Buoyancy Driven Heat Transfer of Water-Based CuO Nanofluids in a Tilted Enclosure with a Heat Conducting Solid Cylinder on its Center

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1 July London U.K. Buoyancy Driven Heat Transer o Water-Based CuO Nanoluids in a Tilted Enclosure with a Heat Conducting Solid Cylinder on its Center Ahmet Cihan Kamil Kahveci and Çiğdem Susantez Abstract Buoyancy driven heat transer o water-based CuO nanoluid in a tilted enclosure with a heat conducting solid circular cylinder on the center is studied numerically with Comsol Multiphysics modeling and simulation sotware. The upper and the bottom walls o the enclosure are kept in adiabatic conditions and the sidewalls o the enclosure are in isothermal conditions. The results show that nanoparticle usage enhances the heat transer rate considerably. The results also show that average Nusselt number shows irst an increase and then a decrease as the inclination angle is increased. The maximum heat transer takes place at =45 deg or Ra=10 4 and at =30 deg or Ra=10 5 and Index Terms nanoluid natural convection enclosure Nusselt number Rayleigh number I I. INTRODUCTION N many engineering applications especially cooling o electronic equipment it is wanted to enhance the heat transer rate. But conventional heat transer luids such as water oil ethylene glycol have lower thermal conductivities. One way to enhance heat transer rate is using nanoluids in these types o application. Nanoluids are heat transer luids whose thermal conductivities are signiicantly high with respect to the conventional heat transer luids [1] [2] [7]. They are obtained by adding nanoparticles with high thermal conductivity to the base luid. In the past because o technological diiculties micron-sized particles have been used to enhance heat transer rate. Micron-sized particles in the luid cause sedimentation and clogging problems. These types o problem are eliminated by nanoparticle usage. Thermal conductivity is the most important parameter or the heat transer enhancement potential o nanoluids. The thermal conductivity o a nanoluid varies with the thermal conductivity o both the base luid and the nanoparticle the shape o the nanoparticles the surace area the distribution o the dispersed particles and the volume raction. Because o the absence o the suitable theoretical ormulas or the thermal conductivity o the nanoluid some models or solid Manuscript received March ; revised April Ahmet Cihan Kamil Kahveci and Çiğdem Susantez are rom Mechanical Engineering Department Trakya University Edirne Turkey ( ahmetcihan@trakya.edu.tr kamilkahveci@trakya.edu.tr cigdemsusantez@trakya.edu.tr; corresponding author to provide phone: ; ax: ). liquid mixtures with micron-sized particles are used to predict the thermal conductivity o the nanoluids. But in these models the thermal conductivity o the nanoluids is not the unction o the size and the distribution o the particles. Maxwell model [3] is a well known thermal conductivity model or this type o solid-liquid mixtures. In this model thermal conductivity is deined as ollows: ks 2k 2ks k k / k (1) k 2k 2 k k s s where k s and k are the thermal conductivity o the solid particle and the base luid respectively and is the solid particle volume raction. Another model or the eective thermal conductivity has been proposed by Yu and Choi [4]. They claimed that a structural model o nanoluids might consist o a bulk liquid solid nanoparticles and solid-like nanolayers. The solid-like nanolayers act as a thermal bridge between a solid nanoparticle and a bulk liquid. I the thermal conductivity o the solid-like nanolayers is assumed to be equal to the thermal conductivity o solid particles this model or spherical nanoparticle case takes the ollowing orm: 3 ks 2k 2ks k 1 k / k (2) 3 k 2k 2 k k 1 s s where is deined as the ratio o the nanolayer thickness to the original particle radius. On the other hand ater comparing the model results or =0.1 with existing experimental results a reasonably good agreement is obtained in the related study. In the present study this model was used or the thermal conductivity o the nanoluids. Brinkman [5] proposed an expression or the eective viscosity or a two-phased mixture. This model given below was used in the present study to determine the viscosity o the nanoluid. /1 2.5 (3) Xuan and Li [6] made an experimental study on the eective viscosity o the water-copper nanoluid and the transormer oil-water nanoluid in the temperature range o C and they ound that the obtained results were compatible with the Brinkman theory. There are a number o studies in the literature on natural convection heat transer o nanoluids. In one o these studies Oztop and Abu-Nada [10] made a study on the

2 July London U.K. buoyancy driven heat transer and luid low in a partially heated enclosure illed with nanoluid. The results show that the heat transer enhancement at low aspect ratios is higher than at high aspect ratios o the enclosure. Koo and Kleinstreuer [11] investigated the laminar nanoluid low in microheatsinks and ound that a high Prandtl number base luid and a high aspect ratio channel give better heat transer perormance. Maiga et al [8] studied orced convection low o nanoluids in a system consisting o uniormly heated tube and parallel coaxial and heated disks and observed that both the Reynolds number and the gap between disks have an insigniicant eect on the heat transer enhancement. Mirmasoumi and Behzadmehr [9] studied laminar mixed convection o Al 2 O 3 -based nanoluids in a horizontal tube and ound that the secondary low strength increases with the increase o the nanoparticle volume raction and increasing solid volume raction has no signiicant eect on the skin riction coeicient in the ully developed region except or the entrance region. In this study buoyancy driven heat transer and luid low o water based CuO nanoluids in a tilted enclosure with a heat conducting solid cylinder on its center is investigated numerically by the Comsol multiphysics modeling and simulation sotware. II. ANALYSIS The investigated geometry and the coordinate system are given in the Fig. 1. While the upper and the bottom walls o the enclosure are in adiabatic conditions the let and the right walls are kept at constant temperatures. * 2 * 2 * * v * v 1 P v v u v * *2 *2 x y y x y T gt TC cos Energy equation or the nanoluid 2 * 2 * u T v T T T *2 *2 x y x y Energy equation or the circular cylinder 2 * 2 * T T 0 *2 *2 x y (6) (7) (8) where u * and v * are velocity components in x and y directions respectively g is gravitational acceleration β T is coeicient o thermal expansion is kinematic viscosity is the thermal diusivity. The nondimensional variables used or the nondimensionalization o the governing equations can be deined as ollows: x y u v x y u v L L / L / L (9) 2 L * T TC 2 TH TC P P T Nondimensional governing equations can thereore be obtained as ollows: Nondimensional continuity equation u v 0 (10) x y g Nondimensional Navier Stokes equations u u P u u u v Pr x y x x y T T RaPrT sin (11) Fig.1 Geometry and coordinate system The low is assumed to be Newtonian two-dimensional steady incompressible and single phase. Depending on these assumptions the governing equations can be expressed as ollows: Continuity equation u v 0 (4) x y Navier-Stokes equations * 2 * 2 * * u * u 1 P u u u v * *2 *2 x y x x y T gt TC sin (5) u v Pr T RaPrT cos v v P v v x y y x y T Nondimensional energy equation or the nanoluid T T T T u v x y x y (12) (13) Nondimensional energy equation or the heat conducting circular cylinder T T 0 (14) x y Rayleigh and Prandtl numbers are deined as ollows: g 3 T L T HTC Pr Ra (15)

3 July London U.K. Thermophysical properties o nanoluid are deined as ollows: 1 (16) s c 1 c c (17) p p s p s 1 (18) T T s T s The appropriate boundary conditions or the nondimensional governing equations could be given as: T T(0 y) 1 T(1 y) 0 0 y T y x1 0 u 0 v 0 s s x0 (19) The boundary conditions on the surace o the solid cylinder could be given as: n q q 0 T T (20) s1 s2 s1 s2 where 1 and 2 stand or luid and cylinder. n is unit normal vector. From the continuity condition given above an extra parameter k r emerges. The parameter k r is deined as the ratio o the thermal conductivity o heat conducting circular cylinder to the thermal conductivity o the base luid. k k / k (21) r cyl Local Nusselt number can be deined as: k T Nu k 0 (22) where is the outer direction normal to the surace k is the thermal conductivity. III. RESULTS AND DISCUSSION In this study natural convection o water-based CuO nanoluids in a tilted enlosure with a heat conducting solid circular cylinder is studied numerically. Computational results are obtained by Comsol Multiphysics modelling and simulation sotware. A direct solver is used or all the examined values o inclination angle solid volume raction and Rayleigh number. The ratio o the cylinder diameter to the enclosure is taken as The ratio o the nanolayer thickness to the original particle radius is taken as =0.1. The thermal conductivity ratio is taken as k r =1. The eects o inclination angle solid volume raction and Rayleigh number on the velocity and temperature ields are investigated or the values o inclination angle and 60; or the values o solid volume raction and or the values o Rayleigh number Computational results are obtained or water based CuO nanoluid. The thermophysical properties o the luid and nanoparticle are given in Table I. Temperature and velocity ields are shown in Figs. 2-5 or various values o inclination angle solid volume raction and the Rayleigh numbers. As it is seen rom the igures the heated luid particles rise along the let wall as a result o buoyancy orces until they reach near the top wall where TABLE I THERMOPHYSICAL PROPERTIES OF THE BASE FLUID AND THE NANOPARTICLE Property Water CuO (kg/m 3 ) c p (J/kgK) k (W/mK) x10 7 (m 2 /s) T x10 6 (1/K) they turn rightward towards the sidewalls. Then they turn downward near those walls and move towards the bottom wall while they are cooled. Finally the restriction imposed by the bottom wall orces the luid particles to turn letward. The low path is completed as the colder luid is entrained to the ascending low along the heated wall. As it can also be seen rom the igures that the low structure evolves toward the boundary layer regime with increasing Rayleigh numbers. This is clear by the increasing steepness o the velocity and temperature proiles near the walls. The strength o convective circulation increases considerably with an increase o Rayleigh number due to higher buoyancy orces. The circulation strength also increases with an increase o solid volume raction. This is due to the increase in thermal energy transport rom the hot wall to the luid particles. Note that an increase in the viscous orces with increasing solid volume raction is also a act although it does not compensate or the increase in the thermal energy rom the hot wall to the nanoluid due to increased thermal conductivity. Hence convective circulation strengthens with increasing solid volume raction. With an increase o inclination angle circulation intensity shows irst an increase then a decrease. As the inclination angle is increased luid particles is directed towards to right sidewall in a more smooth way. This creates a positive eect on the circulation intensity. On the other hand the luid particles begin to move away rom the hot wall without heated enough as the inclination angle is increased. This creates a negative eect on the circulation intensity. Depending on the dominancy o these two eects circulation intensity shows irst an increase then a decrease. The variation o the average Nusselt number on the let wall with the inclination angle solid volume raction and Rayleigh number are given in Table 2. It is obviously seen rom the results that as Rayleigh number increases a considerable increase is seen at the average Nusselt number depending on the strengthening convective circulation. There is also a remarkable increase in the average heat transer rate with increasing solid volume raction due to the increase in thermal energy transport rom the hot wall to the luid particles. The average heat transer rate shows an increasing trend and then a decreasing trend as the inclination angle is increased. The maximum heat transer takes place at =45 deg or Ra=10 4 and at =30 deg or Ra=10 5 and 10 6.

4 July London U.K. IV. CONGLUSION Natural convection in an inclined enclosure which includes a heat conducting circular cylinder on its center is studied. Numerical results are obtained with Comsol Multiphysics modeling and simulation sotware. The results show that adding nanoparticles to the base heat transer luid enhances heat transer rate signiicantly. The results also show that average Nusselt number shows irst an increase and then a decrease as the inclination angle is increased. The maximum heat transer takes place at =45 deg or Ra=10 4 and at =30 deg or Ra=10 5 and ϕ=0.00 Ra=10 4 ϕ=0.00 Ra=10 5 ϕ=0.00 Ra=10 6 ϕ=0.00 Ra=10 4 ϕ=0.00 Ra=10 5 ϕ=0.00 Ra=10 6 ϕ=0.04 Ra=10 4 ϕ=0.04 Ra=10 5 ϕ=0.04 Ra=10 6 ϕ=0.04 Ra=10 4 ϕ=0.04 Ra=10 5 ϕ=0.04 Ra=10 6 ϕ=0.08 Ra=10 4 ϕ=0.08 Ra=10 5 ϕ=0.08 Ra=10 6 Fig. 2 Temperature and velocity ields or inclination angle =0. ϕ=0.08 Ra=10 4 ϕ=0.08 Ra=10 5 ϕ=0.08 Ra=10 6 Fig. 4 Temperature and velocity ields or inclination angle =45. ϕ=0.00 Ra=10 4 ϕ=0.00 Ra=10 5 ϕ=0.00 Ra=10 6 ϕ=0.00 Ra=10 4 ϕ=0.00 Ra=10 5 ϕ=0.00 Ra=10 6 ϕ=0.04 Ra=10 4 ϕ=0.04 Ra=10 5 ϕ=0.04 Ra=10 6 ϕ=0.04 Ra=10 4 ϕ=0.04 Ra=10 5 ϕ=0.04 Ra=10 6 ϕ=0.08 Ra=10 4 ϕ=0.08 Ra=10 5 ϕ=0.08 Ra=10 6 Fig. 3 Temperature and velocity ields or inclination angle =30. ϕ=0.08 Ra=10 4 ϕ=0.08 Ra=10 5 ϕ=0.08 Ra=10 6 Fig. 5 Temperature and velocity ields or inclination angle =60.

5 July London U.K. TABLE I THE AVERAGE NUSSELT NUMBER Ra ϕ Nu a REFERENCES [1] CHOI S. U. S. ZHANG Z. G. YU W. LOCKFOOD F. E. GRULKE E. A. Anomalous thermal conductivity enhancement in nanotube suspensions Appl. Phys. Lett : [2] DAS S. K. PUTRA N. THIESEN P. ROETZEL W. Temperature dependence o thermal conductivity enhancement o nanoluids ASME J. Heat Transer : [3] MAXWELL J. C. A treatise on electricity and magnetism Clarendon Oxord UK [4] YU W. CHOI S. U. S. The role o interacial layers in the enhanced thermal conductivity o nanoluids: a renovated Maxwell model J. Nanopart. Res : [5] BRINKMAN H. C. The viscosity o concentrated suspensions and solutions J. Chem. Phys : [6] XUAN Y. LI Q. Experimental research on the viscosity o nanoluids Report o Nanjing University o Science and Technology 1999 [7] EASTMAN J. A. CHOI S. U. S. LI S. SOYEZ G. THOMPSON L. J. DIMELFI R. J. Novel thermal properties o nanostructured materials J. Metastable Nanocryst. Mater : [8] MAIGA S. E. B. PALM S. J. NGUYEN C. T. ROY G. GALANIS N. Heat transer enhancement by using nanoluids in orced convection lows Int. J. Heat Fluid Flow : [9] MIRMASOUMI S. BEHZADMEHR A. Numerical study o laminar mixed convection o a nanoluid in a horizontal tube using two-phase mixture model Appl. Therm. Eng (7): [10] OZTOP H. F. ABU-NADA E. Numerical study o natural convection in partially heated rectangular enclosures illed with nanoluids Int. J. Heat Fluid Flow (5): [11] KOO J. KLEINSTREUER C. Laminar nanoluid low in microheatsinks Int. J. Heat Mass Transer :