Natural Convection of Water-Based CuO Nanofluid Between Concentric Cylinders

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1 Natural Convection o Water-Baed CuO Nanoluid Between Concentric Cylinder SEMİHA ÖZTUNA KAMİL KAHVECİ BAHA TULU TANJU Mechanical Engineering Department Trakya Univerity Mechanical Engineering Department, Trakya Univerity, Edirne TURKEY kamilk@trakya.edu.tr Abtract: - Natural convection heat traner o water-baed CuO nanoluid between vertical concentric cylinder i invetigated numerically in thi tudy. The governing equation obtained with the Bouineq approximation are olved uing Comol Multiphyic inite element analyi and imulation otware. Computational reult are obtained or nanoparticle olid volume raction in the range o 0%-8% and or Rayleigh number in the range o The reult how that heat traner rate increae coniderably when nanoparticle are ued in the cylindrical encloure. The reult alo how that heat traner rate increae ubtantially with an increae in the Rayleigh number. Key-Word: - Natural convection, nanoluid, CuO, cylinder, Rayleigh number, Nuelt number 1 Introduction Buoyancy-driven luid low and heat traner in encloure have received coniderable attention due to numerou potential engineering application uch a energy traner in building, cooling o electronic device and olar collector. Conventional heat traner luid have been ued a working luid in mot o previou tudie. However, conventional heat traner luid have lower thermal conductivity coeicient, which i the baic limitation o the heat traner perormance o the ytem. Recent tudie have hown that thi limitation can be overcome with the ue o nanoluid. The term nanoluid i ued to decribe a olid and liquid mixture that conit o a bae liquid and nanoparticle o le than 100 nm in ize. Studie how that an anomalou increae i een in thermal conductivity with the uage o nanoparticle [1-3]. Keblinki et al. [4] examined our poible mechanim that could lead to thi unexpected behavior. Thee mechanim are: Brownian motion o nanoparticle, molecular level layering o the liquid at the liquidparticle interace, the nature o heat traner in the nanoparticle, and nanoparticle clutering. Keblinki et al. [4] have alo hown that Brownian motion ha no igniicant eect on conduction while the liquid layering around nanoparticle ha a at. There are many tudie in the literature invetigating the eect o nanoparticle uage on convection heat traner. Xuan and Li [5] oberved that oxide nanoparticle enhance heat traner coniderably. Eatman et al. [6] howed that the convection heat traner rate increae by more than 15% in water with a volume raction o CuO o le than 1%. Izadi et al. [7] perormed a numerical invetigation on the laminar orced convection o an Al 2 O 3 and water nanoluid in an annulu and oberved that the axial velocity proile doe not igniicantly change with nanoparticle volume raction; the temperature proile, however, are aected by the nanoparticle concentration. Khanaer et al. [8] tudied the natural convection o copperbaed nanoluid in a dierentially heated quare cavity. Their reult how that the preence o nanoparticle enhance heat traner by approximately 25% or Gr=10 4 and Gr=10 5 at a volume raction o =0.2. Hwang et al. [9] tudied the buoyancy-driven heat traner o water-baed Al 2 O 3 nanoluid in a rectangular cavity and ound that the ratio o the heat traner coeicient o nanoluid to that o the bae luid decreae with increaing nanoparticle ize. Aminoadati and Ghaemi [10] invetigated the natural convection cooling o a heat ource embedded on the bottom wall o an encloure illed with nanoluid and ound that the type o nanoparticle and the length and location o the heat ource igniicantly aect the maximum temperature o the heat ource. Heat traner augmentation in a two-ided, lid-driven, dierentially heated quare cavity utilizing nanoluid wa tudied numerically by Tiwari and Da [11]. They oberved that when both vertical wall move upward in the ame direction, heat traner i reduced. They alo ound that when ISBN:

2 vertical wall move in the oppoite direction, heat traner i coniderably enhanced or a orced convection-dominated regime. The buoyancy-driven heat traner o water-baed nanoluid in a dierentially heated tilted encloure wa invetigated by Kahveci [12]. He ound that the maximum heat traner take place at =45 or Ra=10 4 and at =30 or Ra=10 5 and The objective o thi tudy i to invetigate natural convection heat traner o water-baed CuO nanoluid between concentric cylinder. and particle are in thermal equilibrium and move with the ame velocity. With the oregoing aumption, the dimenionle governing equation can be given a ollow: 2 Problem Formulation The baic coniguration ued in the analyi i hown in Fig. 1. The cylindrical encloure o height H and diameter D ha a mall cylinder o diameter d in it. Adiabatic g D Adiabatic Fig. 1 Geometry and the coordinate ytem. The ollowing dimenionle variable are ued to nondimenionalize the governing equation: d T H T C H where i the kinematic vicoity o the luid, g i the gravitational acceleration and T i the coeicient o thermal expanion. T* i the temperature dierence. The Prandtl and Rayleigh number are deined a: Nondimenional governing equation are ubjected to the ollowing boundary condition: where *, * are the dimenional velocity component in the r* and z* direction, repectively, p* i the dimenional preure, T* i the dimenional temperature, i the denity, and i the thermal diuivity. The low i aumed to be Newtonian, teady, and incompreible. The buoyancy eect are incorporated in the ormulation by invoking the Bouineq approximation. The vicou diipation term and the thermal radiation are aumed to be negligible. Depite the act that a nanoluid i a two phae mixture, ince the olid particle are o a very mall ize, they are eaily luidized and thereore can be conidered to behave a a luid. Thereore, nanoluid i treated a a ingle phae low. The ingle phae approach aume that the luid phae The ollowing approach propoed by Yu and Choi [13] wa ued or the thermal conductivity prediction o the nanoluid: k 2k 2(k k )(1 ) k e / k, (11) 3 k 2k (k k )(1 ) where i the ratio o the nanolayer thickne to the original particle radiu. Yu and Choi [13] compared their reult or =0.1 with exiting experimental reult rom previou tudie and obtained reaonably good agreement. 3 ISBN:

3 Nanoluid vicoity i generally etimated uing exiting relation or a two-phaed mixture. The ollowing Brinkman model [14] wa ued a the relation or the eective vicoity in thi tudy. 2.5 e /( 1 ) (12) Other propertie o nanoluid that are preent in the governing equation can be deined by the ollowing equation: C p (1 ) Cp Cp e T e ( 1 ) T T (13) (14) where e 1 ) ( (15) The average Nuelt number can be expreed a ollow: 3 Problem Solution The olution o the governing equation are obtained by Comol Multiphyic inite element analyi and imulation otware or Rayleigh number rom 10 5 to CuO wa taken a nanoparticle and the ratio o the nanolayer thickne to the original particle radiu wa taken at a ixed value o 0.1. Water wa ued a the bae luid with Pr=6.2. The thermophyical propertie o the luid and olid phae are hown in Table 1. i elected a convergence criteria, where err i relative error baed on the Euclidean norm: where N i the number o degree o reedom, E i i the error and i the dependent variable and S i the cale actor. Table 1. Thermophyical propertie o bae luid and nanoparticle. Property Water CuO (kg/m 3 ) C p (J/kgK) k (W/mK) x10 7 (m 2 /) T x10 6 (1/K) Concluion The eect o Rayleigh number and nanoparticle uage on the low and heat traner in the cylindrical encloure i een in Fig The heated luid rie along the let wall a a reult o buoyancy orce until it reache near the top wall, where it turn rightward, toward the urace o the outer cylinder, while it i cooled. Then it turn downward near that urace. Finally, the retriction impoed by the bottom wall orce the luid to turn letward. The low path i completed a the colder luid i entrained to the acending low along the hot wall. For low value o Rayleigh number, circulation intenity i weaker due to the weak buoyancy orce. When the Rayleigh number increae, circulation become tronger a the buoyancy orce become dominant. A may be oberved rom the igure, the low tructure evolute toward the boundary layer regime with increaing Rayleigh number. The development o the boundary layer regime with increaing Rayleigh number i clearly illutrated by the increaing teepne o the velocity and temperature proile near the wall. The nanoparticle uage increae energy tranport rom hot urace to the nearby luid becaue o the increae o thermal conductivity coeicient. Thi create a poitive eect on the circulation intenity. The nanoparticle uage alo increae luid vicoity, a een rom Eq. (13). Thi lead to an increae at vicou orce. Becaue thi eect i tronger than the eect caued by thermal conductivity increae, a decreae i een in the circulation intenity due to the uage o nanoparticle in the bae luid. Decreae in circulation intenity along with the increae the thermal conductivity coeicient o the luid. Thereore, iotherm near the bottom wall move away rom the hot wall, iotherm near the top wall get cloer to the hot wall. The variation o the average Nuelt number with the olid volume raction and Rayleigh number i hown in Table 2. The average Nuelt number increae igniicantly with the increae o Rayleigh ISBN:

4 number a the circulation intenity trengthen. There i alo an increae at the average heat traner rate with increaing olid volume raction a the thermal conductivity o nanoluid increae. With the increae o diameter o the inner cylinder, irtly a decreae then an increae i een at the average Nuelt number or low value o the Rayleigh number. The circulation intenity i weak or low value o the Ra number and circulation weaken with the increae o d. Thereore, a decreae i een at the Nu a. For low value o the Ra number, conduction heat traner i at igniicant level. A the hot wall and cold wall get cloer, conduction heat traner increae. Becaue thi eect i dominant, Nu a increae with the urther increae o the diameter o the inner cylinder. For high value o the Ra number, the average Nuelt number decreae with the increae o the diameter o the inner cylinder a the circulation intenity weaken. Fig. 4 Velocity and temperature ield or d=0.25 and Ra=10 7. Fig. 2 Velocity and temperature ield or d=0.25 and Ra=10 5. Fig. 5 Velocity and temperature ield or d=0.50 and Ra=10 5. Fig. 3 Velocity and temperature ield or d=0.25 and Ra=10 6. Fig. 6 Velocity and temperature ield or d=0.50 and Ra=10 6. ISBN:

5 Fig. 7 Velocity and temperature ield or d=0.50 and Ra=10 7. Fig. 9 Velocity and temperature ield or d=0.75 and Ra=10 6. Fig. 8 Velocity and temperature ield or d=0.75 and Ra=10 5. Fig. 10 Velocity and temperature ield or d=0.75 and Ra=10 7. ISBN:

6 Table 2. Variation o the average Nuelt number. d Ra Nu a Reerence: [1] Eatman, J.A., Choi, S.U.S., Yu, W., Thompon, L.J., Anomalouly Increaed Eective Thermal Conductivity o Ethylene Glycol-Baed Nanoluid Containing Copper Nanoparticle, Appl. Phy. Lett., Vol. 78, 2001, pp [2] Choi, S.U.S., Zhang, Z.G., Yu, W., Lockwood, F.E., Grulke, E.A., Anomalou Thermal Conductivity Enhancement in Nanotube Supenion, Appl. Phy. Lett., Vol. 79, 2001, pp [3] Xuan, Y., and Li, Q., Heat Traner Enhancement o Nanoluid, Int. J. Heat & Fluid Flow, Vol. 21, 2000, pp [4] Keblinki, P., Phillpot, S.R., Choi, S.U.S., Eatman, J.A., Mechanim O Heat Flow In Supenion o Nano-Sized Particle (Nanoluid), Int. J. Heat Ma Tran., Vol.45, 2002, pp [5] Xuan, Y., and Li, Q., Heat Traner Enhancement o Nanoluid, Int. J. Heat & Fluid Flow., Vol. 21, 2000, pp [6] Eatman, J.A., Choi, S.U.S., Li, S., Soyez, G., Thompon, L.J., DiMeli, R.J., Novel Thermal Propertie o Nanotructured Material, J. Metatable Nanocryt. Mater., Vol. 2, 1998, pp [7] Izadi, M., Behzadmehr, A., Jalali-Vahida, D., Numerical Study o Developing Laminar Forced Convection o a Nanoluid in an Annulu, Int. J. Therm.Sci., Vol. 48, No. 11, 2009, pp [8] Khanaer, K., Vaai, K., Lighttone, M., Buoyancy Driven Heat Traner Enhancement in a Two-Dimenional Encloure Utilizing Nanoluid, Int. J. Heat Ma Tran., Vol. 46, 2003, pp [9] Hwang, K.S., Lee, J.-H., Jang, S.P., Buoyancy- Driven Heat Traner o Water-Baed Al 2 O 3 Nanoluid in a Rectangular Cavity, Int. J. Heat Ma Tran., Vol. 50, No , 2007, pp [10] Aminoadati, S.M., Ghaemi, B., Natural Convection Cooling o a Localied Heat Source at the Bottom o a Nanoluid-Filled Encloure, Eur. J. Mech. B-Fluid, Vol. 28, No. 5, 2009, pp [11] Tiwari, R.K., Da, M.K., Heat Traner Augmentation in a Two-Sided Lid-Driven Dierentially Heated Square Cavity Utilizing Nanoluid, Int. J. Heat Ma Tran., Vol. 50, 2007, pp [12] Kahveci, K., Buoyancy Driven Heat Traner o Nanoluid in a Tilted Encloure, ASME J. Heat Traner, Vol. 132, No. 6, 2010, Paper No (12 page). [13] Yu, W., Choi, S.U.S., The Role o Interacial Layer in the Enhanced Thermal Conductivity o Nanoluid: A Renovated Maxwell Model, J. Nanopart. Re., Vol. 5, 2003, pp [14] Brinkman, H. C., The Vicoity o Concentrated Supenion and Solution, J. Chemical Phyic, Vol. 20, 1952, pp ISBN: