C. Uysal 1, K. Arslan 2 and H. Kurt 3

Transcription

1 Journa of ied Fuid Mechanics, Vo., No.,. -0, 09. vaiabe onine at ISSN , EISSN DOI: 0.95/jafm Laminar Forced Convection and Entroy Generation of ZnO-Ethyene Gyco Nanofuid Fow through Square Microchanne with using Two-Phase Euerian-Euerian Mode C. Uysa, K. rsan and H. Kurt 3 utomotive Technoogies Program, TOBB Vocationa Schoo of Technica Sciences, Karabuk University, Karabuk, 78050, Turkey Mechanica Engineering Deartment, Facuty of Engineering, Karabuk University, Karabuk, 78050, Turkey 3 Mechanica Engineering Deartment, Facuty of Engineering and rchitecture, Necmettin Erbakan University, Konya, 440, Turkey Corresonding uthor Emai: cuneytuysa@karabuk.edu.tr (ceived December 30, 07; acceted Juy 8, 08) BSTRCT In this aer, convective heat transfer and entroy generation of ZnO- nanofuid fow through a square microchanne are numericay investigated. Fow is modeed by using Euerian-Euerian two hase fow mode. Nanoartice voume fraction of ZnO- nanofuid ranged between %.0 and %4.0. s a resut, it is found that the convective heat transfer coefficient of fow increased from W/m K to W/m K when 4.0% ZnO nanoartice addition to ure at =00. Tota entroy generation of ZnO- nanofuid decreases with increase in nanoartice voume fraction of ZnO- nanofuid. It is aso observed that the Bejan number decreases with increase in nanoartice voume fraction of ZnO- nanofuid. Keywords: Entroy generation; Ethyene gyco; Euerian; Microchanne; Nanofuid; Two-hase. NOMENCLTURE area coefficient defined in Eqs. 3 B coefficient defined in Eqs. Be Bejan number Cd drag coefficient CP secific heat d artice diameter div divergence Dh hydrauic diameter f darcy friction factor F force grad gradient G artice-artice interaction moduus h convective heat transfer coefficient k conductive heat transfer coefficient L ength m mass fow rate Nu Nusset number P ressure Pr Prandt number heat fux ynods number q" entroy generation rate er unit ength T temerature veocity vector friction factor coefficient defined in Eqs. dynamic viscosity density S' gen V voumetric fraction shear stress coefficient defined in Eqs. 4

2 C. Uysa et a. / JFM, Vo., No.,. -0, 09.. INTRODUCTION Therma management techniques rovide better heating and cooing technoogy and high efficient therma systems are very imortant for energy saving and efficiency. One of these techniques is the imroving thermohysica roerties of heat transfer fuids. The searches for this reason finay reveaed nanofuids. Nanofuid is a susension obtained with disersion of nano-sized metaic or non-metaic soid artices into conventiona working iquids such as water, ethyene gyco or oi. The nanofuid term is firsty introduced by Choi in 995. In the ast decade, many researches have numericay and exerimentay investigated the convective heat transfer and fuid fow characteristics of nanofuids. In numerica anaysis, the nanofuids fows are modeed as singe-hase fow generay. This is because of that nanoartices disersed to base fuid has smaer diameter than 00 nm. However, some aers showed that the resuts obtained for nanofuid fows modeed using two-hase mode are in better agreement with exerimenta data comared to that of singe-hase mode. Behzadmehr et a. (007) modeed the turbuent convective heat transfer of Cu-water nanofuid fow through a circuar tube using two-hase mixture mode. They reorted that two-hase mixture mode is more recise than that of singe-hase mode. Kumar and Puranik (07) aso reorted that Lagrangian-Euerian two-hase modeing of turbuent forced convection of water based O3, TiO and Cu nanofuids gives more accurate resuts comared to that of singe hase modeing for nanoartice voume fractions smaer than 0.5%. For higher nanoartice voume fractions, it is on the contrary. Moraveji and rdehai (03) comared the singe-hase mode with voume of fuid, mixture and Euerian two-hase modes for aminar forced convection of O3-water nanofuid fow through minichanne heat sink. They reorted that two-hase modes are more recise by comarison with exerimenta reference data than singe-hase data. Kateh et a. (0) numericay investigated aminar forced convection of Cu-water nanofuid fow through isothermay heated microchanne by using Euerian-Euerian two-hase modeing. It is found that reative veocity and temerature between hases is negigibe. In addition, the obtained resuts for convective heat transfer enhancement with two-hase modeing are higher comared to that of singe-hase and convective heat transfer enhancement increases with decrease in nanoartice diameter. Mahdavi et a. (05) searatey aied the discrete hase mode in the Lagrangian aroach and mixture mode in the Euerian aroach to water based O3, SiO and ZrO nanofuid fows through vertica tube under aminar fow conditions. s a resut, they recommended the discrete hase mode due to its strength and simicity. Moreover, the ressure oss resuts obtained for nanoartice voume fractions ess than 3% is more reiabe in the discrete hase mode. Siavashi and Jamai (06) investigated the turbuent convective heat transfer and entroy generation of TiO-water nanofuid fow through annui for different radius ratios with same cross sectiona area. The fow was modeed with mixture two-hase mode. They exressed that radius ratio has an imortant effect on entroy generation rate and there is an otima ynods number to minimize entroy generation rate. Contrary to iterature mentioned above, some studies reorted that the resuts obtained for singe-hase is more recise than that of two-hase or that singe and two-hase modes shows simiar redictions. Moraveji and Esmaeii (0) studied aminar forced convection heat transfer of O3-water nanofuid through a circuar tube under constant heat fux with using singe and two-hase modes. They reorted that singe and two-hase modes give quite simiar resuts. kbari et a. (0) comared six different combination of viscosity and therma conductivity for singe-hase modeing of turbuent forced convection of O3- water nanofuid and then determined the most aroriate mode with exerimenta resuts within them. Moreover, same robem is modeed as twohase fow with voume of fuid, mixture and Euerian modes. It is reorted that seected singe-hase mode is more aroriate comared to two-hase modes for their study conditions. Behroyan et a. (05) comared five different modes, which are Newtonian and non-newtonian singe-hase modes and mixture, Euerian-Euerian, Euerian-Lagrangian modes, for turbuent forced convection of Cu-water nanofuid fow. s a resut, they recommended Newtonian singe-hase and Euerian-Lagrangian two-hase modes due to their recise resuts. Farzaneh et a. (06) used constructa theory to investigate the using of microchannes with/without oos for cooing rocess of a square eectronic comonent with interna heat generation. They aimed reducing the therma resistance in their study. They reorted that the maximum dimensioness temerature is reduced by 0% and 0%, whie the maximum dimensioness ressure dro is decreased by 5% and 33% for one and two branch reverting microchannes, in comarison with the case without a branch. Ramiar et a. (0) numericay soved conjugate heat transfer robem for a mixture fow of 60% ethyene gyco and 40% water in mass containing O3 nanoartices in two dimensiona microchanne. They reorted that using soid regions with higher therma conductivities enhance heat transfer by increasing Nusset number and amify axia conduction effect. Farzaneh et a. (07) studied the effect of reverting microchannes inside a heat sink having circuar, square and trianguar configurations for geometrica otimization. They founded that square geometry has the east therma resistance. In this study, aminar forced convection and entroy generation of ZnO- nanofuid fow having different nanoartice voume fractions through a square microchanne are numericay investigated. The fow is modeed with Euerian-Euerian twohase mode. The resuts such as convective heat transfer coefficient, Nusset number, ressure dro, Darcy friction factor and entroy generation for different nanoartice voume fraction of ZnO- nanofuid are resented and comared.

3 C. Uysa et a. / JFM, Vo., No.,. -0, 09.. MODEL CONFIGURTION. Geometrica Configuration Convective heat transfer characteristics and entroy generation of ZnO- nanofuid through a square microchanne are numericay investigated. The fow is modeed as Euerian-Euerian two hase mode. The hydrauic diameter of microchanne is assumed to be Dh= 50. This means that dimension of each side of microchanne crosssection is 50 m. The microchanne ength is assumed to be 50 mm. The schematic diagram of microchanne investigated in this study is iustrated in Figure. m ( C,TV ) keff,t h v(t T ) (5) ( C,TV ) keff,t h (T T ) v (6) the subscrits and denote iquid and artice hases, resectivey. In these equations, the foowing reation is vaid. (7) is the voumetric fraction of iquid or artice hases. The momentum equations are incuding drag force ( F ), virtua mass force ( F ) and coision force ( d F co the hases is exressed as foows: vm ). The drag force between F (V V ) (8) d is friction coefficient. For two-hase fows with >0.8, is cacuated by foowing reation: 3 ( ) C V V (9) 4 d.65 d Fig.. Schematic diagram of microchanne considered in this study.. Governing Equations There are three different Euerian-Euerian mutihase, which are the voume of fuid mode, the mixture mode and the Euerian mode. The voume of fuid mode has not searate governing equations for soid and fuid hases. In addition, it is designed for two or more immiscibe fuids. The mixture and the Euerian modes have different governing equations for soid and fuid hases. In this study, Euerian mode is seected for anayses due to that it aows considering granuar temerature, soid-hase shear and buk viscosities. In Euerian-Euerian two-hase modeing; mass, momentum and energy equations are searatey written for each hases, whie the ressure is shared by a hases. The governing equations for artice and iquid hases can be written as foows (NSYS Fuent, 009): ( V ) 0 () ( V ) 0 () ( VV ) P V VT F F ( V V ) P d vm V V T F F F d vm co (3) (4) C d is the drag coefficient and is exressed with foowing equation (Schier and Naumann, 935): C d (0) is the artice ynods number and is cacuated by using foowing equation: V V d () and are density and dynamic viscosity, resectivey. d is artice diameter. Virtua mass force is reated with reative acceeration between two hases and is found by foowing equation: D Fvm 0.5 (V V ) () Dt Coision force is reated with artice-artice interaction and can be cacuated with foowing reation: F G( ) (3) co G is the artice-artice interaction moduus and is exressed with foowing reation: G.0ex (4) The h v term exressed in Equation 6 and 7 is the voumetric interhase convective heat transfer coefficient and is exressed for mono-disersed 3

4 C. Uysa et a. / JFM, Vo., No.,. -0, 09. sherica artices as foows (Kuiers et a., 99): h 6( ) v h (5) d h is the iquid-artice heat transfer coefficient and can be cacuated with foowing reation (Ranz and Marsha, 95): hd Nu. Pr (6) The k eff 0.6 / 3 k is the Prandt number of iquid hase. exressed in Equations 5 and 6 denotes the Pr effective therma conductivity coefficient of iquid and artice hases and is written as foows, resectivey (Kuiers et a., 99). k k k b, eff, (7) eff,, kb, b, (8) k ( ) k (9) b, k ( ) k (0) The coefficient is defined as foows: B( ) B B n B B B B (), and coefficient can be exressed for sherica artices as foows: B.5 B 0 / 9 k () (3) k (4).3 Heat Transfer and Fuid Fow ations The ynods number is defined as foows: ud h (5) The oca convective heat coefficient is exressed as foows: h x q" T T w T w m and T m (6) are wa and mean temeratures, resectivey. The mean temerature for two-hase fows can be cacuated by using foowing equation (Kateh et a., 0): T m i i i i,i i i i,i u C T d u C d (7) the integration is reaized on the crosssection of channe geometry. The oca Nusset number is defined as foows: Nu hd x h x (8) k The oca Darcy friction factor can be written as foows: 8 x fx u x (9) is shear stress of fow. The average vaues of convective heat transfer coefficient, Nusset number and Darcy friction factor are cacuated with foowing equations, resectivey. h hxd (30) Nu Nuxd (3) f f d x (3) For interna fow, the entroy generation er unit ength can be written as foows (Bejan, 98): S' q" D 8m f (33) 3 h gen,tota 5 ktb Nu Tb Dh In Eqs. 33, the first term on the right side exresses entroy generation er unit ength due to heat transfer and the second term exresses entroy generation er unit ength due to fuid friction. The Bejan number is formuated as foows: Be S' S' gen,heattransfer gen,heat transfer S' gen, fuid friction (34) and it is defined as the ratio of entroy generation due to heat transfer to tota entroy generation..4 Boundary Conditions constant heat fux of 000 W/m is aied to bottom surface of microchanne. The inet temerature and veocity distributions of both hases are assumed as uniform and both hases enter to channe same inet temerature and veocity. The inet temerature of both hases is assumed to be 300 K. The inet veocities of both hases are cacuated by secified ynods number ( =0-00) with Equation 5. The diameter of ZnO nanoartices is d =8 nm. In microchanne outet, ressure outet boundary condition is aied for both hases..5 Numerica Procedure The governing equations mentioned above for both 4

5 C. Uysa et a. / JFM, Vo., No.,. -0, 09. hases are discretized by using finite voume method in the view of boundary conditions. In the comutationa domain, a non-uniform grid is emoyed. In the region cose to microchanne was, finer grids are used. For the convective and diffusive terms the first order uwind method is used. For soving veocity-ressure couing, the Phase Coued SIMPLE (Semi Imicit Method for Pressure Linked Equations) method is used. The convergence criterion is seected to be 0-6 for this study..6 Grid Indeendency Test and Code Vaidation The grid indeendency test is erformed to avoid the effect of grid number on the resuts obtained with numerica rocedure. Six different grid numbers ranging from to are used. Same grid numbers are used for each asect ratio of rectanguar microchanne. The seection of otimum grid numbers is reaized by considering the change of resuts with grid numbers. The cacuations are reaized for the mode having seected otimum grid number. To vaidate the accuracy of the numerica mode, the resuts obtained by numerica comutation is comared with the numerica resuts for two-hase mode resented by Moraveji and rdehai (03) and with exerimenta resuts resented by Ho and Chen (03). The comarison of the resuts obtained by this study with the resuts resented in the iterature is shown in Figure. mode. The ynods number is in the range of 0 and 00. Constant heat fux of = 000 W/m is aied to the bottom surface of the microchannes. The veocity distributions of ZnO- nanofuid fow for different nanoartice voume fractions in the outet cross-section of square microchanne and atera section of inet region of square microchanne are shown in Figure 3 and 4, resectivey. (a) (b) q" (c) 0 8 Nu 6 (d) 4 Moraveji and rdehai (03) Ho and Chen (03) Present Study Fig.. Mesh accuracy test. The resuts obtained by this study show good agreement with the resuts resented by Moraveji and rdehai (03) and Ho and Chen (03). The average deviation between the resuts obtained by this study and Moraveji and rdehai (03) is.5%, whie it is 7.55% for the resuts resented by Ho and Chen (03). 3. RESULTS ND DISCUSSION The convective heat transfer characteristics and entroy generation of ZnO- nanofuid fow through a square microchanne are numericay investigated by using Euerian-Euerian two-hase (e) Fig. 3. Veocity distribution of outet section of square microchanne for different nanoartice voume fractions of ZnO- nanofuid (a) =0, (b) =.0%, (c) =.0%, (d) =3.0% and (e) =4.0%. The temerature distributions of ZnO- nanofuid fow for different nanoartice voume fractions in the outet cross-section and outet atera section of square microchanne are shown in Figure 5 and 6, resectivey. 5

6 C. Uysa et a. / JFM, Vo., No.,. -0, 09. (a) nanoartice voume fraction of ZnO- nanofuid and in the ynods number. The maximum convective heat transfer coefficient for this study is obtained to be W/m K at = 00 for ZnO- nanofuid having nanoartice voume fraction of 4.0%. Whereas, the convective heat transfer coefficient obtained for ure at = 00 is W/m K. The reason of increment in convective heat transfer coefficient with nanoartice addition is due to that the difference between wa and buk temeratures of nanofuid decreases with increase in nanoartice addition. (b) (a) (c) (b) (d) (c) (e) Fig. 4. Veocity distribution of atera section of inet region of square microchanne for different nanoartice voume fractions of ZnO- nanofuid (a) =0, (b) =.0%, (c) =.0%, (d) =3.0% and (e) =4.0%. s can be seen from Figure 5 and 6, wa temerature of ZnO- nanofuid decreases with increase in nanoartice voume fraction of ZnO- nanofuid. Moreover, it can be observed that increase in nanoartice voume fraction of ZnO- nanofuid causes to increase in buk temerature of ZnO- nanofuid. The variation of average convective heat transfer coefficient of ZnO- nanofuid fow with the ynods number is iustrated in Figure 7. s can be seen from Figure 7, the convective heat transfer coefficient increases with increase in (d) (e) Fig. 5. Temerature distribution of outet section of square microchanne for different nanoartice voume fractions of ZnO- nanofuid (a) =0, (b) =.0%, (c) =.0%, (d) =3.0% and (e) =4.0%. 6

7 C. Uysa et a. / JFM, Vo., No.,. -0, 09. nanofuid fow with the ynods number is shown in Figure 8. 6 (a) % ZnO- Nu 8 6 (b) (c) (d) 4 Fig. 8. Nusset number. The Nusset number of ZnO- nanofuid fow increases with increasing nanoartice voume fraction and the ynods number. The Nusset number is aready reated with the convective heat transfer coefficient. Therefore, simiar resuts are aso obtained for the Nusset number. t = 00, the Nusset number obtained for ZnO- nanofuid having nanoartice voume fraction of 4.0% is 3.7, whie it is 5.78 for ure. The variation of ressure dro of ZnO- nanofuid with the ynods number is iustrated in Figure 9. e+7 8e+6 4.0% ZnO- (e) Fig. 6. Temerature distribution of atera section of inet region of square microchanne for different nanoartice voume fractions of ZnO- nanofuid (a) (c) =0, (b) =.0%, =.0%, (d) =3.0% and (e) =4.0%. P [Pa] 6e+6 4e+6 e+6 h [W/m K] % ZnO- Fig. 7. Convective heat transfer coefficient. The variation of the Nusset number of ZnO- 0 Fig. 9. Pressure dro. It is ceary seen from Figure 9 that the ressure dro decreases with increase in nanoartice voume fraction of ZnO- nanofuid. The ressure dro obtained for ZnO- nanofuid having nanoartice voume fraction of 4.0% is 3.98% and 3.85 ower comared to that of ure at = 0 and = 00, resectivey. However, for same microchanne geometry, Uysa et a. (06) reorted that ZnO nanoartice addition of 4.0% to increases ressure dro 8.96% and 9.3% at =0 and =00, resectivey, in singe hase consideration. Suganthi et a. (04) showed that ZnO nanoartice addition to cause a reduction in viscosity due to that hydrogen bonding network of 7

8 f C. Uysa et a. / JFM, Vo., No.,. -0, 09. ethyene gyco is reorganized with ZnO nanoartice addition. It may be reason for decrease in ressure dro for two-hase aroach. The variation of Darcy friction factor of ZnO- nanofuid with the ynods number is iustrated in Figure 0. The Darcy friction factor of ZnO- nanofuid decreases with increasing nanoartice voume fraction of ZnO- nanofuid. This is due to that the ressure dro decreases with increase in nanoartice voume fraction of ZnO- nanofuid and the Darcy friction factor is directy reated with ressure dro. due to heat transfer vaues obtained for ure and ZnO- nanofuid having nanoartice voume fraction of 4.0% are W/mK and W/mK, resectivey. Whereas, entroy generation vaues due to heat transfer of W/mK and.74 0 W/mK are obtained for ure and 4.0% ZnO- nanofuid, at =00, resectivey. 7 7 The variation of entroy generation er unit ength due to fuid friction with the ynods number is shown in Figure f % ZnO- S' gen, fuid friction [W/mK] % ZnO- 0 Fig. 0. Darcy friction factor. The variation of entroy generation er unit ength due to heat transfer with the ynods number is shown in Figure. S' gen, heat transfer [W/mK].e-6.0e-6 8.0e-7 6.0e-7 4.0e-7 4.0% ZnO- Fig.. Entroy generation due to fuid friction. Entroy generation due to fuid friction increases with increase in the ynods number. In addition, it decreases with increase in nanoartice voume fraction of ZnO- nanofuid; this decrement is not significant. ZnO nanoartice of 4.0% addition to ure decreases the entroy generation due to fuid friction from W/mK to W/mK and from 0.5 W/mK to W/mK at = 0 and =00, resectivey. The variation of tota entroy generation er unit ength with the ynods number is iustrated in Figure e Fig.. Entroy generation due to heat transfer. s can be seen from Figure, entroy generation due to heat transfer decreases with increase in the ynods number. This decrement tendency decreases with increase in nanoartice voume fraction of ZnO- nanofuid. It is aso found that entroy generation due to heat transfer decreases with increase in nanoartice voume fraction of ZnO- nanofuid. t =0, entroy generation S' gen, tota [W/mK] % ZnO- Fig. 3. Tota entroy generation. 8

9 C. Uysa et a. / JFM, Vo., No.,. -0, 09. Same resuts with entroy generation due to fuid friction are obtained for tota entroy generation. This is due to that the obtained vaues for entroy generation due to heat transfer are negigibe comared to that of entroy generation due to fuid friction. The microchanne considered in this study has a micro-sized hydrauic diameter. This case causes to that entroy generation due to fuid friction is dominant. The variation of the Bejan number with the ynods number is shown in Figure 4. Be 5e-4 4e-4 3e-4 e-4 e-4 0 Fig. 4. Bejan number. 4.0% ZnO- s can be seen from Figure 4, Bejan number decreases with increase in ynods number and nanoartice voume fraction of ZnO- nanofuid. ZnO nanoartice addition to ure decreases the contribution of entroy generation due to heat transfer in the tota entroy generation. 4. CONCLUSION In this study, aminar forced convection and entroy generation of ZnO- nanofuid fow through square microchanne are numericay investigated. The fow is modeed by using Euerian-Euerian two-hase mode. suts showed that 4.0% ZnO nanoartice addition to ure causes to high increment of 87.36% at =0 and of 36.78% at =00 in convective heat transfer coefficient. Simiar high increments in convective heat transfer coefficient and in Nusset number are reorted by Moraveji and rdehai (03) for O3/water nanofuid fow. ZnO nanoartice addition to ure causes to decrease in wa temerature. This eads to increment in convective heat transfer coefficient and in Nusset number. This may be due to that nanoartices inside fow destroyed the boundary ayer. Entroy generation due to heat transfer decreases with increase in nanoartice voume fraction of ZnO- nanofuid, whie entroy generation due to fuid friction increases. For this study, entroy generation due to heat transfer can be negect when it is comared with entroy generation due to fuid friction. This is due to that microchanne considered in this study has sma hydrauic diameter. searchers and/or engineers shoud focus on fuid friction to decrease entroy generation for therma management of microchanne aications. REFERENCES kbari, M., N. Gaanis and. Behzadmehr (0). Comarative assessment of singe and twohase modes for numerica studies of nanofuid turbuent forced convection. Internationa Journa of Heat and Fuid Fow. 37, NSYS Fuent (009). NSYS Fuent.0 Theory Guide, NSYS Inc. Behroyan, I., P. Ganesan, S. He and S. Sivasankaran (05). Turbuent forced convection of Cu-water nanofuid: CFD mode comarison. Internationa Communications in Heat and Mass Transfer. 67, Behzadmehr,., M. Saffar-vva and N. Gaanis (007). Prediction of turbuent forced convection of a nanofuid in a tube with uniform heat fux using a two hase aroach. Internationa Journa of Heat and Fuid Fow. 8, -9. Bejan,. (98). Entroy Generation through Heat and Fuid Fow. John Wiey and Sons: New York. Choi, S. U. S. (995). Enhancing therma conductivity of fuids with nanoartices. SME FED. 3, Farzaneh, M., M. R. Saimour and M. R. Tavakoi (06). Design of bifurcating microchannes with/without oos for cooing of squareshaed eectronic comonents. ied Therma Engineering. 08, Farzaneh, M., M. R. Tavakoi and M. R. Saimour (07). Effect of reverting channes on heat transfer erformance of microchannes with different geometries. Journa of ied Fuid Mechanics 0, Ho, C. J. and W. C. Chen (03). n exerimenta study on therma erformance of O3/water nanofuid in a minichanne heat sink. ied Therma Engineering. 50, Kateh, M.,. bbassi, M. Saffar-vva and J. Harting (0). Euerian-Euerian two-hase numerica simuation of nanofuid aminar forced convection in a microchanne. Internationa Journa of Heat and Fuid Fow. 3, Kuiers, J., W. Prins and W. Van Swaaij (99). Numerica cacuation of wa-to-bed heattransfer coefficients in gas-fuidized beds. ICHE J. 38, Kumar, N. and B. P. Puranik (07). Numerica study of convective heat transfer with nanofuids in turbuent fow using a 9

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