A Numerical Study on Mixed Convection of Water Based Cuo Nanofluids in A Lid-Driven Square Enclosure: Effects of Viscosity Models

Transcription

1 Proceeding o the nd World Congre on Mechanical, Chemical, and Material Engineering (MCM'16 Budapet, Hungary Augut 3, 016 Paper No. HTFF 117 DOI: /ht A Numerical Study on Mixed Convection o Water Baed Cuo Nanoluid in A Lid-Driven Square Encloure: Eect o Vicoity Model Kamil Kahveci 1, Eli Büyük Öğüt 1 Mechanical Engineering Department, Trakya Univerity, 180 Edirne / Turkey kamilk@trakya.edu.tr Vocational School o Gebze, Kocaeli Univerity, Hereke-Kocaeli / Turkey eli.ogut@kocaeli.edu.tr Abtract Eect o variou vicoity model on mixed convection o water-baed CuO nanoluid in a lid-driven quare encloure with a contant heat lux heater were invetigated numerically in thi tudy. The computational reult were obtained or the heater length o The Graho number wa kept at a contant value o 104, and the Reynold number wa varied o that the Richardon number take value in the range o 0.1 to 10. Three dierent nanoparticle volume raction were taken: 0%, 5% and 10%. Reult how that a little increae in circulation intenity or orced convection dominant low regime and a decreae or natural convection dominant regime are een when Pak and Cho vicoity model i ued intead o Eintein vicoity model a a reult o increae in vicoity. Reult alo how that the centre o circulation move upward when the Pak and Cho vicoity model i ued intead o Eintein vicoity model. Finally, Reult how that the Eintein model give the highet average Nuelt number while the Pak and Cho yield the lowet average Nuelt number. Dierence in the average Nuelt number o Eintein, Brinkman and Batchlor model are in inigniicant level. Percentage dierence in the average Nuelt number o Pak and Cho model and other model increae with an increae in olid volume raction except or the Maiga model. Percentage dierence between the average Nuelt number o Pak and Cho model and Maiga model how a decreae with the olid volume raction. Keyword: Mixed convection, quare encloure, nanoluid, heat ource, vicoity model. 1. Introduction Low thermal conductivity o conventional heat traner luid uch a water, oil and ethylene glycol i a primary limitation in enhancing the perormance and the compactne o many device in indutrial application. Thi limitation ha been overcome by the introduction o nanoluid, which are the luid with upended olid particle o high thermal conductivity. The tudie how that nanoluid have ubtantially larger thermal conductivitie than thoe o conventional luid [1]. The mechanim behind thi anomalou increae in thermal conductivity are: Brownian motion o the nanoparticle, molecular liquid layering at the nanoparticle interace, the nature o heat traner, and nanoparticle clutering []. According to Keblinki et al. [], Brownian motion ha a negligible eect on thermal perormance while liquid layering ha a coniderable eect. A there i no olid theory to etimate the thermal conductivity o nanoluid, model propoed or two-phae mixture [3] are ued. However, thee model do not predict the thermal conductivity o nanoluid accurately. The experimental reult how that the thermal conductivitie o nanoluid are much higher than the prediction o thee model. Yu and Choi [4] propoed an alternative thermal conductivity model or nanoluid by conidering the eect o liquid layering around the nanoparticle. Yu and Choi [4] compared their model reult with the exiting experimental reult in literature and ound a good agreement. Yu and Choi [4] model i epecially eective or the nanoparticle with a diameter le than 10 nm. Yu Choi model ha been ued in thi tudy or the prediction o thermal conductivity o nanoluid. There are a number o tudie in the literature on mixed convection heat traner o nanoluid. Abu-Nada and Chamka [5] perormed a numerical tudy on mixed convection low in a lid-driven inclined quare encloure illed with a nanoluid. Their reult how that average Nu number increae igniicantly with an increae in the inclination angle and particle volume raction. Mahmoodi [6] perormed a tudy on mixed convection low and heat traner in a lid-driven encloure illed with a nanoluid. The reult o thi tudy how that the average Nuelt number or the tall encloure i higher than thoe o the hallow encloure. Elhari et al. [7] tudied mixed convection heat traner or nanoluid in a lid-driven hallow HTFF 117-1

2 rectangular encloure uniormly heated and cooled rom the vertical wall. They concluded that the addition o Cunanoparticle into the pure water lead to an enhancement or a degradation in heat traner depending on the value o Re and Ri. Keayati [8] tudied mixed convection o non-newtonian nanoluid in a lid-driven encloure with a inuoidal temperature proile and concluded that the all o the power law index decline heat traner and addition o nanoparticle augment heat traner or tudied parameter. Kahveci and Öğüt [9] perormed a numerical invetigation on mixed convection heat traner and luid low in a lid-driven quare encloure heated with a contant heat lux heater. Their reult how that the preence o nanoparticle in the bae luid caue a igniicant enhancement in heat traner and heat traner rate increae coniderably with a decreae in the Richardon number and the length o the heater. Shahi et al. [10] conducted a numerical invetigation o mixed convection low through a copper water nanoluid in a quare cavity with inlet and outlet port. The reult indicate that increae in olid concentration lead to an increae in the average Nuelt number at the heat ource urace and decreae in the average bulk temperature. Moumni and Sediki [11] worked on mixed convection o nanoluid in a ventilated quare encloure including two heat ource and ound that adding nanoparticle to bae luid and increaing both Re and Ri number enhance heat traner rate. Chamkha and Abu-Nada [1] perormed a numerical invetigation on teady laminar mixed convection low in a quare cavitie illed with a nanoluid. Two vicoity model were ued to approximate nanoluid vicoity: the Brinkman model and the Pak and Cho correlation. Their reult how that the percent increae in the average Nuelt number uing the Pak and Cho correlation i igniicantly higher than thoe correponding to the Brinkman model or all value o nanoparticle volume raction or a double-lid driven encloure. From the above literature, it can be concluded that there are not enough tudie on the eect o dierent vicoity model on mixed convection o nanoluid in an encloure. Thereore, thi tudy aim to invetigate the eect o vicoity model on mixed convection o nanoluid inide a quare encloure heated with a uniorm heat lux.. Analyi The geometry and the coordinate ytem ued in the analyi are hown in Fig. 1. The top wall o the encloure move rom let to the right with a contant velocity. A heater i attached to the bottom wall o the encloure. Temperature o the moving wall i contant and the other wall are adiabatic. The nanoluid in the encloure wa aumed to be Newtonian, incompreible, and laminar and to have contant thermo-phyical propertie except or the denity. The bae luid and nanoparticle were aumed to be in thermal equilibrium. Under thee aumption, dimenionle governing equation in vorticity-tream unction ormulation take the ollowing orm: (1 x y 1 e 1 Gr u v x y n, o Re x y n, o Re x n u v x y 1 Re Pr x y ( (3 where, α, and i the denity, vicoity, thermal expanion coeicient, thermal diuivity, and nanoparticle volume raction, repectively. u and v are the dimenionle velocity component in the x and y direction, repectively. i the dimenionle temperature. The ubcript n,, and tand or the nanoluid, luid, and olid, repectively. and are the dimenionle tream unction and vorticity deined a: The Reynold, Prandtl, and Graho number are deined a: v u u, v, (4 y x x y HTFF 117-

3 3 U L,0, Re, Pr, 0 g L T Gr,0, (5 where L i the length o the quare encloure, g i the gravitational acceleration, and T i the temperature. The dimenionle variable ued in the nondimenionalization o the governing equation are: * x * y * u * v * p x, y, u, v, p, L L U U, 0 U * T - T T C q L T k (6, where U i the velocity o the cold top wall, k i the thermal conductivity, and q i the heat lux. The ubcript c tand or the cold wall. Governing equation are ubjected to the ollowing boundary condition: =0, u =1, v = 0 at y=1 (7 θ/ y =0 at y=0 and 0 x < (a ε/ (8 θ/ y = k /k n at y=0 and (a ε/ x (a + ε/ (9 θ/ y =0 at y=0 and (a + ε/< x 1, (10 u = v = 0 at y=0 (11 where a * i the ditance o the heater midpoint rom the vertical wall. ε i the dimenionle length o the heater deined a ε = w/l and a i the dimenionle ditance o the heater midpoint deined a a = a * /L. Fig. 1: Geometry and the coordinate ytem. Nanoluid vicoity i one o the mot important actor in convective heat traner becaue it ha an important eect on low and heat traner. Several vicoity ormulation baed on nanoparticle volume raction een in Table 1 were ued in thi tudy to reveal the eect o thee model on the low and heat traner. HTFF 117-3

4 Table 1: Vicoity model. Model Eective vicoity Eintein ( 1.5 Brinkman. 5 e e / 1 Batchlor ( Maiga ( Pak and Cho ( The thermal conductivity model propoed by Yu and Choi [13] wa ued in thi tudy to predict the nanoluid thermal conductivity. e e e k k e k k k k 3 k k 1 3 k k 1 (1 where i the ratio o the liquid layering thickne to the original particle radiu. The other thermo-phyical propertie o nanoluid are deined : ( (13 n, o 1, o, o ( c p n 1 (14 n c p c p ( 1 (15 where c p i the peciic heat. The local heat traner coeicient i deined a: h x q (16 T ( x T ( c where h x i the local heat traner coeicient. The local and average Nuelt number or the heated wall can be deined a ollow: hxl 1 Nu (17 k ( x a / ( x where (x i the dimenionle local temperature o the heated wall. a / 1 1 Nu a dx (18 3. Reult and Dicuion The olution o governing equation were obtained by Comol Multiphyic inite element modelling and imulation otware. The thermo-phyical propertie o the bae luid and olid particle (CuO ued in thi tudy are hown in Table. The Graho number wa kept contant with a value o 10 4, and the Reynold number wa varied uch that the Richardon number get value in the range The Richardon number i deined a Ri=Gr/Re and repreent the relative HTFF 117-4

5 importance o buoyancy orce with repect to the hear orce. Three dierent nanoparticle volume raction were conidered in thi tudy: 0, 5, and 10 and the ratio o the liquid layering to the original particle radiu, wa taken a 0.1. Table : Thermo-phyical propertie o the bae luid and nanoparticle. Property Water CuO (kg/m c p (j/kg K k (W/m K x10 7 (m / (K Streamline and iotherm inide the encloure are hown in Figure or the Eintein vicoity model. A it can be oberved rom Figure, a clockwie rotating circulation cell orm the low ield or all value o the Richardon number by the eect o lid moving rom let to right. Circulation centre i in the upper part o the encloure a a reult o the higher hear orce in the upper part o encloure. With an increae in the Richardon number, circulation centre move upward becaue o the increae in the buoyancy orce. Variation in the circulation intenity with an increae in the nanoparticle volume raction eem to be inigniicant becaue o the counter-eect o the increaed thermal conductivity and vicoity. An increae in the olid particle volume raction increae the thermal conductivity and vicoity. An increae in the thermal conductivity ha a poitive eect on the circulation intenity. On the other hand, an increae in the vicoity ha a negative eect on the circulation intenity. A a reult, change in circulation intenity remain in inigniicant level. Becaue o the clockwie rotating low, iotherm along the heater are more compreed on the right ide o the encloure, and they become more eparated a the luid particle are heated during their journey toward let. Temperature alo take higher value toward the let ide wall o the encloure due to the clockwie rotating circulation. With an increae in the olid volume raction, the lope o iotherm inide the encloure decreae becaue o the increaing energy tranport rom the hot wall to the nanoluid due to the higher thermal conductivity. The treamline and iotherm inide the encloure are hown in Figure or the Pak and Cho vicoity model. Pak and Cho vicoity model produce highet vicoity prediction or nanoluid vicoity. Thereore, an increae in circulation intenity or orced convection dominant low regime and a decreae or natural convection dominant regime are een when thi model i ued. The circulation centre move upward a a reult o increae in the hear orce with the increae in the vicoity. A a reult o circulation centre cloer to the top wall or low value o Richardon number and low circulation intenity or the high value o the Richardon number, iotherm along the heater are more eparated in the vertical direction. The variation o the average Nuelt number i hown in Table 3 or the vicoity model conidered in thi tudy. It can be concluded rom Table 3 that the Eintein model give the highet average Nuelt number and the Pak and Cho yield the lowet average Nuelt number. On the other hand, dierence between the reult o Eintein, Brinkman and Batchlor model are in inigniicant level. Percentage dierence in the average Nuelt number o the Pak and Cho model and other model increae with an increae in the olid volume raction except or the Maiga model. Percentage dierence in the average Nuelt number o the Maiga model and Pak and Cho model how a decreae with the olid volume raction. HTFF 117-5

6 =0.0 =0.10 a Ri=0.1 =0.0 =0.10 b Ri= 1 =0.0 =0.10 c Ri= 10 Fig. 3: Streamline and iotherm or the Eintein model or a Ri=0.1, b Ri=1, c Ri=10. HTFF 117-6

7 =0.0 =0.10 a Ri=0.1 =0.0 =0.10 b Ri= 1 =0.0 =0.10 c Ri= 10 Fig. 4: Streamline and iotherm or the Pak and Cho model or a Ri=0.1, b Ri=1, c Ri=10. Table 3: Variation o the average Nuelt number or dierent vicoity model. Ri M1 Eintein M Brinkman M3 Batchlor M4 Maiga M5 Pak and Cho HTFF 117-7

8 4. Concluion In thi tudy, eect o variou vicoity model on mixed convection heat traner and luid low in a lid driven quare encloure with a contant heat lux heater ha been invetigated numerically. The concluding remark are a ollow: An increae or orced convection dominant low regime and a decreae or natural convection dominant regime are een in the circulation intenity when the Pak and Cho vicoity model i ued intead o the Eintein vicoity model. Circulation centre get cloer to the top wall when the Pak and Cho vicoity model i ued intead o the Eintein model. The Eintein model give the highet average Nuelt number while the Pak and Cho yield the lowet average Nuelt number. The circulation centre move upward when the Pak and Cho vicoity model i ued intead o Eintein vicoity model. Dierence in the average Nuelt number o the Eintein, Brinkman and Batchlor model are in inigniicant level. Percentage dierence in the average Nuelt number o the Pak and Cho model and other model increae with an increae in olid volume raction except or the Maiga model. Percentage dierence between the average Nuelt number o the Maiga model and Pak and Cho model how a decreae with the olid volume raction. Reerence [1] J. A. Eatman, S. U. S. Choi, S. Li, W. Yu, and L. J. Thompon, Anomalouly increaed eective thermal conductivitie o Ethylene glycol-baed nanoluid containing copper nanoparticle, Applied Phyic Letter, vol. 78, pp , 001. [] P. Keblinki, S. R. Phillpot, S. U. S. Choi, and J. A. Eatman, Mechanim o heat low in upenion o nano-ized particle (nanoluid, International Journal o Heat and Ma Traner, vol. 45, pp , 00. [3] R. L. Hamilton and O. K. Croer, Thermal conductivity o heterogeneou two-component ytem, I & EC Fundamental, vol. 1, pp , 196. [4] W. Yu and S. U. S. Choi, The role o interacial layer in the enhanced thermal conductivity o nanoluid: a renovated Maxwell model, Journal o Nanoparticle Reearch, vol. 5, pp , 003. [5] E. Abu-Nada and A. J. Chamkha, Mixed convection low in a lid-driven inclined quare encloure illed with a nanoluid, European Journal o Mechanic B/Fluid, vol. 9, pp , 010. [6] M. Mahmoodi, Mixed convection inide nanoluid illed rectangular encloure with moving bottom wall, Thermal Science, vol. 15, no. 3, pp , 011. [7] H. Elhari, M. Naimi, M. Lamaadi, A. Raji, and M. Hanaoui, Mixed convection heat traner or nanoluid in a liddriven hallow rectangular cavity uniormly heated and cooled rom the vertical ide: the cooperative cae, ISRN Thermodynamic, vol. 01, pp. 1-16, 01. [8] G. H. R. Keayati, Mixed convection o non-newtonian nanoluid low in a lid-driven encloure with inuoidal temperature proile uing FDLBM, Powder Technology, vol. 66, pp , 014. [9] K. Kahveci and E.B. Öğüt, Mixed convection o water-baed nanoluid in a lid-driven quare encloure with a heat ource, Heat Traner Reearch, vol. 4, no. 8, pp , 011. [10] M. Shahi, A. H. Mahmoudi, and F. Talebi, Numerical tudy o mixed convective cooling in a quare cavity ventilated and partially heated rom the below utilizing nanoluid, International Communication in Heat and Ma Traner, vol. 37, no., pp , 010. [11] H. Moumni and E. Sediki, Enhanced mixed convection and heat traner by nanoluid in ventilated quare encloure including two heat ource, Computational Thermal Science: An Internatinal Journal, vol. 7, no. 1, pp , 015. [1] A. J. Chamkhaa and E. Abu-Nada, Mixed convection low in ingle- and double-lid driven quare cavitie illed with water Al O 3 nanoluid: eect o vicoity model, European Journal o Mechanic B/Fluid, vol. 36, pp. 8-96, 01. [13] W. Yu and S. U. S. Choi, The role o interacial layer in the enhanced thermal conductivity o nanoluid: a renovated Maxwell model, Journal o Nanoparticle Reearch, vol. 5, pp , 003. HTFF 117-8