International Journal of Heat and Mass Transfer 54 (2011) 4376–4388 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmtNumerical investigation of effective parameters in convective heat transferof nanoﬂuids ﬂowing under a laminar ﬂow regimeEhsan Ebrahimnia-Bajestan a,⇑, Hamid Niazmand a, Weerapun Duangthongsuk b, Somchai Wongwises c,da Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iranb Department of Mechanical Engineering, South-East Asia University, Bangkok, Thailandc Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Laboratory (FUTURE), Department of Mechanical Engineering,King Mongkut’s University of Technology Thonburi, Bangmod, Bangkok 10140, Thailandd The Royal Institute of Thailand, Academy of Science, Sanam Sueapa, Dusit, Bangkok 10300, Thailand.a r t i c l e i n f o a b s t r a c tArticle history: This article presents a numerical investigation on heat transfer performance and pressure drop of nano-Received 3 December 2010 ﬂuids ﬂows through a straight circular pipe in a laminar ﬂow regime and constant heat ﬂux boundaryReceived in revised form 29 April 2011 condition. Al2O3, CuO, carbon nanotube (CNT) and titanate nanotube (TNT) nanoparticles dispersed inAccepted 29 April 2011 water and ethylene glycol/water with particle concentrations ranging between 0 and 6 vol.% were usedAvailable online 27 May 2011 as working ﬂuids for simulating the heat transfer and ﬂow behaviours of nanoﬂuids. The proposed model has been validated with the available experimental data and correlations. The effects of particle concen-Keywords: trations, particle diameter, particles Brownian motions, Reynolds number, type of the nanoparticles andNanoﬂuidsHeat transfer performance base ﬂuid on the heat transfer coefﬁcient and pressure drop of nanoﬂuids were determined and discussedPressure drop in details. The results indicated that the particle volume concentration, Brownian motion and aspect ratioNumerical study of nanoparticles similar to ﬂow Reynolds number increase the heat transfer coefﬁcient, while the nano-Thermal conductivity particle diameter has an opposite effect on the heat transfer coefﬁcient. Finally, the present study pro- vides some considerations for the appropriate choice of the nanoﬂuids for practical applications. Ó 2011 Elsevier Ltd. All rights reserved.1. Introduction thermophysical properties and ﬂow characteristics of nanoﬂuids [3–6]. However, this article is aimed at reviewing only the novel Common heat transfer ﬂuids such as oil, water and ethylene literature considering convective heat transfer of nanoﬂuids withglycol have inherently poor thermal conductivity compared to a numerical approach. These studies are brieﬂy described asmost solids. This problem is the primary obstacle to the high follows.compactness, light in weight and effectiveness of heat exchangers. Mirmasoumi and Behzadmehr  reported the effect of nano-In order to enhance the thermal conductivity of conventional heat particle diameter on convective heat transfer performance oftransfer ﬂuids, it has been tried to develop a new type of modern Al2O3/water nanoﬂuid ﬂowing under a fully developed laminarheat transfer ﬂuid by suspending ultraﬁne solid particles in base ﬂow regime numerically. In their study, a two-phase mixture mod-ﬂuids. In 1993, Masuda et al.  studied the heat transfer perfor- el was used. The results demonstrated that the heat transfer coef-mance of liquids with solid nanoparticles suspension. However, ﬁcient of the nanoﬂuid dramatically increases with decreasing thethe term of ‘‘nanoﬂuid’’ was ﬁrst named by Choi  in 1995, and diameter of nanoparticle. Moreover, the results also indicated thatsuccessively gained popularity. Because of the extensively greater nanoparticle diameter has no signiﬁcant effect on the skin frictionthermal conductivity and heat transfer performance of the nanoﬂ- coefﬁcient.uids as compared to the base ﬂuids, they are expected to be ideally Kalteh et al.  numerically studied forced convective heatsuited for practical applications. transfer of Cu/water nanoﬂuid inside an isothermally heated Since a decade ago, research publications related to the use of microchannel under a laminar ﬂow regime. An Eulerian two-ﬂuidnanoﬂuids as working ﬂuids have been reported both numerically model was used to simulate the heat transfer characteristic ofand experimentally. There are also some review papers that the nanoﬂuid. The results indicated that the heat transfer perfor-elaborate on the current stage in the thermal behaviours, mance increases with increasing Reynolds number as well as particle volume fraction. On the contrary, heat transfer enhance- ment increases with decreasing nanoparticle diameter. Finally, ⇑ Corresponding author. Tel.: +98 915 300 6795; fax: +98 511 876 3304. the results also showed that the pressure drop of nanoﬂuids is E-mail address: email@example.com (E. Ebrahimnia-Bajestan). slightly higher than that of base ﬂuids.0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijheatmasstransfer.2011.05.006
E. Ebrahimnia-Bajestan et al. / International Journal of Heat and Mass Transfer 54 (2011) 4376–4388 4377 Mirmasoumi and Behzadmehr  investigated the laminar indicated that the average Nusselt number of the nanoﬂuid in-mixed convection heat transfer of Al2O3/water nanoﬂuid ﬂowing creases with increasing particle concentration. In contrast, the re-through a horizontal tube numerically. A two-phase mixture mod- sults also showed that the bulk temperature of the nanoﬂuidel was used to describe the hydrodynamic and thermal behaviour decreases with increasing particle concentration.of the nanoﬂuid. The numerical results indicated that in the fully Akbarinia and Laur  presented the laminar mixed convec-developed region the particle concentration has insigniﬁcant ef- tion heat transfer of Al2O3/water nanoﬂuid ﬂows in a circularfects on the hydrodynamic parameters, while it has important ef- curved tube numerically. A two-phase mixture model and thefects on the thermal parameters. Moreover, the results showed control-volume technique were used to investigate the effect ofthat nanoparticle concentration is higher at the bottom of the test particle diameter on the hydrodynamic and thermal parameters.tube and at the near wall region. Their results indicated that the Nusselt number and secondary ﬂow Akbarinia  and Akbarinia and Behzadmehr  numerically decrease with increasing the particle diameter and uniform distri-investigated the fully developed laminar mixed convection of bution of nanoparticles is observed.Al2O3/water nanoﬂuid ﬂowing through a horizontal curved tube. Zeinali Heris et al.  numerically investigated the convectiveIn their studies, three-dimensional elliptic governing equations heat transfer of nanoﬂuid in a circular tube with constant wallwere used. The effects of the buoyancy force, centrifugal force temperature, employing a dispersion model. Their results showedand particle concentration on the heat transfer performance were that decreasing nanoparticle size and increasing nanoparticle con-presented. The results showed that the particle concentration has centration augment the heat transfer coefﬁcient.no direct effect on the secondary ﬂow, axial velocity and skin fric- Raisi et al.  carried out a numerical study on laminar con-tion coefﬁcient. However, when the buoyancy force is more impor- vective heat transfer of Cu/water nanoﬂuid inside a microchanneltant than the centrifugal force, the effect of particle concentration with slip and no slip boundary conditions. They investigated the ef-on the entire ﬂuid temperature can affect the hydrodynamic fect of different parameters such as Reynolds number, particle con-parameters. Moreover, the results also indicated that the buoyancy centration, and slip velocity coefﬁcient on the nanoﬂuid heatforce decreases the Nusselt number whereas the particle concen- transfer characteristics. The results indicated that the particle con-tration has a positive effect on the heat transfer enhancement centration and slip velocity coefﬁcient have signiﬁcant effects onand on the skin friction reduction. the heat transfer rate at high Reynolds numbers. Izadi et al.  studied the hydrodynamic and thermal behav- Ghasemi and Aminossadati  investigated the natural con-iours of an Al2O3/water nanoﬂuid ﬂowing through an annulus vective heat transfer of CuO/water nanoﬂuid inside an inclinedunder a laminar ﬂow regime. In their study, a single-phase model enclosure with top and bottom wall at different temperatures.was used for nanoﬂuid simulation. The results indicated that the The effects of Rayleigh number, inclination angle, and particle con-particle volume concentration has no signiﬁcant effect on the centration on heat transfer performance were studied. The resultsdimensionless axial velocity, but affects the temperature ﬁeld showed that the ﬂow pattern, temperature ﬁeld and heat transferand increases the heat transfer coefﬁcient. rate are affected by inclination angle at high Rayleigh numbers. He et al.  numerically studied the convective heat transfer Furthermore, it was found that the heat transfer rate is maximisedof a nanoﬂuid with TiO2 nanoparticles dispersed in water under at speciﬁc particle concentration and inclination angle.laminar ﬂow conditions. A single-phase model and combined Euler Zhou et al.  presented the lattice Boltzman method (LBand Lagrange methods were used to investigate the effects of vol- method) to study the microscale characteristics of the multicom-ume concentration, Reynolds number and aggregate size on the ponent ﬂow of nanoﬂuids. In this method, the computation domainconvective heat transfer and ﬂow behaviour of the nanoﬂuid. Their was separated into ﬁne mesh and coarse mesh regions, respec-results indicated that the nanoﬂuid signiﬁcantly enhances the Nus- tively. The multicomponent LB method was used in the ﬁne meshselt number, especially in the entrance region. Moreover, the region and the single-component LB method was applied in thenumerical results were consistent with experimental data. coarse mesh region. The results indicated that the present model Bianco et al.  investigated the heat transfer performance of can be used to predict the microscopic characteristics of thean Al2O3/water nanoﬂuid ﬂowing through a circular tube under a nanoﬂuid and the computational efﬁciency can be signiﬁcantlylaminar ﬂow regime numerically. A single-phase model and two- improved.phase model were used to determine the heat transfer coefﬁcient Although numerous papers are currently available on theof the nanoﬂuid. The results demonstrated that the heat transfer numerical study of laminar convective heat transfer of nanoﬂuids,performance increases with increasing Reynolds number as well there is no comprehensive study on different effective parametersas particle volume concentration. Moreover, differences in the in this ﬁeld. The effect of several parameters such as nanoparticleaverage heat transfer coefﬁcient between the single-phase and shape, based ﬂuid type and nanoparticle material are not consid-two-phase models were observed as approximately 11%. ered in literature. On the other hand, naturally the increase in heat Kumar et al.  used a single-phase thermal dispersion model transfer performance due to the nanoﬂuids is accompanied byto numerically investigate the thermal properties and ﬂow ﬁeld several undesirable effects such as an increase in pressure drop.of a Cu/water nanoﬂuid in a thermally driven cavity. The results Therefore, it needs to ﬁnd the suitable nanoﬂuid for optimum oper-indicated that the Grashof number, particle volume fraction and ation. No signiﬁcant attention is paid to ﬁnd some criteria for theparticle shape factor augment the average Nusselt number of choice of appropriate nanoﬂuids in different heat transfer applica-nanoﬂuids. tions. In the present study a modiﬁed single-phase model for pre- Talebi et al.  presented the numerical formulation to evalu- dicting the heat transfer performance of nanoﬂuids is proposedate the laminar mixed convection heat transfer of Cu/water nano- and a home-made FORTRAN computer program is developed. Theﬂuid ﬂowing through a square lid-driven cavity. They found that, at model has been validated against the measured data of Kim et al.a given Reynolds number, the particle concentration affects the  and the predicted values from Shah and London  for thethermal behaviour and ﬂow characteristic at larger Rayleigh num- base ﬂuid. The effects of particle concentration, mean particlebers. Moreover, the effect of particle concentration decreased with diameter, Reynolds number, Brownian motion, nanoparticle mate-increasing Reynolds number. rial and shape, and type of base ﬂuid on the heat transfer perfor- Shahi et al.  reported a numerical investigation to simulate mance of nanoﬂuids are then investigated in detail. Finally, somethe heat transfer performance of Cu/water nanoﬂuid ﬂowing guidelines related to choice of the appropriate nanoﬂuid for partic-through a square cavity under a laminar ﬂow regime. Their results ular applications are provided.
4378 E. Ebrahimnia-Bajestan et al. / International Journal of Heat and Mass Transfer 54 (2011) 4376–43882. Mathematical modelling thermal conductivity and viscosity of the nanoﬂuids according to the ﬁrst method. Normally, two different approaches can be used in predicting 0:0475745 0:42561the heat transfer performance of nanoﬂuids. One is the two-phase le ¼ À0:0001953 þ À T T2model, where solid particles are treated as a solid phase in the base ﬂuid, and the other is the single-phase model, where the presence for 20 C 6 T 6 80 C ð6Þof the nanoparticles is accounted for by introducing the effectivethermophysical properties for the nanoﬂuid. A single-phase model ke ¼ 0:65 þ 4:864 Â 10À7 T 3 for 22 C 6 T 6 52 C ð7Þis simpler to implement and requires less computational time, and where T is the temperature in Celsius. However, it should be men-therefore, adopted here to describe the heat transfer characteristics tioned that above correlations are valid only for Al2O3/water nano-of nanoﬂuids ﬂowing through a straight circular tube under con- ﬂuid containing 3 vol.% of suspended particles.stant wall heat ﬂux and laminar ﬂow regime, as shown in Fig. 1. As for the second method, the Vajjha et al.’s  model is takenOn the basis of this model, the governing equations are as follows. for viscosity with two parameters A and B, which are determined For continuity equation: according to the experimental data of Kim et al. .ZZ qe ~ Á d~ ¼ 0: V A ð1Þ le ¼ lf ðTÞA expðB/Þ ð8Þ This correlation applies for 20 °C 6 T 6 90 °C and 1% 6 / 6 10%,For momentum equation: with A = 0.9 and B = 10.0359.Z ZZ ZZ ZZ For thermal conductivity, the model presented by Koo and Kle- @~ V ~q ~ Á d~ ¼ À qe d8 þ V eV A p~ Á d~ þ n A le r~ Á d~ ~V A ð2Þ instreuer  and modiﬁed by Vajjha and Das  is employed. 8 @t The model consists of static thermal conductivity based on theFor energy equation: Maxwell’s theory and dynamic thermal conductivity to includeZ ZZ ZZ Brownian motion of nanoparticles. This model is expressed as @T ðqC p Þe d8 þ ðqC p Þe T ~ Á d~ ¼ V A ke rT Á d~ ~ A ð3Þ follows: 8 @t kp þ 2kf À 2ðkf À kp Þ/where ~ p, T, t, , ~ and ~ are the velocity vector, pressure, temper- V, A n ke ¼ kf þ ð5 Â 104 b/qf C p;f Þ kp þ 2kf þ ðkf À kp Þ/ature, time, volume, cross-sectional area vector and normal unit sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃvector, respectively. The effective thermophysical properties of jðT þ 273:15Þ Â f ðT; /Þ ð9Þthe nanoﬂuid indicated by the subscript e are density (q), thermal qp dpconductivity (k), dynamic viscosity (l), and heat capacity (Cp). Theseeffective properties are modelled as temperature dependent vari- ðT þ 273:15Þables using available correlations and experimental data as follows. f ðT; /Þ ¼ ð2:8217 Â 10À2 / þ 3:917 Â 10À3 Þ ðT 0 þ 273:15Þ Density: þ ðÀ3:0669 Â 10À2 / À 3:91123 Â 10À3 Þ ð10Þqe ð/; TÞ ¼ ð1 À /Þqf ðTÞ þ /qp ð4ÞHeat capacity: b ¼ 8:4407ð100/ÞÀ1:07304 ð11Þ ð1 À /ÞðqðTÞC p ðTÞÞf þ /ðqp C p Þp where j is the Boltzmann constant (1.381 Â 10À23 J/K), dp is theC p;e ð/; TÞ ¼ ð5Þ nanoparticle diameter (m), and T is the temperature (°C). T0 = 0 °C ð1 À /Þqf ðTÞ þ /qp is the reference temperature. The correlation is valid forwhere / is the volume fraction of the nanoparticles, and the sub- 25 °C 6 T 6 90 °C and the volume fractions between 1% and 10%scripts p and f indicate the nanoparticle and base ﬂuid, respectively. for Al2O3 nanoﬂuids . It should be mentioned that all thermo- Regarding the dynamic viscosity and thermal conductivity of physical properties of the base ﬂuid (lf, kf, Cp,f and qf) are consid-nanoﬂuids two different methods have been considered. In the ﬁrst ered as functions of temperature. For water as the base ﬂuid,method, available measured data of these properties in static con- density, heat capacity and thermal conductivity are obtained fromdition are used. However, in the second method, available models the curve-ﬁts applied to available data , while for dynamic vis-for dynamic viscosity and thermal conductivity of nanoﬂuids, cosity the following correlation is employed :where different effects such as base ﬂuid type, Brownian motions, lwater ¼ 0:00002414 Â 10½247:8=ðTþ133Þ ð12Þvolume concentration, and nanoparticle diameters are also in-cluded are employed. Clearly, these models are designed to accu- The above methods for effective viscosity (Eqs. (6) and (8)) haverately predict the heat transfer coefﬁcient. been compared with measured data of Kim et al.  for 3.0 vol.% In the present study, the measured data of Kim et al.  is used Al2O3/water nanoﬂuids, where reasonable agreements areto develop the following correlations for predicting the effective observed (Fig. 2). Similarly, the temperature variations of thermal L=2m Flow D= 4.57 mm D x q = const. Fig. 1. Flow geometry and numerical grid distributions.
E. Ebrahimnia-Bajestan et al. / International Journal of Heat and Mass Transfer 54 (2011) 4376–4388 4379conductivity according to Eqs. (7) and (9) have been compared walls. For the thermal ﬁeld, constant heat ﬂux of 60 W (2089.56 W/with the measured data of Kim et al.  as shown in Fig. 3. It m2) and the inlet temperature of 22 °C are employed correspond-can be seen that Eq. (9) over predicts the thermal conductivity as ing to the data of Kim et al. , while constant temperature gra-compared to the measured data, however it can predict the heat dient is applied at the outlet.transfer coefﬁcient more accurately as compared to Eq. (7) as will In order to simulate the nanoﬂuid ﬂow, pipe geometry withbe discussed later. 4.57 mm in diameter and 2 m long has been adopted according to the ﬂow geometry in the experimental work of Kim et al.  as shown in Fig. 1. The problem under investigation is steady, how-3. Solution methodology ever, in the numerical scheme the steady solution is obtained through sufﬁcient integrations in time. The governing equations In order to evaluate the heat transfer coefﬁcient of nanoﬂuids are solved numerically in a body-ﬁtted coordinate system using anumerically, the following assumptions are required. control-volume technique. The numerical solution is based on a As for boundary conditions for velocity ﬁled, a uniform velocity projection-type method which solves the ﬂow ﬁeld in two steps.proﬁle is assumed at the inlet, while zero gradients are applied to Firstly, an intermediate velocity ﬁeld is obtained using the avail-all hydrodynamic variables at the outlet, with no-slip condition at able pressure ﬁeld. Secondly, velocity and pressure corrections .0014 Measured data of Kim et al.  Eq. (6) .0012 Eq. (8) .0010 Viscosity (Pa.s) .0008 .0006 .0004 .0002 10 20 30 40 50 60 70 80 90 o Temperature ( C) Fig. 2. Comparison of the predicted viscosity using Eqs. (6) and (8) with the measured data. .90 Measured data of Kim et al.  Eq. (7) .85 Eq. (9) Thermal conductivity (W/mK) .80 .75 .70 .65 .60 10 20 30 40 50 60 70 Temperature (oC) Fig. 3. Comparison of the predicted thermal conductivity using Eqs. (7) and (9) with the measured data.
4380 E. Ebrahimnia-Bajestan et al. / International Journal of Heat and Mass Transfer 54 (2011) 4376–4388are calculated from a Poisson equation designed to satisfy the con- 4. Model validationtinuity equation. The numerical scheme was originally developedby Chorin  and improved further by Dwyer  as well as Ren- For validating the present numerical scheme, the axial varia-ksizbulut and Niazmand . tions of the local Nusselt number have been compared with the Moreover, extensive computations have been performed to experimental data of Kim et al.  and the results of Shah andidentify the number of grid points that produce reasonably grid London  as shown in Fig. 5. A laminar water ﬂow in a straightindependent results. In Fig. 4 the grid resolution effects on the axial circular pipe geometry, as mentioned above, has been consideredvariations of the centreline velocity (nondimensionalized with the under the constant heat ﬂux condition of 60 W (2089.56 W/m2)inlet velocity) and the heat transfer coefﬁcient for just four differ- at Reynolds number of 1620. The Shah and London  equa-ent mesh distributions are presented. It is clear that the grid sys- tion for the axial variations of the local Nusselt number istem of 41 Â 50 Â 150 points in respective directions of radial, expressed as:azimuthal, and axial adequately resolve the velocity and thermal 8 3:302xÀ1=3 À 1; Ã xÃ 6 0:00005ﬁelds with reasonable accuracy. Uniform grid spacing is used inthe azimuthal direction, while the expansion ratios of 1.15 and NuðxÞ ¼ 1:302xÀ1=3 À 0:5; Ã 0:00005 xÃ 0:0015 :1.02 are employed in the radial and axial directions. 4:264 þ 8:68ð103 xÃ ÞÀ0:506 expðÀ41xÃ Þ; xÃ 0:001 ð13Þ (a) 2.0 1.8 Dimensionless velocity r θ x 1.6 21 x 30 x 70 41 x 50 x 150 51 x 50 x 170 61 x 50 x 190 1.4 1.2 1.0 0.0 .5 1.0 1.5 2.0 x (m) (b) 2500 Heat transfer coefficient (W/m K) 2 2000 r θ x 21 x 30 x 70 41 x 50 x 150 1500 51 x 50 x 170 61 x 50 x 190 1000 500 0.0 .5 1.0 1.5 2.0 x (m)Fig. 4. Grid resolution effects on the axial variations of (a) dimensionless centreline velocity and (b) heat transfer coefﬁcient for 6.0 vol.% Al2O3/water nanoﬂuid at Reynoldsnumber of 1460.
E. Ebrahimnia-Bajestan et al. / International Journal of Heat and Mass Transfer 54 (2011) 4376–4388 4381 x=Dwhere xÃ ¼ Re Pr. Excellent agreements between the results can be Other numerical scheme validations for nanoﬂuids can be foundobserved in Fig. 5. in Ebrahimnia-Bajestan et al. , which are not repeated here for For the validation of the effective nanoﬂuid properties models, conciseness.the convective heat transfer of nanoﬂuid in a straight pipe has beenconsidered. Fig. 6 shows the axial variations of heat transfer coef-ﬁcient of Al2O3/water nanoﬂuid containing 3.0 vol.% of nanoparti- 5. Results and discussioncles for Reynolds number of 1460. The results indicate that thesecond method (Eqs. (8) and (9)) agrees better with the measured As shown in Fig. 6, the second method of nanoﬂuid propertiesdata of Kim et al.  as compared to the ﬁrst method (Eqs. (6) and models predicts the heat transfer coefﬁcient more accurately than(7)). This implies that the changes in thermal conductivity of nano- the ﬁrst method. In addition, the second method is more generalﬂuids at static condition cannot justify the enhancement in heat than the ﬁrst method, which is only valid for 3.0 vol.% Al2O3/water.transfer coefﬁcient of nanoﬂuids and a model, which adjusts the Therefore, the second method has been employed for the evalua-thermal conductivity to accurately estimate the heat transfer coef- tions of the effective thermal conductivity and viscosity in allﬁcient, is required. numerical computations reported here. Moreover, the effects of 30 Measured data of Kim et al.  Present model 25 Shah and London  20 Nusselt number 15 10 5 0 0.0 .5 1.0 1.5 2.0 x (m) Fig. 5. Comparison of the axial variations of the Nusselt number with available data in literature at Reynolds number of 1620. 2000 Measured data of Kim et al.  1800 Present model (Using Eqs. 6 7) Present model (Using Eqs. 8 9) Heat transfer coefficient (W/m K) 2 1600 1400 1200 1000 800 600 400 0.0 .5 1.0 1.5 2.0 x (m) Fig. 6. Comparison of the local heat transfer coefﬁcient with measured data of 3.0 vol.% Al2O3/water nanoﬂuid at Reynolds number of 1460.
4382 E. Ebrahimnia-Bajestan et al. / International Journal of Heat and Mass Transfer 54 (2011) 4376–4388several parameters on the convective heat transfer characteristics 5.2. The effect of nanoparticle diameterof nanoﬂuids will be examined in detail. The effect of nanoparticle diameter on the heat transfer perfor- mance of nanoﬂuid for Reynolds number of 1460 and heat ﬂux of5.1. The effect of nanoparticle concentration 2089.56 W/m2 is shown in Fig. 8. The results show that the nano- ﬂuid with smaller nanoparticle diameter slightly increases the heat Fig. 7 shows the effect of particle volume concentration on the transfer coefﬁcient as compared to the larger particle diameter,heat transfer coefﬁcient along the pipe for Reynolds number of especially at lower volume concentrations. In general, according1460 and heat ﬂux of 2089.56 W/m2. The results indicate that to Eq. (9) the nanoparticle diameter has a negative effect on thethe heat transfer coefﬁcient of nanoﬂuid increases with increasing thermal conductivity and consequently on the heat transferparticle volume concentration. According to Eq. (9), nanoﬂuids coefﬁcient.with higher particle concentrations have higher static and dynamicthermal conductivities, which in turn increase the heat transfer 5.3. The effect of Reynolds numbercoefﬁcient. For example, in the case of 6.0 vol.%, the local heattransfer coefﬁcient is about 22% larger than pure water at the Fig. 9 presents the effect of Reynolds number on the heatend of the pipe. transfer coefﬁcient along the pipe for Al2O3/water nanoﬂuid with 2000 water 1800 2.0 vol.% Heat transfer coefficient (W/m K) 4.0 vol.% 2 6.0 vol.% 1600 1400 1200 1000 800 600 Particle type : Al2O3 Re = 1460 400 0.0 .5 1.0 1.5 2.0 x (m) Fig. 7. Axial variations of heat transfer coefﬁcient for different particle volume concentrations of Al2O3/water nanoﬂuid at Reynolds number of 1460. 2000 dp = 20 nm dp = 100 nm 1800 2.0 vol.% 2.0 vol.% Heat transfer coefficient (W/m K) 6.0 vol.% 6.0 vol.% 2 1600 1400 1200 1000 800 600 Particle type : Al2O3 Re = 1460 400 0.0 .5 1.0 1.5 2.0 x (m) Fig. 8. Axial variations of heat transfer coefﬁcient for different particle diameters and concentrations of Al2O3/water nanoﬂuid at Reynolds number of 1460.
E. Ebrahimnia-Bajestan et al. / International Journal of Heat and Mass Transfer 54 (2011) 4376–4388 4383particle diameter of 20 nm. The results indicate that the heat trans- with the new nanoﬂuid thermal conductivity model. Fig. 10 com-fer coefﬁcient of nanoﬂuid increases with increasing Reynolds pares the axial variations of the heat transfer coefﬁcient of Al2O3/number. This is due to the fact that higher Reynolds numbers lead water nanoﬂuid with and without Brownian motion effects onto higher velocity and temperature gradients at the pipe wall. thermal conductivity model for various particle concentrations at Reynolds number of 1460 and particle diameter of 20 nm. It is clearly seen that the Brownian motion has signiﬁcant effects on5.4. The effect of Brownian motion of nanoparticles the heat transfer coefﬁcient of the nanoﬂuids. According to Eq. (9), the second term is related to the dynamicthermal conductivity and reﬂects the Brownian motion effects on 5.5. The effect of nanoparticle materialthe thermal characteristics of nanoﬂuids. In order to study the ef-fects of Brownian motion on the heat transfer performance of The nanoparticle material affects the nanoﬂuid properties andnanoﬂuids, Eq. (9) without the dynamic thermal conductivity term consequently is an important factor in heat transfer performance.is used to simulate the convective heat transfer. It means that the In order to study the effect of nanoparticle material, the CuO/waterclassical two-phase model of Maxwell is employed and compared nanoﬂuid is selected to compare with the results of the Al2O3/ 2000 dp = 20 nm 1800 Particle type : Al2O3 Heat transfer coefficient (W/m K) φ = 0 vol.% φ = 4.0 vol.% 2 1600 Re = 500 Re = 500 Re = 1000 Re = 1000 1400 Re = 1460 Re = 1460 1200 1000 800 600 400 0.0 .5 1.0 1.5 2.0 x (m) Fig. 9. Axial variations of heat transfer coefﬁcient for different Reynolds numbers and particle concentrations of Al2O3/water nanoﬂuid. 2200 φ = 2.0 vol.% φ = 6.0 vol.% 2000 with Brownian effect with Brownian effect without Brownian effect without Brownian effect Heat transfer coefficient (W/m K) 1800 2 1600 1400 1200 1000 800 Re = 1460 600 Particle type : Al2O3 400 0.0 .5 1.0 1.5 2.0 x (m) Fig. 10. Effects of Brownian motion on the local heat transfer coefﬁcient as a function of particle concentration for Al2O3/water nanoﬂuid at Reynolds number of 1460.
4384 E. Ebrahimnia-Bajestan et al. / International Journal of Heat and Mass Transfer 54 (2011) 4376–4388water nanoﬂuid. For the viscosity of the CuO/water nanoﬂuid, Eq. 5.6. The effect of base ﬂuid properties(8) is employed, where constants A = 0.9197 and B = 22.8539 areobtained following Vajjha et al. . The thermal conductivity of Another important factor in the heat transfer characteristics ofCuO/water is evaluated based on Eqs. (9) and (10), however, the nanoﬂuids is the type of base ﬂuid. In addition to water, a commonparameter b is determined from  as expressed below, which base ﬂuid consists of 60% ethylene glycol and 40% water (60% EG/is valid for 25 °C 6 T 6 90 °C and 1% 6 / 6 6%. water) by mass has also been considered. This kind of heat transfer ﬂuid is common in cold regions of the world because of its lowb ¼ 9:881ð100/ÞÀ0:9446 ð14Þ freezing point. The thermophysical properties of 60% EG/water as functions of temperature are obtained from  as follows: As shown in Fig. 11, CuO/water nanoﬂuids give higher convec-tive heat transfer coefﬁcients than the Al2O3/water nanoﬂuids. q60%EG=water ¼ À2:475 Â 10À3 T 2 À 0:35T þ 1090:93 ð15ÞFor example, the heat transfer coefﬁcient of 4.0 vol.% CuO/waternanoﬂuids is greater than that of the 6.0 vol.% Al2O3/water nanoﬂ- C p;60%EG=water ¼ 4:248T þ 3042:74 ð16Þuids. This is because of the fact that the thermal conductivity ofCuO nanoparticles is much larger than the thermal conductivity k60%EG=water ¼ À3:196 Â 10À6 T 2 þ 7:54 Â 10À4 T þ 0:34 ð17Þof Al2O3 nanoparticles. 2000 CuO Al2O3 2.0 vol.% 2.0 vol.% 1800 4.0 vol.% 4.0 vol.% Heat transfer coefficient (W/m K) 6.0 vol.% 6.0 vol.% 2 1600 1400 1200 1000 800 dp = 20 nm Re = 1460 600 0.0 .5 1.0 1.5 2.0 x (m) Fig. 11. Effects of particle type and particle concentration on the local heat transfer coefﬁcient at Reynolds number of 1460 and particle diameter of 20 nm. 2000 Water 1800 60%EG/Water Heat transfer coefficient (W/m K) 4.0 vol.% (Al2O3 - Water nanofluid) 2 1600 4.0 vol.% (Al2O3 - 60%EG/Water nanofluid) 1400 1200 1000 800 600 dp = 40 nm Re = 1460 400 0.0 .5 1.0 1.5 2.0 x (m) Fig. 12. Axial variations of heat transfer coefﬁcient for different base ﬂuids at Reynolds number of 1460 and particle diameter of 20 nm.
E. Ebrahimnia-Bajestan et al. / International Journal of Heat and Mass Transfer 54 (2011) 4376–4388 4385Table 1Properties of CNT/water and TNT/water nanoﬂuids. Nanoﬂuids Nanoparticles aspect ratio Nanoparticles concentration (vol.%) Viscosity (Pa s) Thermal conductivity (W/m K) k = a + bT + cT2 a b c CNT/water 100 0.0384 0.00308 51.88156 À0.35487 6.14 Â 10À4 TNT/water %10 0.6 0.0015 0.42548 6.4 Â 10À4 0 2000 0.0384 vol.% (CNT-Water) 1800 0.6 vol.% (TNT-Water) 2.0 vol.% (Al2O3-Water) Heat transfer coefficient (W/m K) 2 4.0 vol.% (Al2O3-Water) 1600 4.0 vol.% (CuO-Water) 1400 1200 1000 800 600 Re = 1460 400 0.0 .5 1.0 1.5 2.0 x (m) Fig. 13. Effects of particle shape on the local heat transfer coefﬁcient at Reynolds number of 1460. 3135:6 Table 2l60%EG=water ¼ 0:001 exp À 8:9367 ð18Þ Different nanoﬂuids ﬂow conditions simulated in the present study and their T þ 273:15 corresponding temperature increase, pressure drop, and pumping power.These correlations are valid for 0 °C 6 T 6 97 °C. Type of Re dp (nm) / D T DP Pump According to Vajjha and Das , Eqs. (8)–(11) are still applica- working ﬂuids (vol.%) (°C) (Pa) power (W)ble for the evaluation of viscosity and thermal conductivity of 60% Al2O3/60% EG/water 1460 20 4 0.56 43240 1.38EG/water base nanoﬂuids. 60% EG/water 1460 – – 0.68 26240 0.69 CNT/water 1460 Lp/dp 100 0.038 0.9 9625 0.16 In Fig. 12, the heat transfer coefﬁcients of Al2O3 nanoparticles in CuO/water 1460 20 6 1.05 8838 0.12both water and 60% EG/water base ﬂuids are compared. The results CuO/water 1460 20 4 1.52 3830 0.04indicate that the heat transfer characteristics of nanoﬂuids are TNT/water 1460 dp = 10, Lp = 100 0.6 1.8 2241 0.017strongly inﬂuenced by the type of the base ﬂuid. Al2O3/water 1460 100 6 2.05 2020 0.014 Al2O3/water 1460 40 6 2.06 2020 0.014 Al2O3/water 1460 20 6 2.08 2020 0.0145.7. The effect of nanoparticle shape CuO/water 1460 20 2 2.18 1670 0.011 Al2O3/water 1460 40 4 2.39 1416 0.008 Al2O3/water 1460 20 4 2.39 1417 0.008 It has been shown that nanoﬂuids containing nanoparticles Al2O3/water 1460 20 3 2.52 1188 0.007with a higher aspect ratio have better thermal properties [35,36]. Water 1620 – – 2.6 974 0.005For example, the cylindrical nanoparticles give higher thermal con- Al2O3/water 1460 20 2 2.72 996 0.005ductivity and heat transfer coefﬁcient than the spherical nanopar- Al2O3/water 1460 100 2 2.72 995 0.005 Al2O3/water 1460 40 2 2.73 995 0.005ticles. To study the effect of nanoparticle shape, two kinds of Water 1460 – – 2.78 869 0.004cylindrical nanoparticles, which are CNT and TNT are used and Al2O3/water 1000 20 4 3.44 936 0.004then compared with the nanoﬂuids with spherical nanoparticles. Water 1000 – – 4.08 572 0.002He et al.  studied the heat transfer performance of CNT/water Al2O3/water 500 20 4 6.91 438 0.0009 Water 500 – – 8.19 266 0.0004nanoﬂuid containing 0.1 wt.% (0.0384 vol.%) and TNT/water nano-ﬂuid containing 2.5 wt.% (0.6 vol.%) numerically and experimen-tally. They indicated that, at a given temperature, the shearviscosity of both nanoﬂuids decreases with increasing shear rate, water and TNT/water nanoﬂuids, respectively. They simulated theexhibiting a shear thinning behaviour. Moreover, the shear viscos- convective heat transfer of nanoﬂuids as both Newtonian andity approaches a constant minimum value at higher shear rate. The non-Newtonian ﬂuids. Their results showed that the heat transfermeasured viscosity did not show an important change versus share coefﬁcients based on the non-Newtonian model agree well withrate, more than the shear rates of 200 1/s and 500 1/s for the CNT/ the measured data. Furthermore, they indicated that, when the
4386 E. Ebrahimnia-Bajestan et al. / International Journal of Heat and Mass Transfer 54 (2011) 4376–4388nanoﬂuid is considered as Newtonian with the constant minimum On the other hand, because of the low aspect ratio of TNT (%10)value of viscosity, the heat transfer coefﬁcient has also reasonable and its lower thermal conductivity as compared with Al2O3, CuOagreement with the result of non-Newtonian model. and CNT, the heat transfer coefﬁcient of TNT/water nanoﬂuid is In the present work, the constant minimum value of viscosity lower than those. Yet, it should be mentioned that the concentra-presented by He et al.  was adopted as the effective viscosity. tion of TNT is lower than Al2O3, CuO. The TNT/water nanoﬂuid con-Similarly, the thermal conductivity of nanoﬂuids as a function of taining 0.6 vol.% nanoparticle shows approximately the same heattemperature is taken from  as listed in Table 1. transfer coefﬁcient as that of Al2O3/water nanoﬂuid containing Fig. 13 presents the comparison of axial heat transfer coefﬁ- 2 vol.%, which also indicates the considerable effect of nanoparticlecients for nanoparticles with different aspect ratios at Reynolds shape on the heat transfer characteristics of nanoﬂuids.number of 1460. The results show that the heat transfer coefﬁcient Thus far, several inﬂuential parameters on the heat transfer ofof the CNT/water nanoﬂuid is signiﬁcantly greater than that of the nanoﬂuids are investigated; yet the important question is whichother nanoﬂuids, which can be attributed to its large aspect ratio nanoﬂuid is more appropriate for a speciﬁc application. In this arti-(100) as listed in Table 1. In addition to the nanoparticle shape, cle, considering a constant wall heat ﬂux condition, two importantthe higher thermal conductivity of CNTs compared with Al2O3 factors are considered as the criteria for the choice of proper nano-and CuO is the reason of substantial thermal characteristics ﬂuids. These factors are pressure drop and temperature differenceenhancement of CNT/water nanoﬂuids, even at low concentrations. along the pipe. For a constant wall heat ﬂux condition with a given 2000 Particle type : Al2O3 Re = 1460 dP = 20 nm 1800 2.6 1600 ΔP (Pa) ΔT ( C) o ΔT 2.4 1400 ΔP 1200 2.2 1000 0 1 2 3 4 5 6 Particle volume fraction (%)Fig. 14. Temperature differences and pressure drops for different particle volume concentrations of Al2O3/water nanoﬂuid at Reynolds number of 1460 and particle diameterof 20 nm. Particle type : CuO 2.6 8000 Re = 1460 dP = 20 nm 2.4 2.2 6000 ΔP (Pa) ΔT ( C) 2.0 o ΔT 1.8 ΔP 4000 1.6 1.4 2000 1.2 0 1 2 3 4 5 6 Particle volume fraction (%)Fig. 15. Temperature differences and pressure drops for different particle volume concentrations of CuO/water nanoﬂuid at Reynolds number of 1460 and particle diameterof 20 nm.
E. Ebrahimnia-Bajestan et al. / International Journal of Heat and Mass Transfer 54 (2011) 4376–4388 4387amount of heat transfer to the ﬂuid, the lower temperature differ- motion, particle diameter, particle shape, particle material andence along the pipe can be considered as an advantage in some type of base ﬂuid on the heat transfer performance of nanoﬂuidsapplications. On the other hand, lower pressure drop reduces the are examined in details. Major ﬁndings can be summarised aspumping cost. follows: In the view of these two criteria, all cases simulated in the pres-ent study are listed in Table 2, which have been sorted by pressure – The predicted heat transfer coefﬁcients based on the thermo-drop. It can be concluded from the table that almost all cases with physical properties of nanoﬂuids in a static condition are lowerlower pressure drops have higher temperature differences, which than the experimental data. This means that the static thermalalso implies that nanoﬂuids should be selected according to the conductivity increase is not the only reason of convective heatapplication requirements. transfer enhancement of nanoﬂuids. From Table 2 it is observed that considerable pressure drop are – A thermal conductivity model which considers the effect ofassociated with high particle concentration of nanoﬂuids, while Brownian motion of nanoparticles predicts the heat transfermuch less pressure drop has been reported in numerical studies coefﬁcient of nanoﬂuids more accurately as compared to theof [37,38] for similar ﬂow conditions. It must be emphasised that models based on the pure static conditions of the nanoﬂuids.the viscosity model, le ¼ lf ð1 À /ÞÀ2:5 , which has been used in – The particle volume concentration, Brownian motion and aspectthese studies produces much lower values for viscosity as com- ratio of nanoparticles similar to the ﬂow Reynolds numberpared to the present experimental data  and consequently increase the heat transfer coefﬁcient of nanoﬂuids, while theleads to relatively lower pressure drops. However, the applied vis- particle diameter has an opposite effect. Moreover, the heatcosity model in the present study (Eq. (8)) represents the experi- transfer characteristics of nanoﬂuids are strongly inﬂuencedmental data with reasonable accuracy and therefore, the by the type of both base ﬂuid and nanoparticle.resulting pressure drops are higher. – There are several parameters to select the proper nanoﬂuids for Another related issue to the pressure drop is the relative in- convective heat transfer of nanoﬂuids in pipes. These parame-crease in viscosity with respect to thermal conductivity as the ters are the amount of heat transfer enhancement, pump power,nanoparticle concentration increases. In general, the advantage of stability, cost, toxicity and chemical corrosion of pipe wall. Also,the nanoﬂuids for the heat transfer applications is directly related there are some other restrictions in the special applicationsto the amount of the thermal conductivity increase, leading to the such as low freezing temperature nanoﬂuids as the anti-refrig-heat transfer enhancement, to the amount of the viscosity increase erant ﬂuids in cold region.associated with higher pressure drops. For the nanoﬂuids used inthe present study, the viscosity of the base ﬂuid increases fasterthan its thermal conductivity as nanoparticle concentration in- Acknowledgementscreases, and therefore, the heat transfer enhancements come atthe expense of relatively considerable pressure drop. The authors wish to thank Ferdowsi University of Mashhad Considering Table 2, the temperature increase along the pipe (Iran), South-East Asia University (Thailand), King Mongkut’s Uni-and the pressure drop behave in an opposite manner. In Figs. 14 versity of Technology Thonburi (Thailand) for the valuable supportand 15 these parameters are plotted versus the particle volume in the present study. The fourth author would like to acknowledgefraction to see if an optimum nanoparticle concentration for a spe- the Thailand Research Fund and the National Research Universityciﬁc application can be identiﬁed. Fig. 14 shows the Al2O3 nanopar- Project for ﬁnancial supporting.ticles in water with particle diameter of 20 nm and Reynoldsnumber of 1460. From this ﬁgure, the optimum choice for the ReferencesAl2O3/water nanoﬂuid is the volume fraction of about 4 vol.%,which has more reasonable temperature increase and pressure  H. Masuda, A. Ebata, K. Teramae, N. Hishinuma, Alteration of thermal conduc- tivity and viscosity of liquid by dispersing ultra-ﬁne particles (dispersion ofdrop. 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