Research Article Heat Transfer Enhancement and ...

Research ArticleHeat Transfer Enhancement and HydrodynamicCharacteristics of Nanofluid in Turbulent Flow Regime

Mohammad Nasiri-lohesara

Department of Mechanical Engineering, Babol University of Technology, Shariati Street, Babol 47148-71167, Iran

Correspondence should be addressed to Mohammad Nasiri-lohesara; [email protected]

Received 19 September 2014; Accepted 15 January 2015

Academic Editor: Guobing Zhou

Copyright © 2015 Mohammad Nasiri-lohesara.This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

Turbulent forced convection of 𝛾-Al2O3/water nanofluid in a concentric double tube heat exchanger has been investigated

numerically using mixture two-phase model. Nanofluids are used as coolants flowing in the inner tube while hot pure water flowsin outer tube. The studies are conducted for Reynolds numbers ranging from 20,000 to 50,000 and nanoparticle volume fractionsof 2, 3, 4, and 6 percent. Results showed that nanofluid has no effects on fully developed length and average heat transfer coefficientenhances with lower slope than wall shear stress. Comparisons with experimental correlation in literature are conducted and goodagreement with present numerical study is achieved.

1. Introduction

With progresses of technology heat transfer augmentationis one of the most challenges for developing Hi-tech indus-tries.

Application of additives to liquids is oneway of enhancingheat transfer. Augmenting of fluid thermal conductivity is themain purpose in improvement of the heat transfer character-istic of liquids.

Recently progress inmaterial engineering and developingnew technologies cause the basis of producing nanosizedparticles. Masuda et al. [1] introduced the liquid suspensionof nanosized particles and thenChoi [2] for the first time pro-posed the name of nanofluid to this suspension. Nanofluidschange the thermal and hydraulic feature of base fluids andcause enormous heat transfer enhancement.

Many researcher investigated the thermophysical proper-ties of nanofluid [3, 4]. But research about the forced convec-tion of nanofluids is important for the practical application ofnanofluids in heat transfer devices. For this purpose differentpapers focused on the nanofluids convection experimentallyand numerically.

Pak and Cho [5] investigated experimentally the convec-tive heat transfer inside a circular tube. They investigated theconvective heat transfer of 𝛾-Al

2O3(13 nm)/water and TiO

2

(27 nm)/water nanofluids in the turbulent flow regime. Con-stant wall heat flux boundary condition was considered in theanalysis. It was indicated that the heat transfer enhancementobtained with 𝛾-Al

2O3particles is higher than that obtained

with TiO2particles. They proposed a new correlation for

Nusselt number.Li and Xuan [6] presented experimental study to inves-

tigate the heat transfer coefficient and friction factor ofCu/water nanofluid in both laminar and turbulent flowregimes up to 2% volume concentration. Constant wall heatflux boundary condition was exposed and observed Nusseltenhancements up to 60% with 2% volume concentration. Itwas seen that the heat transfer coefficient enhancement ratio(heat transfer coefficient of nanofluid divided by the heattransfer coefficient of base fluid) increases with increasingReynolds number.

Maıga et al. [7] numerically studied laminar and turbu-lent force convection inside a circular tube under constantwall heat flux boundary condition. They used single-phaseassumption and simulate the nanofluids of Al

2O3/water and

Al2O3/ethylene glycol, showing that the wall shear stress and

heat transfer enhance with increasing volume fraction whilethe latter nanofluid showed better heat transfer enhancementin identical Reynolds number and volume fraction.

Hindawi Publishing CorporationJournal of EnergyVolume 2015, Article ID 814717, 6 pageshttp://dx.doi.org/10.1155/2015/814717

2 Journal of Energy

Bianco et al. considered the laminar [8] and turbulent [9]flow of Al

2O3/water nanofluid under constant and uniform

heat flux at the wall. They analyzed the problem by usingboth single- and two-phase models. The results showed heattransfer enhances with increasing particles volume concen-tration and Reynolds number and it showed that two-phasemodels for the simulation of nanofluid are satisfactory withcomparing of experimental data.

In this study turbulent heat transfer and hydrodynamiccharacteristic of 𝛾-Al

2O3/water nanofluid have been investi-

gated usingmixture two-phase model. Nanofluid flows in theinner tube while hot pure water flows in the outer tube. Theanalyses are conducted for different Reynolds numbers andvolume fractions ranging from 20,000 to 50,000 and 2, 3, 4,and 6 percent, respectively. For validation of the numericalsolution, the results are compared with Pak and Cho [5]correlation.The aim of this study is to addmore contributionto turbulent convection heat transfer using nanofluid.

2. Physical Model and Mathematical Modelling

Figure 1 shows the considered configuration cross-sectionconsisting of the double tube counterflow heat exchangerwith a length of 0.65m and with inner and outer diameterof 0.01m and 0.015m, respectively. Nanofluids that enterthe inner tubes are composed of 𝛾-Al

2O3/water with mean

particle diameter of 20 nm. Table 1 shows the thermophysicalproperties of base fluid and nanoparticle.

Nanofluid thermophysical properties play important rolein accuracy of the results. For density of nanofluids thefollowing equation has been used [5]:

𝜌eff = (1 − 𝜙) 𝜌𝑏𝑓 + 𝜙𝜌𝑝. (1)

Also specific heat of nanofluid is achieved by the followingequation [10]:

𝑐𝑝eff =

(1 − 𝜑) (𝜌𝑐𝑝)𝑏𝑓+ 𝜑 (𝜌𝑐

𝑝)𝑝

(1 − 𝜑) 𝜌𝑏𝑓+ 𝜑𝜌𝑝

. (2)

Chon et al. [11] proposed a correlation for thermal conductiv-ity. Correlation equation (2), except the volume fraction andparticles diameter, considers the temperature and Brownianmotion which is defined as follows:

𝑘eff𝑘𝑓

= 1 + 64.7 × 𝜙0.746

× (𝑑𝑏𝑓

𝑑𝑝

)

0.369

× (𝑘𝑝

𝑘𝑓

)

0.746

× Pr0.9955 × Re1.2321,

(3)

where Prandtl and Brownian Reynolds numbers areexpressed as follows:

Pr =𝜇

𝜌𝑓𝛼𝑓

, Re =𝜌𝑓𝑘𝑏𝑇

3𝜋𝜇2𝐿𝑓

, (4)

Table 1: Thermophysical properties of material under considera-tion.

Materials Density (kg/m3)Thermal

conductivity(W/mK)

Specific heat(J/kgK)

Water 1000 0.6 4179𝛾-Al2O3 3880 36 773

Figure 1: Geometrical configuration for present study.

where 𝐿𝑓is the base fluid mean free path (0.17 nm for water)

and 𝜇 is temperature-dependent viscosity of the base fluidwhich is defined as

𝜇 = 𝐴 × 10𝐵/(𝑇−𝐶)

. (5)

The constants𝐴, 𝐵, 𝐶 for water are equal to 2.414 ∗ 10−5, 247,and 140, respectively.

One equation for effective dynamic viscosity of nanofluidis defined as

𝜇nf𝜇𝑏𝑓

= 123𝜙2+ 7.3𝜙 + 1. (6)

Equation (6) was obtained by [7] with cure fitting based onexperimental data of Wang et al. [12].

Mixture model is used for modelling of nanofluid. Thismodel solves continuity, momentum, and energy equationsfor the mixture as well as the volume fraction equation forthe secondary phase and algebraic expression for the relativevelocities (slip velocities). With neglecting dissipation andpressure work and for steady state the governing equationsfor this model are expressed as follows.

Continuity equation:

∇ ⋅ (𝜌eff��mix) = 0. (7)

Momentum equation:

∇ ⋅ (𝜌eff��mix��mix) = −∇𝑃 + ∇ ⋅ (𝜇eff (∇��mix + ∇��mix𝑇))

+ ∇ ⋅ (

𝑛

∑

𝑘=1

𝜙𝑘𝜌𝑘��𝑑𝑟,𝑘

��𝑑𝑟,𝑘

) .

(8)

Journal of Energy 3

Energy equation:

∇ ⋅

𝑛

∑

𝑘=1

(𝜙𝑘𝑉𝑘(𝜌𝑘𝐸𝑘+ 𝑃)) = ∇ ⋅ (𝑘eff∇𝑇) . (9)

Volume fraction:

∇ ⋅ (𝜙𝑝𝜌𝑝��mix) = −∇ ⋅ (𝜙𝑝𝜌𝑝��𝑑𝑟,𝑝) , (10)

where ��𝑑𝑟,𝑘

= ��𝑘− ��mix is the drift velocity for the secondary

phase and it is related to slip velocity by the followingequation:

��𝑑𝑟,𝑝

= ��𝑝𝑓−

𝑛

∑

𝑘=1

𝜙𝑘𝜌𝑘

𝜌𝑚

��𝑓𝑘. (11)

Manninen et al. [13] proposed an equation for calculating slipvelocity equation (13). For determining the drag coefficientSchiller and Naumann [14] equation is used from (14):

��𝑝𝑓=

𝜌𝑓𝑑2

𝑝

18𝜇𝑞

⋅(𝜌𝑝− 𝜌mix)

𝑓drag𝜌𝑝𝑎, (12)

𝑓drag = {1 + 0.15Re0.687, Re ≤ 1000,0.0183Re, Re ≥ 1000,

(13)

where

Re𝑝=𝑉mix𝑑𝑝

]eff. (14)

From (13) the acceleration is given as

𝑎 = 𝑔 − (��mix ⋅ ∇) ��mix. (15)

Standard 𝑘-𝜀 two-equation eddy-viscosity model is usedfor closing the above governing equations. This model isproposed by Lauder and Spalding [15] and it is based on thesolution of equations for turbulent kinetic energy 𝑘 and theturbulent dissipation rate 𝜀. Their equations can be expressedas follows:

∇ ⋅ (𝜌mix𝑉mix𝑘) = ∇ ⋅ (𝜇𝑡,mix

𝜎𝑘

∇𝑘) + 𝐺𝑘,mix − 𝜌mix𝜀,

∇ ⋅ (𝜌mix𝑉mix𝜀) = ∇ ⋅ (𝜇𝑡,mix

𝜎𝜀

∇𝜀) +𝜀

𝑘(𝑐1𝐺𝑘,mix − 𝑐2𝜌mix) ,

(16)

where subscript of mix, indicating mixture and turbulentkinetic generation, is expressed as follows:

𝐺𝑘,mix = 𝜇𝑡,mix (∇𝑉mix + (∇𝑉mix)

𝑇

) . (17)

With constant values of 𝑐1= 1.44, 𝑐

2= 1.92, 𝑐𝜇 = 0.09, 𝜎

𝜀=

1.3, 𝜎𝑘= 1.

The above equations are solved for the following bound-ary conditions. At inner tube inlet uniform velocity andtemperature profile for 𝑇in = 298K are assumed. Pure

Re10000 20000 30000 40000 50000 60000

50

100

150

200

250

300

Inner tube,145800 cellsInner tube, 238000 cells

Inner tube, 315000 cellsInner tube, 396000 cells

Nu a

veFigure 2: Different grids for independency of solution.

water enters in the annulus with uniform and constantvelocity and temperature 𝑉in,an = 2.407m/s and 𝑇in,an =

360K, respectively. Inner tube is without thickness and outertube is thermally insulated. At tubes outlet fully developedconditions and on the walls, the nonslip conditions areconsidered. Moreover, a constant turbulent intensity, equal to1%, is imposed for both sides.

3. Computational Procedure and Validation

In the numerical solution, finite volumemethod is utilized forsolving the above equations. PRESTO and QUICK schemeis used for pressure correction and volume fraction, respec-tively. For other equations second order upwind is adoptedfor numerical solution.

The SIMPLE algorithm is used for pressure-velocitycoupling. Different nonuniform grids are tested to insureindependency of solution (Figure 2). 315000 cells for innertube is sufficient for the present study. Finermesh is used nearthe wall because of higher velocity and temperature gradient.Mean Nusselt number is calculated as follows:

Nu =ℎave𝑑

𝑘eff. (18)

In Figure 3 validation takes place with a correlation proposedbyDittus andBoelter [16] for pure fluid in turbulent pipe flow.

4. Results and Discussions

Results of numerical solution of convective heat transfer of𝛾-Al2O3/water nanofluid in a tube with two-phase models of

mixture and different volume concentration (2, 3, 4, and 6) atturbulent flow are presented.Themean diameters of 𝛾-Al

2O3

4 Journal of Energy

Re10000 20000 30000 40000 50000 6000060

80

100

120

140

160

180

200

220

240

260

280

300

Inner tube, Dittus-BoelterInner tube, present study

Nu a

ve

Figure 3: Grid validation for inner tube and annulus by correlationproposed by Dittus and Boelter [16].

nanoparticles are assumed to be 20 nm. Fully developed(hydrodynamically and thermally) turbulent flow is assumedfor inner tube for 𝐿/𝐷 = 65 [17].

Constant velocity inlet and turbulent intensity for purewater equal to 2.407m/s and 1% are assumed for annulus forall runs.

Figure 4 depicts centerline turbulent kinetic energy fordifferent nanoparticle volume fraction along the tube length.As shown in the figure, turbulent kinetic energy increasesby increasing nanoparticle volume fraction. Also, resultsshow fully developed region for 𝑋/𝐷 = 45 for differentnanoparticle volume fraction and pure water that provesnanofluid has no effects on fully developed length.

Heat transfer coefficient increases by augmentingnanoparticle volume fraction and Reynolds number, asdepicted in Figure 5(a). A comparison between present studyand experimental correlation proposed by Pak and Cho [5]showed that present study results are in good agreementwith this correlation. As reported in the figure maximumconvection coefficient can be achieved in maximumnanoparticle concentration and Reynolds number. Also, asshown in Figure 5(b), heat transfer coefficient enhances withan appropriate slope by increasing volume fraction of nano-particle.

Despite an enhancement in heat transfer coefficient byincreasing volume fraction, wall shear stress increases withincreasing nanoparticle concentration (Figure 6) as reportedby Bianco et al. [9].

Table 2 reports enhancing average heat transfer coeffi-cient ratio in comparison to wall shear stress ratio. By aug-menting nanoparticle volume fraction, convectionheat trans-fer coefficient increases by lower slope than averagewall shearstress. It seems that, for the highest concentration considered,

x

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Pure waterMix, Vf.% = 2

Mix, Vf.% = 4Kc

Figure 4: Centerline turbulent kinetic energy for different nanopar-ticle volume fraction at Re = 20000.

Table 2: Average heat transfer coefficient ratio in comparison towallshear stress ratio.

Nanoparticlevolume fraction (ℎnf/ℎ𝑓)(𝛾-Al2O3) (𝜏nf/𝜏𝑓)(𝛾-Al2O3)

0 1 12 1.07 1.353 1.12 1.634 1.18 26 1.32 3.02

𝜑 = 7%, the increase in wall shear stress about 3 times biggerthan base fluid (pure water) is achieved that proves usingnanofluid at higher volume fractions is not appropriate.

Figure 7 illustrates turbulent kinetic energy distributionalong the tube for fixed Reynolds number, Re = 20000,and different nanoparticle concentration. Because of highervelocity gradient in the vicinity of walls, the turbulent kineticenergy is high and then decreases by moving to center oftube. It is obvious that turbulent kinetic energy increases byaugmenting nanoparticle volume fraction.

Dimensional velocity profile at Re = 40000 and differentnanoparticle concentration is depicted in Figure 8 for afixed value of Reynolds number; velocity increases by aug-menting nanoparticle volume fraction. Effect of augmentingnanoparticle volume fraction on thermophysical propertiesof nanofluid is the reason for this increase in velocity.

5. Conclusions

In the present paper, turbulent forced convection of 𝛾-Al2O3/water nanofluid inside a double tube concentric heat

Journal of Energy 5

Vf.%0 1 2 3 4 5 6 7

10000

15000

20000

25000

30000

Re = 20000 (present study)Re = 30000 (present study)Re = 40000 (present study)Re = 50000 (present study)

Re = 20000 (Pak and Cho)Re = 30000 (Pakand Cho)Re = 40000 (Pakand Cho)Re = 50000 (Pakand Cho)

hav

e

(a)

Vf.%0 1 2 3 4 5 6 7

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

hnf/h

f

(b)

Figure 5: Effect of nanoparticle concentration on (a) average heattransfer coefficient and (b) heat transfer coefficient ratio.

exchanger was numerically investigated using mixture two-phase approaches. A comparison with experimental correla-tion proposed by [5] showed numerical results are in goodagreement with this correlation. The following results wereobtained.

(i) Nanofluid has no effects on fully developed lengthwith increasing nanoparticle concentration.

(ii) Heat transfer coefficient enhances by augmentingnanoparticle volume fraction as well as Reynolds

1

1.5

2

2.5

3

3.5

4

𝜏nf/𝜏

f

Vf.%0 1 2 3 4 5 6 7

Figure 6: Effect of nanoparticle concentration on average wall shearstress ratio.

Turb

kin

etic

ener

gy

0.070.06634110.06268210.05902320.05536420.05170530.04804630.04438740.04072840.03706950.03341050.02975160.02609260.02243370.01877470.01511580.01145680.007797890.004138950.00048

Pure water

2%

4%

Figure 7: Turbulent kinetic energy distribution along the tube fordifferent nanoparticle concentration (Re = 20000).

number. But, convection heat transfer coefficientincreases by lower slope than averagewall shear stress.

(iii) For a fixed value of Reynolds number, velocity profileincreases by augmenting nanoparticle volume frac-tion.

Notations

𝑘: Thermal conductivity, W/mK𝑘𝑏: Boltzmann’s constant

𝑑: Diameter, mℎ: Heat transfer coefficient, W/m2 KPr: Prandtl number, Pr = 𝜇𝑐

𝑝/𝑘

Re: Reynolds number, Re = 𝜌V𝑑/𝜇𝑇: Temperature, K𝑉: Velocity, m/s𝑃: Pressure, pa𝑔: Gravitational acceleration, m/s2.

6 Journal of Energy

V

r/D

0 1 2 3 4 5 6 7

−0.4

−0.2

0

0.2

0.4

Pure waterVf.% = 2

Vf.% = 4

Figure 8: Effect of nanoparticle concentration on fully developedvelocity profile for fixed Re = 40000.

Greek Letters

𝜑: Particle volume concentration𝜌: Fluid density, kg/m3𝜇: Fluid dynamic viscosity, kg/m s𝜏: Wall shear stress, Pa.

Subscripts

nf: Nanofluid𝑏: Base fluid𝑝: Particleeff: Effective properties.

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper.

References

[1] H. Masuda, A. Ebata, K. Teramae, and N. Hishinuma, “Alter-ation of thermal conductivity and viscosity of liquid by dispers-ing ultra-fine particles (dispersion of 𝛾-Al

2O3, SiO2, and TiO

2

ultra-fine particles),” Netsu Bussei, vol. 7, no. 4, pp. 227–233,1993.

[2] S. U. S. Choi, “Enhancing thermal conductivity of fluids withnanoparticles,” in Developments and Applications of Non-New-tonian Flows, ASME Publications FED-Vol. 231/MD-Vol. 66, pp.99–105, The American Society of Mechanical Engineers, NewYork, NY, USA, 1995.

[3] S. Lee, S.U. S. Choi, S. Li, and J. A. Eastman, “Measuring thermalconductivity of fluids containing oxide nanoparticles,” Journalof Heat Transfer, vol. 121, no. 2, pp. 280–289, 1999.

[4] X. Wang, X. Xu, and S. U. S. Choi, “Thermal conductivityof nanoparticle—fluid mixture,” Journal of Thermophysics andHeat Transfer, vol. 13, no. 4, pp. 474–480, 1999.

[5] B. C. Pak and Y. I. Cho, “Hydrodynamic and heat transfer studyof dispersed fluids with submicron metallic oxide particles,”Experimental Heat Transfer, vol. 11, no. 2, pp. 151–170, 1998.

[6] Q. Li and Y. Xuan, “Convective heat transfer and flow char-acteristics of Cu-water nanofluid,” Science in China, Series E:Technological Sciences, vol. 45, no. 4, pp. 408–416, 2002.

[7] S. E. B. Maıga, C. T. Nguyen, N. Galanis, and G. Roy, “Heattransfer behaviours of nanofluids in a uniformly heated tube,”Superlattices and Microstructures, vol. 35, no. 3–6, pp. 543–557,2004.

[8] V. Bianco, F. Chiacchio, O. Manca, and S. Nardini, “Numericalinvestigation of nanofluids forced convection in circular tubes,”Applied Thermal Engineering, vol. 29, no. 17-18, pp. 3632–3642,2009.

[9] V. Bianco, O. Manca, and S. Nardini, “Numerical investigationon nanofluids turbulent convection heat transfer inside acircular tube,” International Journal ofThermal Sciences, vol. 50,no. 3, pp. 341–349, 2011.

[10] K. Khanafer andK.Vafai, “A critical synthesis of thermophysicalcharacteristics of nanofluids,” International Journal of Heat andMass Transfer, vol. 54, no. 19-20, pp. 4410–4428, 2011.

[11] C. H. Chon, K. D. Kihm, S. P. Lee, and S. U. S. Choi, “Empiricalcorrelation finding the role of temperature and particle size fornanofluid (Al

2O3) thermal conductivity enhancement,”Applied

Physics Letters, vol. 87, Article ID 153107, pp. 1–3, 2005.[12] X. Wang, X. Xu, and S. U. S. Choi, “Thermal conductivity of

nanoparticle-fluid mixture,” Journal of Thermophysics and HeatTransfer, vol. 13, no. 4, pp. 474–480, 1999.

[13] M. Manninen, V. Taivassalo, and S. Kallio, “On the mixturemodel for multiphase flow,” Technical Research Center ofFinland 288, VTT Publications, 1996.

[14] L. Schiller and A. Naumann, “A drag coefficient correlation,”Zeitschrift des Vereines Deutscher Ingenieure, vol. 77, pp. 318–320, 1935.

[15] B.-E. Lauder and D.-B. Spalding, Lectures in MathematicalModels of Turbulence, Academic Press, London, UK, 1972.

[16] F. W. Dittus and L. M. K. Boelter, “Heat transfer in automobileradiators of the tubular type,” International Communications inHeat and Mass Transfer, vol. 12, no. 1, pp. 3–22, 1985.

[17] F. P. Incropera, D. P. DeWitt, T. L. Bergman, and A. S. Lavine,Fundamentals of Heat and Mass Transfer, Wiley, 6th edition,2006.

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