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 Β© 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 πΎ-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 πΎ-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 πΎ-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.
MaΔ±ga 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 πΎ-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 πΎ-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]:
πeff = (1 β π) πππ + πππ. (1)
Also specific heat of nanofluid is achieved by the followingequation [10]:
ππeff =
(1 β π) (πππ)ππ+ π (ππ
π)π
(1 β π) πππ+ πππ
. (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:
πeffππ
= 1 + 64.7 Γ π0.746
Γ (πππ
ππ
)
0.369
Γ (ππ
ππ
)
0.746
Γ Pr0.9955 Γ Re1.2321,
(3)
where Prandtl and Brownian Reynolds numbers areexpressed as follows:
Pr =π
πππΌπ
, Re =πππππ
3ππ2πΏπ
, (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 4179πΎ-Al2O3 3880 36 773
Figure 1: Geometrical configuration for present study.
where πΏπis the base fluid mean free path (0.17 nm for water)
and π is temperature-dependent viscosity of the base fluidwhich is defined as
π = π΄ Γ 10π΅/(πβπΆ)
. (5)
The constantsπ΄, π΅, πΆ for water are equal to 2.414 β 10β5, 247,and 140, respectively.
One equation for effective dynamic viscosity of nanofluidis defined as
πnfπππ
= 123π2+ 7.3π + 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:
β β (πeffοΏ½οΏ½mix) = 0. (7)
Momentum equation:
β β (πeffοΏ½οΏ½mixοΏ½οΏ½mix) = ββπ + β β (πeff (βοΏ½οΏ½mix + βοΏ½οΏ½mixπ))
+ β β (
π
β
π=1
πππποΏ½οΏ½ππ,π
οΏ½οΏ½ππ,π
) .
(8)
Journal of Energy 3
Energy equation:
β β
π
β
π=1
(ππππ(πππΈπ+ π)) = β β (πeffβπ) . (9)
Volume fraction:
β β (πππποΏ½οΏ½mix) = ββ β (πππποΏ½οΏ½ππ,π) , (10)
where οΏ½οΏ½ππ,π
= οΏ½οΏ½πβ οΏ½οΏ½mix is the drift velocity for the secondary
phase and it is related to slip velocity by the followingequation:
οΏ½οΏ½ππ,π
= οΏ½οΏ½ππβ
π
β
π=1
ππππ
ππ
οΏ½οΏ½ππ. (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):
οΏ½οΏ½ππ=
πππ2
π
18ππ
β (ππβ πmix)
πdragπππ, (12)
πdrag = {1 + 0.15Re0.687, Re β€ 1000,0.0183Re, Re β₯ 1000,
(13)
where
Reπ=πmixππ
]eff. (14)
From (13) the acceleration is given as
π = π β (οΏ½οΏ½mix β β) οΏ½οΏ½mix. (15)
Standard π-π 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 π and theturbulent dissipation rate π. Their equations can be expressedas follows:
β β (πmixπmixπ) = β β (ππ‘,mix
ππ
βπ) + πΊπ,mix β πmixπ,
β β (πmixπmixπ) = β β (ππ‘,mix
ππ
βπ) +π
π(π1πΊπ,mix β π2πmix) ,
(16)
where subscript of mix, indicating mixture and turbulentkinetic generation, is expressed as follows:
πΊπ,mix = ππ‘,mix (βπmix + (βπmix)
π
) . (17)
With constant values of π1= 1.44, π
2= 1.92, ππ = 0.09, π
π=
1.3, ππ= 1.
The above equations are solved for the following bound-ary conditions. At inner tube inlet uniform velocity andtemperature profile for πin = 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 πin,an = 2.407m/s and πin,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 =βaveπ
πeff. (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 ofπΎ-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 πΎ-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 πΏ/π· = 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 π/π· = 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 (βnf/βπ)(πΎ-Al2O3) (πnf/ππ)(πΎ-Al2O3)
0 1 12 1.07 1.353 1.12 1.634 1.18 26 1.32 3.02
π = 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 πΎ-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
πnf/π
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
π: Thermal conductivity, W/mKππ: Boltzmannβs constant
π: Diameter, mβ: Heat transfer coefficient, W/m2 KPr: Prandtl number, Pr = ππ
π/π
Re: Reynolds number, Re = πVπ/ππ: Temperature, Kπ: Velocity, m/sπ: Pressure, paπ: Gravitational acceleration, m/s2.
6 Journal of Energy
V
r/D
0 1 2 3 4 5 6 7
β0.4
β0.2
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
π: Particle volume concentrationπ: Fluid density, kg/m3π: Fluid dynamic viscosity, kg/m sπ: Wall shear stress, Pa.
Subscripts
nf: Nanofluidπ: Base fluidπ: Particleeff: Effective properties.
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper.
References
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