NUMERICAL STUDY OF MIXED CONVECTION HEAT TRANSFER IN LID-DRIVEN CAVITY UTILIZING NANOFLUID: EFFECT OF TYPE AND MODEL OF NANOFLUID

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1 NUMERICAL STUDY OF MIXED CONVECTION HEAT TRANSFER IN LID-DRIVEN CAVITY UTILIZING NANOFLUID: EFFECT OF TYPE AND MODEL OF NANOFLUID by Nader POURMAHMOUD 1,a, Ashkan GHAFOURI 1,b,*, Iraj MIRZAEE 1,c 1 Department o Mechanical Engineering, Urmia University, Urmia, Iran a Associate Proessor, n.pormahmod@urmia.ac.ir b,* Ph.D Student, a.ghaouri@urmia.ac.ir c Proessor, i.mirzaee@urmia.ac.ir Numerical investigation o the laminar mixed convection in two-dimensional lid driven cavity illed with water-al O 3, water-cu or water-tio nanoluids is done in this work. In the present study, the top and bottom horizontal walls are thermally insulated while the vertical walls are kept at constant but dierent temperatures. The governing equations are given in term o the stream unction-vorticity ormulation in the non-dimensionalized orm and then solved numerically by second-order central dierence scheme. The thermal conductivity and eective viscosity o nanoluid have been calculated by Maxwell-Garnett and Brinkman models, respectively. An excellent agreement between the current work and previously published data on the basis o special cases are ound. The governing parameters are 3 6 Rayleigh number 10 Ra 10 and solid concentration 0 0. at constant Reynolds and Prandtl numbers. An increase in mean Nusselt number is ound as the volume raction o nanoparticles increases or the whole range o Rayleigh numbers. In addition, it is ound that signiicant heat transer enhancement can be obtained by increasing thermal conductivity coeicient o additive particles. At Ra= , the Nusselt number increases by about 1% or TiO -Water, and almost 5% or Al O 3 - Water, and inally around 40% or Cu-Water nanoluid. Thereore, the highest values are obtained when using Cu nanoparticles. The result obtained using variable thermal conductivity and variable viscosity models are also compared to the results acquired by the Maxwell-Garnett and the Brinkman model. Nomenclature Key words: Nanoluid, Mixed convection, Heat transer, Lid-driven cavity, Rayleigh number, Solid volume raction C P Speciic heat at constant pressure, [J kg 1 K 1 ] g Gravitational acceleration, [m s ] Gr Grasho number (=gβ (T H T C ) L 3 ν - ), [ ] H Local heat transer coeicient, [W m K 1 ] 1

2 k Thermal conductivity, [W m 1 K 1 ] k b Boltzmann s constant (= ) L Length o Cavity, [m] Nu Nusselt number (= hl/k ), [ ] p Dimensional Pressure, [kg m 1 s ] P Dimensionless Pressure (=p ρ 1 n U m ), [ ] Pr Prandtl number (= ν /α ), [ ] Ra Rayleigh number (= Gr pr), [ ] Re Reynolds number (= U m L/ν ), [ ] Ri Richardson number (= Gr/Re ), [ ] T Dimensional temperature, [ C] u, v Dimensional x and y components o velocity, [m s 1 ] U, V Dimensionless velocities (V = v/u m, U = u/u m ), [ ] U m Lid velocity, [m s 1 ] x, y Dimensional coordinates, [m] X, Y Dimensionless coordinates (X = x/l, Y = y/l), [ ] Greek symbols α Fluid thermal diusivity, [m s 1 ] β Thermal expansion coeicient, [K 1 ] ε Numerical tolerance, [ ] φ Nanoparticle volume raction, [ ] ν Kinematic viscosity, [m s 1 ] θ Dimensionless temperature, ( (T T C ) / (T H T C )), [ ] λ Transport quantity ψ Dimensional stream unction, [m s 1 ] Ψ Dimensionless stream unction (= ψ/u m L), [ ] ω Dimensional vorticity [s 1 ] Ω Dimensionless vorticity (=ωl/u m ), [ ] ρ Density, [kg m 3 ] μ Dynamic viscosity, [N s m ] Subscripts avg Average Fluid H Hot C Cold n Nanoluid s Solid Particle Superscripts * Normalized 1. Introduction The main restriction o common luids used or heat transer application such as water, ethylene glycol, mineral oil or propylene glycol is their low thermal conductivity. Nanoluid, which is a mixture o nano-size particles suspended in base luid, has a superior thermal conductivity compared to the base luid. Due to their potential in enhancement o heat transer, nanoluids have attracted enormous interest or researchers and artisans such that many researchers have investigated dierent aspects o nanoluids [1]. Eastman et al. [], in their experimental work, showed that an increase in thermal conductivity o nearly 60% could be obtained or a nanoluid considering o water and 0.05 solid volume raction CuO nano particles. Lee et al. [3] measured the thermal conductivity o Al O 3 -Water and Cu-Water nanoluids and demonstrated that the thermal conductivity o nanoluids increases with solid volume raction. Das et al. [4] expressed -4-times increase in thermal conductivity enhancement or water-based nanoluids containing Al O 3 or CuO nanoparticles. Various models or estimating thermal conductivity developed that mostly ocused on several parameters such as temperature, size and shape o nanoparticles, Brownian motion, mean path o luid particles etc. Maxwell [5] proposed a model to predict the thermal conductivity o low dense mixture that contains solid particles. Several other models have been proposed or calculating the eective thermal conductivity o solid-luid system Maxwell-Garnet [6], Bruggeman [7], Hamilton and Crosser [8], Wasp [9], Yu and Choi [10], Petal et al.[11] and Chon et al. [1]. Since the very small nanoparticles are added to the base luid, nanoluids as single phase lows have been considered [5]. Furthermore, various viscosity correlations such as Brinkman [13], Nguyen et al. [14], Pak and Cho [15], etc. have been developed or several nanoluids [16, 17].

3 Fluid low and heat transer in -D square cavity driven by buoyancy and shear have been studied extensively in the literature [18-]. Mixed convection in lid-driven cavity low problems are encountered in variety o thermal engineering application including cooling o electronic devices, multi-shield structures used or nuclear reactors, urnaces, lubrication technologies, chemical processing equipment, ood processing, high-perormance building insulation, glass production, solar power collectors, drying technologies, etc [3]. Arpaci and Larson [4] have presented an analytical treatment o the mixed convection heat transer in cavity, which had one vertical side moving, vertical boundaries at dierent temperatures and horizontal boundaries adiabatic. A review on numerical studied reveals that they can be classiied into two groups as the ollowing: the irst one is denoted as mixed convection in pure base luid concerned with horizontal top or bottom wall or both walls sliding lid driven cavities, in which the walls have a constant velocity [5-7] or oscillating [8, 9] and another walls are maintained at dierent constant temperatures while upper and bottom walls are thermally insulated. Any other rotation in the boundary conditions in this group can be considered [30]. The second group o numerical investigations particularly deals with mixed convection lows in a lid-driven square cavity utilizing nanoluid. Tiwari and Das [1] numerically investigated the heat transer augmentation in a lid-driven cavity illed with nanoluid. They ound that the presence o nanoparticles in a base luid is capable o increasing the heat transer capacity o the base luid. Chamkha and Abu-Nada [31] ocused on the low in single and double-lid square cavity illed with a water-al O 3 nanoluid. Two viscosity models are used, namely, Brinkman [13] and Pak and Cho [15] correlation. Their results showed that a signiicant heat transer enhancement could be obtained by increasing the nanoparticle volume ractions at moderate and large Richardson number using both nanoluid models. Talebi et al. [3] investigated the laminar mixed convection low through a Copper- Water nanoluid in a square lid-driven cavity. They ound that at ixed Reynolds number, the solid concentration aects on the low pattern and thermal behavior particularly or higher Rayleigh number. Also their results showed that the eect o solid concentration decreases by the increase o Reynolds number. Muthtamilselvan et al. [33] reported on the heat transer enhancement o Copper- Water nanoluids in a lid-driven enclosure with dierent aspect ratios. The main motivation o this study is to investigate the mixed convection heat transer in liddriven cavity utilized with nanoluids. Three dierent nanoparticles as Al O 3, Cu and TiO and also two variable viscosity and thermal conductivity models are used to study the eect o nanoparticles on mixed convection low and temperature ields and also comprehensive study on the change o type and used model o nanoluid along with other parameters determining the low pattern is perormed. In the present study, the stream unction-vorticity ormulation has been applied or simulation the low eature o nanoluids and the results will be obtained or a wide range o Rayleigh number ( Ra ) and volume raction o solid particles ( ).. Problem Description Figure 1 depicts schematics o the two-dimensional (-D) lid-driven cavity considered in this paper. The luid in the cavity is a water-based nanoluid containing dierent type o nanoparticles Cu, Al O 3 and TiO. The nanoluid is assumed as incompressible and the low is assumed to be laminar. It is supposed that the base luid (i.e. water) and the nanoparticles are in thermal equilibrium and no slip occurs between them. The shape and the size o solid particles are urthermore assumed to be uniorm and their diameter to be equal to 100 nm. The top and bottom horizontal walls are thermally insulated 3

4 while the vertical walls are kept at constant but dierent temperatures. In order to induce the buoyancy eect, the let vertical wall is kept at a relatively high temperature (T H ) and right vertical wall is maintained at a relatively low temperature (T C ). Top wall slides rom let to right with uniorm velocity. The thermo-physical properties o the pure water and the nanoluid at temperature o 5 o C are given in tab. 1. The thermo-physical properties o the nanoluid are assumed to be constant except or the density variation, which is approximated by the Boussinesq model. Table 1. Thermo-physical properties o luid and nanoparticles. Physical properties Fluid phase (Water) Cu Al O 3 TiO C p ( J / KgK ) ( kg / m ) k ( W / MK) (1/ K) Mathematical Formulation Figure 1. Schematic o problem. The steady-state equations that govern the conservation o mass, momentum and energy can be written in the ollowing non-dimensional orms U X V Y 0, (1) U V X U U X U V Y P X 1 Re n n ( U V V Y P Y n n 1 Re ( V X V Y ) () n n X U ), () Y Ra, (3) Pr.Re U V X Y n 1 Re.Pr ( X ). (4) Y In the above equations, the ollowing non-dimensional parameters are used x y u v p T Tc X, Y, U, V, P,, L L T T U m U m n U m 3 U Re m L gl ( T ), Pr, H T Gr c, Ra Gr. Pr, H c Ri Gr Re. (5) The viscosity o the nanoluid can be approximated as viscosity o the base luid ( ) containing dilute suspension o ine spherical particles. In the current study, two models are used to model the 4

5 viscosity o the nanoluids, which are the Brinkman model [13] and the Pak and Cho correlation [15]. Main results o this study are based on Brinkman model and eect o second model is expressed in the inal results at the end o the article. The Brinkman model deined as: n 1.5. (6) (1) Table. Code validation: Comparison o the average Nusselt at the top wall 3 Ra 10 4 Ra 10 5 Ra 10 6 Ra 10 Present Khanaer et al. [18] Fusegi et al. [36] Markatos and pericleous[37] de Val Davis [38] The eective density o the nanoluid at the reerence temperature is and the heat capacitance o nanoluid is n (1) s, (7) (c p ) n (1)(c p ) (c p ) s. (8) As given by Xuan and Li [37], also the eective thermal conductivity o the nanoluid is approximated by the Maxwell-Garnett model [6]: k k n ks k s k k ( k ( k k k s s ) ) (9) Figure. Grid independence study with dierent Rayleigh number. Figure 3. Comparison between present work and other published data or the temperature distribution In term o the stream unction-vorticity ormulation, the governing equations are written as 5

6 n U V X Y (1) s U V X Y X, (10) Y 1 Re ( X Y ) ((1) s k n k (1) (c p ) s (c p ) a b c Ra ) Pr.Re X, (11) 1 Re.Pr ( X ). (1) Y d e g h i Figure 4. The eect o solid volume raction, Richardson number and type o nanoparticle on the Streamline or a) TiO, Ri=0.1 b)tio, Ri=1 c) TiO, Ri=10 d) Al O 3, Ri=0.1 e) Al O 3, Ri=1 ) Al O 3, Ri=10 g) Cu, Ri=0.1 h) Cu, Ri=1 i) Cu, Ri=10, φ=0%( ) and φ=10%(-----). 6

7 The additional dimensionless variables in the above equations are deined as, U.L m.l (13) U m The dimensionless horizontal and vertical velocities are converted to U, V (14) Y X The appropriate dimensionless boundary conditions can be written as: a b c d e g h i Figure 5. The eect o solid volume raction, Richardson number and type o nanoparticle on the Vertical velocity at mid line o cavity (Y=0.5) or a) TiO, Ri=0.1 b)tio, Ri=1 c) TiO, Ri=10 d) Al O 3, Ri=0.1 e) Al O 3, Ri=1 ) Al O 3, Ri=10 g) Cu, Ri=0.1 h) Cu, Ri=1 i) Cu, Ri=10. 7

8 1- On the let wall: U V 0, 1 and (15a) X - On the right wall: U V 0, 0 and X (15b) 3- On the top wall: V 0, U 1, 0 and Y Y (15c) 4- On the bottom wall: U V 0, 0 and (15d) Y Y In order to estimate the heat transer enhancement, Nusselt number ( Nu (X ) ) and average Nusselt number ( Nu ) are calculated using eq.(16) and eq.(17) respectively. avg a b c d e g h i Figure 6. The eect o solid volume raction, Richardson number and type o nanoparticle on the horizontal velocity at mid line o cavity (X=0.5) or a) TiO, Ri=0.1 b)tio, Ri=1 c) TiO, Ri=10 d) Al O 3, Ri=0.1 e) Al O 3, Ri=1 ) Al O 3, Ri=10 g) Cu, Ri=0.1 h) Cu, Ri=1 i) Cu, Ri=10. 8

9 Nu k n ( X ) X 0 k X (16) 1 Nu avg Nu ( X ) dy (17) 0 To evaluate Eq.(17), a 1/3 Simpson's rule o integration is implemented. For convenience, a normalized average Nusselt number is deined as the ratio o Nusselt number at any volume raction o nanoparticles to that o pure water that is [35], Nu avg() Nu * avg() Nu avg ( 0). (18) a b c d e g h i Figure 7. The eect o solid volume raction, Richardson number and type o nanoparticle on the isotherms or a) TiO, Ri=0.1 b)tio, Ri=1 c) TiO, Ri=10 d) Al O 3, Ri=0.1 e) Al O 3, Ri=1 ) Al O 3, Ri=10 g) Cu, Ri=0.1 h) Cu, Ri=1 i) Cu, Ri=10, φ=0%( ) and φ=10%(-----). 9

10 3.1. Variable nanoluid models What is common in most o the previous reerenced work on nanoluid natural and mixed convection problems is the use o the Brinkman viscosity model and Maxwell-Garnett thermal conductivity models or a nanoluid and thereore, predict enhancement o heat transer due to the presence o nanoparticles. Hence, one o the objectives o this work is to show that a dierent predictions with using the Pak and Cho viscosity model [15] and Chon et al. thermal conductivity model [1] can be obtained, which are shown in the results (only in Fig.15). These correlations are given respectively as n ( ), (19) k n k where Pr T and Re T are deined by : Pr T and ( d ) ( k s ) Pr d s k T Re 1.31 T, (0) Re T k b T 3 l. (1) The symbol k b is the Boltzman constant = [JK -1 ]. Also l is the mean path o luid particles given as 0.17 nm [1]. In this model, the temperature and size eects in nanoparticles are considered. 4. Numerical method The set o nonlinear coupled governing mass, momentum and energy equations (i.e., eq. (1)-(4)) are developed in terms o stream unction-vorticity ormulation and then solved numerically with the corresponding boundary condition given in eq. (15). The equations are approximated by second-order central dierence scheme and successive over relaxation (SOR) method is used to solve stream unction equation. The convergence criterion is deined by the ollowing expression: j M in n 1 n j 1 i1 j M in n 1 j 1 i1 10 6, () where represents the tolerance, also M and N are the number o grid points in the X and Y direction, respectively. The symbol denotes any scalar transport quantity namely, or. An accurate representation o vorticity at the surace is the most critical step in the stream unction vorticity ormulation. A second-order accurate ormula is used or the vorticity boundary condition. For example, the vorticity at the top wall is expressed as: i, M i, M 8 i, M 1 7 Y The last term in the numerator vanishes or static walls. 5. Grid testing and code validation i, M 6YUm (3) 10

11 An extensive mesh testing procedure was conducted to guarantee a grid-independent solution. Six dierent uniorm grids, namely, 1 1, 41 41, 61 61, 81 81, and are employed or the case o Re = 100. The present code was tested or grid independence by calculating the average Nusselt number on the let wall. As it can be observed rom Fig., an uniorm grid is suiciently ine to ensure a grid independent solution. Another grid-independence study was perormed using Cu water nanoluid. It was conirmed that the same grid size ensures a gridindependent solution. The present numerical solution is urther validated by comparing the present code results or temperature distribution at Ra = 10 5 and Pr = 0.70 against the experiment o Krane and Jessee [40] and numerical simulation o Khanaer et al. [18] and also Oztop and Abu-Nada [39]. It is clear that the present code is in good agreement with other works reported in literature as shown in Fig. 3. In addition the governing equations have been solved or the natural convection low in an enclosed cavity illed by pure luid, in order to compare the results with those obtained by Khanaer et al. [18], Fusegi et al. [36], Markatos and pericleous [37] and de Vahl Davis [38]. This comparison revealed good agreements between the results, which are shown in tab.. 6. Discussion and results Two-dimensional mixed convection is studied in a square lid-driven cavity or Ra= and solid volume raction 0 to 0. or a Cu water, TiO -Water and Al O 3 -Water nanoluids. Figure 4 illustrates the streamlines at range Ra= to , and Re=100 or a pure luid and nanoluid with =10% using Brinkman and Maxwell-Garnett models. Figure 4 (a)-(c) shows the comparison between TiO -water nanoluid (plotted by dashed lines) and pure luid (plotted by solid lines) on streamlines or various values o the Rayleigh number. At Ra= ( Ri 1, orced convection-dominated regime), Fig. 4(a) indicates that the buoyancy eect is overwhelmed by the mechanical or shear eect due to movement o the top lid and the low eatures are similar to those o a viscosity low o a non-stratiied luid in the lid driven cavity. In this case, the increment o solid concentration does not have considerable eect on the low pattern. The increase in Rayleigh number enhances the buoyancy eect and thereore the intensity o low. However, the dominant eect o the orce convection is still observed. Furthermore, at Ra= ( Ri 1, mixed convection-dominated Figure 8. The average Nusselt number at the let wall or TiO -water Figure 9. The Normalized average Nusselt number at the let wall or TiO -water 11

12 Figure 10. The average Nusselt number at the let wall or Al O 3 -water Figure 11. The Normalized average Nusselt number at the let wall or Al O 3 -water Figure 1. The average Nusselt number at the let wall or Cu-water Figure 13. The Normalized average Nusselt number at the let wall or Cu-water regime), Fig. 4(b) indicates that the buoyancy eect is relatively comparable magnitude o the shear eect due to the sliding top wall lid. In this case, as the solid concentration increases the value o the stream unction increases at the center o the cavity. Moreover, or Ra= ( Ri 1, natural convection-dominated regime), Fig. 4(c) suggests that the eect o lid-driven low is insigniicant and the value o the stream unction increases to a greater extent than previous case as a result o an increase about 10% in the solid concentration. The streamlines or Al O 3 -Water nanoluid and Cu water nanoluid at various Rayleigh numbers or two case o pure luid and 10% concentration o nanoluid are presented in Fig. 4(d)-() and Fig. 4(g)-(i), respectively. Figure 5(a)-(c) demonstrates the eect o solid concentration on the vertical velocity distribution or various Rayleigh numbers at mid line o cavity (Y=0.5). It is obvious rom this igure that or Ra= the eect o buoyancy predominate the orced convection eect. Upward low and downward low are symmetric with respect to the center o the cavity thanks to the laminar behavior o the low. As seen, the increase in solid concentration leads to enhance the low intensity such that the maximum value o the velocity is obtained at the maximum solid concentration. The increase o both Rayleigh number and solid concentration augments the strength o buoyancy. Thereore, the higher Rayleigh number, the solid concentration has more eect to enhance the velocity 1

13 with respect to the pure luid. So or TiO -Water at Ra= , the concentration does not aect on the vertical velocity. However, as Ra increases, a mixed eect o buoyancy and lid-driven within the cavity is observed. For instance, at Ra= and 10% solid concentration, the horizontal component o velocity increases by about 8%. Aluminum nanoparticles change rom 0 to 10 percent is the analogous procedure. Due to distinguished thermo-physical properties o Cu, this value can be raised to 5% as shown in Fig. 5(i). The eect o the solid concentration on the horizontal velocity distribution or various Rayleigh number at mid-line o the cavity (Y=0.5) is shown in Fig. 6. It turns out that the solid volume raction increases rom 0 to 10% or Cu-Water, the horizontal component o velocity increases by almost 0% at Ra= and by about 9% at Ra= Other variations in Fig. 6(a)-(i) are signiicant. Figure 14. The normalized average Nusselt in various solid concentration and Rayleigh number; eect o type o nanoluid Figure 15. The average Nusselt in various solid concentrations and Rayleigh number; eect o nanoluid model or Al O 3 -Water The eect o the presence o nanoparticle on the thermal behavior and temperature distribution contours or pure water are overlaid with that or nanoluid with o 0.1. The results or Cu-Water, Al O 3 -Water and TiO -Water at the three Rayleigh number are illustrated in Fig. 7. As seen, at the lower Rayleigh number, the solid concentration is more eective to increases the heat penetration because the conduction heat transer has a stronger contribution at the lower Rayleigh number. On the other hand, the increase o the eective thermal conductivity o the nanoluid with solid concentration leads to enhance the conduction mod. But the eect o conduction heat transer decreases as the Ra increases. Consequently, at this condition, the solid concentration has a smaller eect on the thermal distribution. Figures. 8, 10 and 1 illustrates the variation o the average Nusselt number on the let wall (hot wall) or TiO -water, Al O 3 -Water and Cu-Water, respectively. The increase o the solid concentration augments the eective thermal conductivity, and hence, the energy transer. The increase o the solid concentration also augments the low intensity. Both o two actors indeed enhance the average Nusselt number with solid concentration. The increase o Rayleigh number also enhances the heat transer rate and hence average Nusselt number. It is clear that the solid concentration has more eect on the average Nusselt number at higher Ra. This is in act similar to those shown in Figs. 5 and 6. Figure 9, 11 and 13 depicts the normalized average Nusselt number Nu * avg or various value o the volume raction o nanoparticles and Rayleigh number or TiO -water, Al O 3 -Water and Cu-Water, 13

14 respectively. It is observed that as solid volume raction increases rom 0 to 0% at Ra= , the Nusselt number increases by about 1% or TiO -Water, and almost 5% or Al O 3 -Water, and inally around 40% or Cu-Water nanoluid. The signiicance o other variations at dierent Rayleigh number is shown in Fig. 14 in a comparative ashion. As outlined in Fig. 15, it is clear that when Chon et al. and Pak and Cho models are used, (shown in Fig.15 by Ch-P abbreviation), Nusselt number o the hot wall has higher values at all Ra numbers and φ than that obtained by the Maxwell-Garnett and Brinkman ormula, which is shown in Fig.15 by MG-B abbreviation. The dierences between Nu avg are obtained using the dierent ormulas. Moreover, a decrease in Rayleigh number results in an increase in the shear orce and the orced convection, when a constant nanoparticle volume-raction utilized, and this causes the dierence between average Nusselt numbers calculated by two combinations o ormula to increase. It is recognized rom Fig. 15, when the Maxwell-Garnett and Brinkman ormula are used, the heat transer increases with increasing solid volume raction and Nu avg has an irregular manner when Chon et al. and Pak and Cho correlations are utilized. It is ound that at low Rayleigh number the average Nusselt number is more sensitive to viscosity models and thermal conductivity models. 7. Conclusions A numerical study has been perormed to investigate the eect o using dierent nanoluids on mixed convection low ield and temperature distributions in lid-driven square cavity rom the let vertical hot wall using Maxwell-Garnet thermal conductivity and Brinkman viscosity models. The top and bottom walls o the cavity are kept insulated and the top wall moved to the right at the constant speed. The important conclusions drawn as the ollowing: Increasing the value o Rayleigh number and volume raction o nanoparticles enhances the heat transer keeping other parameters ixed. The type o nanoluid is a key actor to heat transer enhancement. The highest values are obtained when using Cu nanoparticles. For assumed Reynolds number, the increase in the solid concentration augments the streamunction, also U and V-component o velocity, particularly at the higher Rayleigh number. It was recognized that at low Rayleigh numbers, Nu avg was more sensitive to the viscosity and the thermal conductivity models. Present research is conined to study o two viscosity models and two thermal conductivity models or Al O 3 -water nanoluid. Anyway, the results show that the utilized model, apart rom the type o nanoparticle, can be eective on heat transer enhancement. In the uture, the study can be extended or more thermal conductivity models, viscosity models and dierent Reynolds number. An optimization study may be necessary or this work to ind out the best model which has most compatibility with experimental results or cavity coniguration. Reerences [1] Godson, L., et al., Enhancement o Heat Transer Using Nanoluids an Overview, Renewable Sustainable Energy Rev. 14 (010), pp [] Eastman, J.A., et al., Enhanced Thermal Conductivity through the Development o Nanoluids, in: Komarneni, S., Parker, J.C., Wollenberger, H.J., (Eds.), Nanophase and Nanocomposite Materials II, MRS, Pittsburg, PA, (1997), pp

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