Constantine, Algeria. Received Accepted Keywords: Copper nanoparticles; heat transfer; circular cylinder; steady regime.

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1 Metallurgical and Materials Engineering Association o Metallurgical Engineers o Serbia AMES Scientiic paper UDC: NUMERICAL INVESTIGATION OF FLUID FLOW AND HEAT TRANSFER AROUND A CIRCULAR CYLINDER UTILIZING NANOFLUID FOR DIFFERENT THERMAL BOUNDARY CONDITION IN THE STEADY REGIME R. Bouakkaz 1*, F. Salhi 2, Y. Khelili 3, M. Ouazzazi 4, K. Talbi 4 1 Military academy o Cherchell, Tipaza, Algeria 2 Département de Génie Mécanique, université Mouloud Mammeri Tizi ouzou, Algeria 3 Department o Mechanical Engineering, University Saad Dahlab, Blida 1, Algeria 4 Département de Génie Mécanique, université Constantine 1, Constantine, Algeria Received Accepted Abstract In this work, steady low-ield and heat transer through a copper water nanoluid around a circular cylinder, under the inluence o both the standard thermal boundary conditions i.e. uniorm heat lux (UHF) and constant wall temperature (CWT) was investigated numerically by using a inite-volume method or Reynolds numbers o 10 to 40. Furthermore, the range o nanoparticle volume ractions (φ) considered is 0 φ 5%. The variation o the local and the average Nusselt numbers with Reynolds number, and volume ractions are presented or the range o conditions. The average Nusselt number is ound to increase with increasing the nanoparticle volume ractions. Keywords: Copper nanoparticles; heat transer; circular cylinder; steady regime. Introduction Fluid low and heat transer around blu body has been a subject o great interest or researchers due to its high applicability in many industrial developments. The applications may include heat exchangers [1, 2], cylindrical cooling devices in plastics and glass industries, ood processing and nuclear power plants. In these lows, the results depend on the Reynolds number (Re), expressed as: * Corresponding author: Raik Bouakkaz: r.bouakkaz@gmail.com

2 132 Metall. Mater. Eng. Vol 23 (2) 2017 p UD Re 1 v The authors o the work [3] using standard boundary conditions namely constant wall temperature (CWT) studied the local and average heat transer characteristics around a circular cylinder or the Re number range o to and Pr number range o 0.7 to 176. Three regions o low: laminar boundary layer, reattachment o shear layer and periodic vortex regions was indicated around the cylinder or subcritical low. Further, they developed an empirical correlation or predicting the overall heat transer rom these three regions. Also, the authors [4] using uniorm dissipating heat lux boundary conditions (UHF) investigated numerically the ree stream low and orced convection heat transer across a rotating cylinder or Reynolds numbers o 10 to 45 and 0.7 <Pr < 400. Their results show that the heat transer is increase with an increase in Re and/or Pr numbers. The low and heat transer over an isothermal across a rotating cylinder in the range 0 α 6 with Re number varying rom 20 to 160 was studied in literature [5-7]. In depth analysis, it was revealed that the rotation can be used as a drag reduction and heat transer suppression technique. Further, authors [8] studied numerically the ree stream low and orced convection heat transer across a rotating cylinder, dissipating heat lux or Reynolds numbers o 20 to 160 and a Prandtl number o 0.7. Their results show that, at higher rotational velocity, the Nusselt number is almost independent o Reynolds number and the thermal boundary conditions. In past studies, the luids used have a low value o thermal conductivity, which limits heat transer. For this reason, there are several methods to improve the heat transer characteristics, which consist in adding high conducting solid particles in the base luid. The resulting luid is called nanoluid [9 11]. The steady low-ield and heat transer through a copper water nanoluid around circular cylinder was numerically simulated [12]. The values o vorticity, pressure coeicient, and recirculation length are increased by the addition o nanoparticles into base luid. Subsequently, [13] they examined the eect o heat treatment process with a new cooling medium (nanoluid), which contains water with Cu, Ag, or Al 2 O 3 particles, on heat transer characteristics and mechanical properties o an unsteady continuous moving cylinder in the thermal orces. They reported that the Al 2 O 3 nanoluid is the best type o nanoluid or improving the mechanical properties o the surace (increase the heat lux). This nanoluid is also the best type or decreasing the surace shear stress. Recently, authors [14] have ocused on numerical study o heat transer phenomena over an isothermal cylinder or low Reynolds number low o nanoluid. They have shown that at a given Nusselt number, drag coeicient, recirculation length, and pressure coeicient increase by increasing the volume raction o nanoparticles. On the other hand, authors [15] have studied the momentum and orced convection heat transer or a laminar and steady ree stream low o nanoluids past a square cylinder. Dierent nanoluids consisting o Al 2 O 3 and CuO with base luids o water and ethylene glycol, 60:40 (by mass), were selected to evaluate their superiority over conventional luids. They showed that or any given particle diameter there is an optimum value o particle concentration that results in the highest heat transer coeicient. The luid low and heat transer around a square cylinder utilizing Al 2 O 3 H 2 O nanoluid over low Reynolds numbers varied within the range o 1 to 40 and the

3 Bouakkaz et al. - Numerical Investigation o Fluid Flow and Heat Transer Around 133 volume raction o nanoparticles (φ) is varied within the range o 0 < φ < was investigated [16]. It was ound that the increasing the nanoparticles volume ractions augments the drag coeicient. Moreover, pressure coeicient increases by increasing the solid volume raction or sides where pressure gradient is inverse but or sides where the pressure gradient is avourable the pressure coeicient decreases. The present investigation had been motivated by increased interest and research in potential improvements in heat transer characteristics using nanoluids. Eort has been made to investigate numerically the steady low o nanoluid and heat transer characteristics under the inluence o both the standard thermal or a range o Reynolds numbers (10 Re 40), and particle volumetric concentrations ranging rom 0% to 5%. Problem statement, governing equations, and boundary conditions The system here consists o a 2D ininitely long circular cylinder having a diameter D t. It is exposed to a constant ree stream velocity o U at a uniorm temperature o T at the inlet. The nanoparticles are assumed to be uniorm shape and size. In addition, we have assumed that nanoparticles are in thermal equilibrium state and lowing at the same velocity. Flow coniguration is shown in Figure 1. Fig. 1. Schematic o the unconined low past a circular cylinder Governing equations and boundary conditions The governing partial dierential equations here are the Navier-Stokes and energy equations in two dimensions and steady state nanoluid low around a circular cylinder are given blow: U V 0 X Y 2 U U P U V X Y X 1 Re v U U v X Y n 3 V V P U V X Y Y 1 Re vn V V v X Y 4

4 134 Metall. Mater. Eng. Vol 23 (2) 2017 p U 1 n V X Y Re Pr X Y 5 with the ollowing correlations: u v x y p v U Dt U ; V ; X ; Y ; P ; Pr ; Re, U U D D U v 2 t t n where U and V are the velocity components along X and Y axes, T denotes the temperature, P is the pressure, ρ is the density, μ the dynamic viscosity. The subscript n stands or nanoluid, the subscript stands or base luid and the subscript s stands or solid nanoparticles. The thermophysical properties taken rom literature [12], or the base luid and copper oxide (at 300 K) are shown in Table 1. Table 1. Thermo-physical properties o the base luid and the Cu nanoparticles Property Water Copper C p (J kg -1 K-1 ) ρ(kg m -3 ) k(w m -1 K) The eective density, the thermal diusivity, the heat capacitance, the eective dynamic viscosity and the eective thermal conductivity o the nanoluid are calculated using the ollowing expressions: 1 6 n s C p 1 C p C p 7 n s n k n C p n 8 n k n k b k s k 2 k ks k 2k k k s 2 10 s where φ is the solid volume raction.

5 Bouakkaz et al. - Numerical Investigation o Fluid Flow and Heat Transer Around 135 Boundary conditions The dimensionless boundary conditions or the low across a rotating circular cylinder can be written as (Figure1): The let-hand arc is the inlow section or upstream section, where there is a Dirichlet-type boundary condition or the Cartesian velocity components: V = 0 and θ = 0 11 The right-hand arc represents the outlow boundary, where it is considered that the diusion lux in the direction normal to the exit surace is zero or all variables: U V 0 X X X 12 Finally, the dimensionless peripheral or tangential velocity is prescribed on the surace o the cylinder, along with a no-slip boundary condition: ( U 0; V 0), 1( oruhf ); 1( orcwt ) n s 13 Here, in case o CWT, non-dimensional temperature is given as θ = T T while T W T or UHF, the non-dimensional temperature is given as θ = T T, where ns is the (q w D/k) normal unit direction vector away rom the cylinder surace. Numerical details The steady, laminar, segregated solver was employed here to solve the incompressible low on the collocated grid arrangement. Semi implicit method or the pressure linked equations (SIMPLE) was used to solve Navier-Stokes and energy equations or above noted boundary conditions. Second order upwind scheme is used to discretize the convective terms o momentum equations, whereas the diusive terms are discretized by central dierence method. A convergence criterion o 10-8 is used or continuity, and x-y components o momentum equations; or energy equation, the criteria o convergence was Table 2. Eect o grid number on averaged Nusselt number at Re=40, Pr=4.76 (φ=0.05) Mesh Cells Nt h Dt D t Nu M M M Domain independence study The mesh used or all the two-dimensional computations consisted o quadrilateral cells and nodes. The cylinder (o diameter D t ) resides in a computational domain whose outer edges are located at a distance o H rom the center

6 136 Metall. Mater. Eng. Vol 23 (2) 2017 p o the cylinder (Figure 1). There are N t points in the circumerential direction on the cylinder surace and the radial thickness o the irst layer o cells (i.e., cells attached to the wall) is h Dt. In this study, ollowing literature data [5, 6], the computational domain extends 40 times the diameter o the cylinder in all directions. The grids sensitivity analysis is perormed or Re=40 and φ=0.05. Table 2 lists the details or the meshes that were employed. As a Regarding the inluence o the number o grid points on the average Nusselt number on the wall o cylinder, it was decided to carry out the computations in this work with mesh M2. Results and discussion Comparison with other results The irst step was to validate the problem set-up, the choice o numerical methods and mesh attributes by comparing results rom our numerical simulations with results obtained rom the literature. The outcomes included in the comparison were the mean Nusselt number. Table 3. Comparison o Nu number computed in the present study with literature data (Pr = 0.7) UHF CWT Paramane et al. [6] Present study Relative error (%) Re= Re= Paramane et al. [8] Present study Relative error (%) Re= Re= Streamlines pattern The streamlines around cylinder are compared between base luid and nanoluid (φ=0.05) in igure 2 at Reynolds number o 20 and 40 at UHF B.C. For high Reynolds number, the recirculation bubble becomes big and strong at the downstream side o the cylinder or both base luid and nanoluid. However, in nanoluid the center o bubbles is slightly pushed away rom the surace o the cylinder comparing with base luid. Isotherm patterns The isotherms proiles around the rotating cylinder or Reynolds number o 40 or UHF B.C are compared between base luid and nanoluid (φ=0.05) in Figure 3. Clearly, the temperature distribution contours or base luid are overlaid with that or nanoluid. This can be explained as the addition o solid particles to the base luid increases the Reynolds number o nanoluid. Hence, a higher capacity o transerring the heat rom the cylinder. It is obvious rom Figure 3 that the isotherms have maximum density close to the ront surace o the cylinder; this indicates high values o the local Nusselt number near the ront stagnation point on the ront surace as compared to other points on the cylinder surace.

7 Bouakkaz et al. - Numerical Investigation o Fluid Flow and Heat Transer Around 137 (a) Fig. 2. Streamlines contours or the low around the cylinder (solid line reers to base luid and dashed line reers to nanoluid with solid volume raction or UHF B.C. at (a) Re=20, (b) Re=40 (b) Fig. 3. Temperature contours or the low around the cylinder (solid line reers to base luid and dashed line reers to nanoluid with solid volume raction 0.05) or UHF B.C. at Re=40 Local Nusselt number Figure 4 shows the variation o local Nusselt number (Nu) on the surace o the cylinder with increase in Re or various volume raction φ. When the solid concentration increases the thermal conductivity improves and consequently the local Nusselt number. Additionally, the thermal boundary layer is decreased by any increase in solid volume raction. Thereore, the local Nusselt number is enhanced by any increasing in solid volume raction (φ).

8 138 Metall. Mater. Eng. Vol 23 (2) 2017 p Fig. 4. Local Nusselt number variation at various solid volume ractions or varying values o Reynolds number and rotation rate, UHF B.C On the other hand, or all Re, the variation o Nusselt ound to be symmetrical at ϕ = 180. The value o the local Nu number is maximum on the ront (ϕ =0) and minimum on the rear (ϕ = 180 ) side o the cylinder. Also, at Re=40, a kink is observed in the values o local Nusselt number. It can be explained on the basis that higher Reynolds number results in lager recirculation region. Table 4 presents the dierence due to adding solid nanoparticles raction in Nu. As expected, the table shows that the values o Numax or Numin is greater or UHF boundary condition. Table 4. Local Nusselt number comparison Re=40 Nu max Nu max Dierence Nu min Nu min Dierence UHF CWT UHF-CWT UHF CWT UHF-CWT Averaged Nusselt number The average Nusselt number variation is presented in Figure 5, or the solid volume raction varying rom 0 to 0.05 in the steady regime. This igure indicates that the averaged Nusselt number increases linearly with increasing solid volume raction o nanoparticles (φ) at dierent Reynold numbers. This can be explained as when Re number increases the inertia o low increases thus increasing the heat transer. The eect o Reynold numbers also increases with increase in volume raction number (the Reynold and Prandtl numbers o nanoluids can be expressed as): C k 14 n n P, n Ren Re ; Prn Pr n CP, kn

9 Bouakkaz et al. - Numerical Investigation o Fluid Flow and Heat Transer Around 139 Further, the UHF boundary condition yields higher values o the average Nusselt number. Fig. 5. Variation o average Nusselt number at various solid volume ractions or varying values o Reynold numbers Fig. 6. Average Nusselt number variation or 0 φ 5 at UHF (Solid lines) and CWT (Dashed lines) Conclusions The present study ocuses on the unconined laminar low o nanoluid and heat transer characteristics around a circular cylinder under the inluence o both the thermal boundary conditions i.e. UHF and CWT in the steady regime. The illustrative streamline patterns and isotherm patterns are presented and examined or the above range o conditions. It was showed that at a given Reynolds number, local and average Nusselt numbers were enhanced by adding nanoparticles to base luid. Moreover, the UHF boundary condition yields higher values o the average Nusselt number.

10 140 Metall. Mater. Eng. Vol 23 (2) 2017 p Nomenclature C D Drag coeicient C L Lit coeicient D Drag orce N D t Diameter o the cylinder m L Lit orce N Nuaver Average Nusselt number Nu Local Nusselt number P Local pressure N/m 2 Re Reynolds number Pr Prandtl number T Free-surace temperature K U Free-stream velocity m s -1 u Stream-wise velocity m s -1 U Non-dimensional streamwise velocity (= u/u ) v Cross-stream velocity m s -1 V Non-dimensional cross-stream velocity (= v/ U ) Greek symbols φ Nanoparticle volume ractions ϕ Angular displacement rom the ront stagnation point ϴ Non-dimensional temperature ν Kinematic viscosity m 2 s -1 Reerences [1] M. Hatami, M. Jaaryar, D. D. Ganji, M. Gorji-Bandpy: Int Commun Heat Mass Transer, 57, [2] M. Hatami, D. D. Ganji, M. Gorji-Bandpy: Case Studies in Therm Eng, 4 (2014): [3] S. Sanitjai, R. J. Goldstein: Int J Heat Mass Transer, 47 (2004) [4] R. P. Bharti, R. P. Chhabra, V. Eswaran: Heat Mass Transer, 43 (2007) [5] M. Suyan, S. Manzoor, N. A. Sheikh: Arabian J Sci Eng, 39 (2014) [6] S. B. Paramane, A. Sharma: Int J Heat Mass Transer, 52 (2009) [7] R. Bouakkaz, K. Talbi, Y. Khelil, F. Salhi, N. Belghar, M. Ouazizi: Thermophysics and Aeromechanics, 21(2014) [8] S. B. Paramane, A. Sharma: Int J Heat Mass Transer, 53(2010) [9] H. C. Brinkman: J Chem Phys, 20 (1952) [10] H. Chang, C. S. Jwo, C. H. Lo, T. T. Tsung, M. J. Kao, H. M. Lin: Rev Adv Mater Sci, 10 (2005) [11] C. J. Ho, M. W. Chen, Z. W. Li: Int J Heat Mass Transer, 51 (2008) [12] M. S. Valipour, A. Z. Ghadi: Int Commun Heat Mass Transer, 38 (2011) [13] E. S. El-bashbeshy, T. G. Emam, M. S. Abdel-Wahed: Therm Sci, 19 (2015)

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