A Numerical Investigation of Turbulent Magnetic Nanofluid Flow inside Square Straight Channel

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1 A Nuerical Investigation of Turbulent Magnetic Nanofluid Flow inside Square Straight Channel M. R. Abdulwahab Technical College of Mosul, Mosul, Iraq Abstract A nuerical study using coputational fluid dynaics ethod with a single-phase approach has been presented in order to deterine the effects of the concentration of nanoparticles and flow rate on the convective heat transfer and friction factor in turbulent regie flowing through a square duct with Reynolds nuber range of Re using constant applied heat flux around the duct. The nanofluid used consisted of Fe 3O 4 agnetic nanoparticles with an average diaeter of 13 n dispersed in water with six volue fractions (0, 0.6, 0.8, 1, 1.5 and 2%). The results revealed that as volue fraction and Reynolds nuber increased, Nusselt nuber increased, and friction factor decreased as Reynolds nuber increased. Copyright All rights reserved. Keywords: Magnetic Nanofluid, Turbulent Fluid Flow, Convection Heat Transfer, Square Duct, Single Phase Flow 1.0 INTRODUCTION Nanotechnology has opened new challenges in various streas of fundaental science and engineering applications. The coon applied heat carrier fluids lie oil, water and ethylene glycol have a low theral conductivity copared to ost solids [1,2]. Iproving heat exchangers, changing boundary conditions and enhancing the therophysical properties of the fluid are soe effective ways to decrease energy consuption [3,4]. The first effort in establishing a solid-liquid ixture was by Maxwell [5,6], which was to increase the theral conductivity of the base fluid using icroeter or illieter size. This lead to so any probles lie fouling, erosion and high losses due to pressure drop [7,8]. A new generation of fluids has been introduced, nown as nanofluid and have been used in heat exchangers. The ters have been used first tie by Choi [9] in The new fluids consist of a base fluid (water) and dispersed nanoeter-sized particles (1-100 n) such as copper, aluinu and other oxides. An iproveent has been noticed in the theral properties of the base fluid when nanoparticles with a high theral conductivity have been ixed with the base fluid [3,10]. Xuan and Li [11] investigated experientally the convective heat transfer and flow characteristics for a CuO-water nanofluid flowing through a straight tube with a constant heat flux under lainar and turbulent flow conditions. The results of the experient showed that the suspended nanoparticles rearably enhanced the heat transfer perforance of the conventional base fluid, and their friction factor coincided well with that of the water. 44

2 Furtherore, they also proposed new convective heat transfer correlations for the prediction of heat transfer coefficients of the nanofluid for both lainar and turbulent flow conditions. Tsai et al. [12] investigated gold-deionized water nanofluid flowing in a conventional heat pipe with a diaeter of 6 and a length of 170. Their data showed that the nanofluid caused a significant reduction in the theral resistance of the heat pipe copared with deionized water at given concentrations. Moraveji and Hejazian [13] nuerically studied a fully developed turbulent of heat convection nanofluid flow inside a straight channel using CFD ethod without the influence of agnetic field with Reynolds nuber ranging between 3000 and They used agnetic nanofluid consisted of Fe3O4 as the nanoparticles with the average diaeter of 36 n and water as a base fluid with nanoparticles volue concentrations of 0.02, 0.1 and 0.6%. They proposed a correlation to estiate Nusselt nuber and friction factor, which was in good agreeent with the experiental wor. Forced convection heat transfer with turbulent nanofluid flow inside a tube was experientally studied by Sundar et al. [7]. The nanofluid used was agnetic nanoparticles Fe3O4 suspended in water with nanoparticles volue concentrations fro 0 to 0.6% and the range of Reynolds nuber fro 3000 to New correlation was proposed to estiate Nusselt nuber and friction factor. The results revealed that the heat transfer was enhanced by 30.93%. Heris et al. [14] nuerically analyzed lainar flow-forced convective heat transfer of Al2O3 water nanofluid in a triangular duct, where a constant wall teperature was applied to the triangle walls. Their results showed that the average Nusselt nuber increased with increasing nanoparticles concentration and decreased nanoparticles diaeter with increasing Reynolds nuber. In this paper, the odeling of 3D turbulent flow containing agnetic nanofluid with average nanoparticle diaeter of 13 n having different volue fractions was nuerically investigated using CFD tools (FLUENT) in a horizontal straight square duct. The essential target of this research is to exaine the effect of flow rate, nanofluid volue fraction and change of Reynolds nuber in the range fro 10 3 to 10 6 without the effect of agnetic field on the theral and flow field. 2.0 MATHEMATICAL MODELING In this wor, a 3D coputational fluid dynaics odel was developed for nanofluid turbulent flow inside three geoetries based on a single phase approach and steady state. The nanofluid as a single phase fluid with relatively different physical properties such as density, theral conductivity and viscosity was used. The fluid phase was assued to be as a continuity phase, and the governing equations (continuity, oentu and energy) are presented as follows: Conservation of ass: ( ) = 0 ρν (1) Conservation of oentu: 45

3 ( ρν ) = +.(τ ) p (2) Conservation of energy:.( ρvc T ) =.( λ T C ρν ) (3) p p 3.0 THERMOPHYSICAL PROPERTIES OF NANOFLUID The effective properties of the nanofluid are defined as follows [1]: Density: ρ = ( 1 φ) ρ + φρ (4) nf bf p Heat capacitance: C nf = (5) ( 1 ϕ ) Cbf + ϕcfe 3O4 where and are the density and specific heat of the nanofluid respectively. The theral conductivity and viscosity of nanofluid are coputed as follows [15]: Theral conductivity: nf = bf ( ϕ ) (6) Viscosity: ϕ µ nf = µ bf (1 ) (7) The turbulence odel that was proposed by Launder and Splading [16] was used. The odel introduces two new equations; one for the turbulent inetic energy and the other is for the turbulent dissipation rate. The two equations are expressed as the following for: µ t,.( ρv) =.( ) + G ρε (8) σ, µ t, ε.( ρv) =.( ) + ( C1G, C2ρε ) (9) σ where 2 ρ C t, = (10) ε µ µ G, T = µ ( V + ( V ) ) (11) t, 46

4 with C1 = 1.44, C2 = 1.92, Cµ = 0.09, σ = 1and ε = Physical odel A 3D square duct that has been exained in this study with w= 0.01 and L= 1.8 with the applied heat flux of 50 w c 2 is shown below. Figure 1: Geoetry of the present study 4.0 BOUNDARY CONDITIONS At the channel inlet, the profiles of unifor axial velocity, and teperature =293 were assued. At the channel exit section, the fully developed conditions were considered, i.e., all axial derivatives are zero. On the channel wall, the non-slip conditions and unifor heat flux were iposed, while both turbulent inetic energy and dissipation of turbulent inetic energy were equal to zero. 5.0 NUMERICAL METHOD IMPLEMENTATION AND VALIDATION The coputational fluid dynaic code FLUENT [17] was used to solve the proble. The governing equations (1)-(3) were solved by control volue approach. This ethod is based on the spatial integration of conservation equations over finite control volues. The conversion of the governing equations to a set of algebraic discretized equations resulting fro this spatial integration process was sequentially solved throughout the physical doain. FLUENT [17] solves the systes resulting fro the discretization schees using a nuerical ethod. In order to ensure the accuracy and consistency of nuerical results, several unifor grids have been subjected to an extensive testing procedure for each case considered. The results have shown that for the proble under consideration, the unifor grid appears to be satisfactory in ensuring the accuracy of the nuerical results, as well as their independency with respect to the nuber of nodes used.the results are successfully validated with the correlations reported for therally and hydraulically developed flow. 47

5 6.0 RESULTS AND DISCUSSIONS The results were obtained using a single phase approach for volue fraction of = 0,0.6,0.8,1,1.5 and 2% with the range of Reynolds nuber of 10000!"#! The average heat transfer coefficient and the average Nusselt nuber for turbulent flow were coputed using the following forulas [17]: q h = (12) T wall T b h D Nu = (13) where q, h, D,, $%&& '() * are the heat flux, average heat transfer coefficient, hydraulic diaeter, theral conductivity of the fluid, average wall teperature and bul teperature respectively. 6.1 Effect of Nanoparticle Volue Fraction on Nusselt Nuber Fig. 2 represents a plot of Nusselt nuber versus Reynolds nuber for various volue fractions of the nanoparticles. Figure 2: Effect of nanofluid concentrations and Reynolds nuber on average Nusselt nuber. It is obvious that increased Reynolds nuber and volue fraction of nanoparticles lead to the increase of the value of Nusselt nuber. According to Eq. 5, nanofluid with higher volue fraction has higher theral conductivities, which in turn increases the heat transfer coefficient. For exaple, in the case of 0.8% volue fraction and Reynolds nuber of 50000, the ean heat transfer coefficient is about 19.15% larger than the base fluid (pure water). The obtained 48

6 results are in good agreeent with Pa & Choi s correlation [18] for the prediction of Nusselt nuber ore than Gilinisi s correlation [19]. Figure 3: Coparison of coputed results with the correlations at 0.6% volue fraction Figure 4: Coparison of coputed results with the correlations at 0.8% volue fraction 49

7 6.2 Effect of Nanoparticle Volue Fraction on Friction Factor Fig. 5 shows the friction factor for pure water copared to Blasius forula [20]. It is obvious fro the figure that the friction factor for square channel decreased as Reynolds nuber increased. Figure 5: Coparison of coputed results of friction factor of pure water with the correlation of Blasius 7.0 CONCLUSIONS In this article, nuerical investigations were carried out to investigate the effect of flow rate and nanofluid concentration on the average Nusselt nuber and friction factor using coercial software. Iportant conclusions drawn fro this wor include: 1. The Nusselt nuber and the aount of heat transfer increase with the increasing of Reynolds nuber and volue concentration of nanoparticles. 2. Friction factor decreases as Reynolds nuber increases. 3. By applying the siulation results, an equation of Nusselt nuber prediction based on the diensionless nubers was correlated. REFERENCES [1] S. Kaaç, A. Prauanjaroenij, Review of convective heat transfer enhanceent with nanofluids, International Journal of Heat and Mass Transfer 52(13) (2009)

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