol. 5, p. 9, 0. [] S.Eamsa-ard,P.Promvonge, Numercal study on heat transfer of turbulent channel flow over perodc grooves. Internatonal Communcatons n Heat and Mass Transfer, 35, pp , 008. [3] T.Adacha, Y.Tashroa, H.Armab, Y.Ikegam(009), Pressure drop characterstcs of flow n a symmetrc channel wth perodcally expanded grooves, Chemcal Engneerng Scence, vol.64, pp , 009. [4] T.Adach, H.Uehara, Correlaton between heat transfer and pressure drop n channels wth perodcally grooved parts, Internatonal Journal of Heat and Mass Transfer, vol. 44, 00. [5] S.Eamsa-ard, P.Promvonge, Thermal characterstcs of turbulent rb-grooved channel flows, Internatonal Communcatons n Heat and Mass Transfer, vol. 36, pp , 009. [6] J R. Kamal,A.R. Bnesh, The mportance of rb shape effects on the local heat transfer and flow frcton characterstcs of square ducts wth rbbed nternal surfaces, Internatonal Communcatons n Heat and Mass Transfer, vol. 35, pp , 008. [7] H.Shokouhmand,K.Vahdkhah, M.A.Esmael, Numercal Analyss of Ar Flow and Conjugated Heat Transfer n Internally Grooved Parallel- Plate Channels, World Academy of Scence, Engneerng and Technology, vol. 73, 0. [8] M.Grener, F,Fscher,M.Tufo, Two-Dmensonal Smulatons of Enhanced Heat Transfer n an Intermttently Grooved Channel, Journal of Heat Transfer, Vol. 4, June 00. [9] M C. Herman, E. Kang, Comparatve evaluaton of three heat transfer enhancement strateges n a grooved channel, Heat and Mass Transfer, vol. 37, pp , 00. [0] L.Ortz, A. Hernandez-Guerrero, C. Rubo-Arana, R. Romero-Mendez, Heat transfer enhancement n a horzontal channel by the addton of curved deflectors, Internatonal Journal of Heat and Mass Transfer, vol. 5, pp , 008. [] Oronzo Manca, S.N., Danele Rcc, A numercal study of nanoflud forced convecton n rbbed channels. Appled Thermal Engneerng,vol. 37, pp. 80-9, 0. [] A.A. Al-aswad, H.A.M., N.H. Shuab, Antono Campo, Lamnar forced convecton flow over a backward facng step usng nanofluds. Internatonal Communcatons n Heat and Mass Transfer, vol 37, 00. [3] Héctor Barros-Pna, Stéphane Vazzo, Claude Rey, A numercal study of lamnar and transtonal mxed convecton flow over a backward-facng step, J Computers & Fluds, vol 56,pp. 77 9, 0. [4] S A.Sh. Kherbeet, H.A.M., B.H. Salman, The effect of nanofluds flow on mxed convecton heat transfer over mcroscale backward-facng step. Internatonal Journal of Heat and Mass Transfer, 0. [5] H.R Seyf, M.Fezbakhsh, Computatonal Analyss of Nanoflud Effects on Convectve Heat Transfer Enhancement of Mcro-Pn-Fn Heat snks, Internatonal Journal of Thermal Scences, vol,58,0,pp