- Email: [email protected]
Experimental investigation of turbulent flow and convective heat transfer characteristics of alumina water nanofluids in fully developed flow regime
International Communications in Heat and Mass Transfer 39 (2012) 1272–1278
Contents lists available at SciVerse ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Experimental investigation of turbulent flow and convective heat transfer characteristics of alumina water nanofluids in fully developed flow regime☆ M.M. Heyhat a,⁎, F. Kowsary a, A.M. Rashidi b, S. Alem Varzane Esfehani a, A. Amrollahi b a b
Mechanical Engineering Department, University College of Engineering, University of Tehran, Tehran, Iran Nanotechnology Research Center, Institute of Petroleum Industry (RIPI), Azadi Complex, Tehran, Iran
a r t i c l e
i n f o
Available online 27 June 2012 Keywords: Nanofluids Convective heat transfer Pressure drop Turbulent flow Fully developed
a b s t r a c t In this paper the convective heat transfer and friction factor of the nanofluids in a circular tube with constant wall temperature under turbulent flow conditions were investigated experimentally. Al2O3 nanoparticles with diameters of 40 nm dispersed in distilled water with volume concentrations of 0.1–2 vol.% were used as the test fluid. All physical properties of the Al2O3–water nanofluids needed to calculate the pressure drop and the convective heat transfer coefficient were measured. The results show that the heat transfer coefficient of nanofluid is higher than that of the base fluid and increased with increasing the particle concentrations. Moreover, the Reynolds number has a little effect on heat transfer enhancement. The experimental data were compared with traditional convective heat transfer and viscous pressure drop correlations for fully developed turbulent flow. It was found that if the measured thermal conductivities and viscosities of the nanofluids were used in calculating the Reynolds, Prandtl, and Nusselt numbers, the existing correlations perfectly predict the convective heat transfer and viscous pressure drop in tubes. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Nanofluids are a new class of nanotechnology-based heat transfer fluids produced by dispersing nanoparticles with sizes typically smaller than 100 nm into traditional heat transfer fluids such as water, ethylene glycol, and engine oil. Due to small sizes and very large specific surface areas of the nanoparticles, nanofluids have novel properties like high thermal conductivity, superior critical heat flux (CHF), minimal clogging in flow, and improved heat transfer coefficient. These characteristics of nanofluids make them potentially useful in a plethora of engineering applications ranging from use in the automotive industry to the medical field to use in power plant cooling systems. A comprehensive literature review on the applications and challenges of nanofluids has been provided by Saidur et al. [1]. Various experimental investigations have been performed on the performance of convective heat transfer of nanofluids in laminar flow [2–6]. It is found that adding nanoparticles to the base liquid can improve the heat transfer and there is a pressure drop augmentation as a penalty. However, compared with the traditional techniques for improving heat transfer by adding millimeter and/or micrometersized particles in fluids, nanofluids incur little penalty in pressure drop because the nanoparticles are so small that the nanofluid behaves like a pure fluid.
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (M.M. Heyhat). 0735-1933/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2012.06.024
Most of fluid flow regime in practical situations such as heating or cooling systems is turbulent. Because of the existence of chaotic and unsteady vortexes, the turbulent flow has more potential to remove heat. Therefore, the investigations on turbulent flow of nanofluids can be more useful for practical applications. Pak and Cho [7] investigated the convective heat transfer performance of alumina–water and titania–water nanofluids in a horizontal tube with a constant heat flux under turbulent flow conditions experimentally. Their results showed that the Nusselt number of nanofluids increased with increasing Reynolds number and the volume concentration. However, they found that the convective heat transfer coefficient of the nanofluids with 3 vol.% nanoparticles was 12% lower than that of pure water at a given condition. Xuan and Li [8] built an experimental system to investigate the turbulent flow and convective heat transfer of the Cu–water nanofluids in a tube. Their results showed that the ratio of the Nusselt number of the Cu–water nanofluid to that of water varies from 1.06 to 1.39 while the volume fraction of the Cu nanoparticles increased from 0.5% to 2.0% under the same Reynolds number. Fotukian and Nasr Esfahany [9] investigated the turbulent convective heat transfer and pressure drop of very dilute CuO/water nanofluid flowing through a circular tube, experimentally. Their results showed that the convective heat transfer increased by 25% while the pressure drop was 20% higher than that of pure water. In a similar work [10] they conducted an experimental investigation to study a turbulent forced convection heat transfer of dilute Al2O3–water nanofluid inside a circular tube with constant wall temperature. Results indicated that addition of small amounts of nanoparticles to the base
M.M. Heyhat et al. / International Communications in Heat and Mass Transfer 39 (2012) 1272–1278
Nomenclature C D dp h k L Nu Pr Re T u
specific heat capacity (J/kg.K) diameter of tube (m) nanoparticle diameter, (m) heat transfer coefficient, (W/m 2.K) thermal conductivity (W/m.K) length of the tube, (m) Nusselt number Prandtl number Reynolds number temperature (K) fluid velocity, (m 2/s)
Greek Symbols φ nanoparticle volumetric fraction μ dynamic viscosity (Pa.s) ρ density (kg/m 3) ν kinematic viscosity (m 2/s)
Superscript _ average
Subscripts bf base fluid nf nanofluid m mean n nanoparticle
fluid augmented heat transfer remarkably while the pressure drop for the dilute nanofluid was much greater than that of the base fluid. The maximum value of 48% increase in heat transfer coefficient compared to pure water for 0.054% volume concentration at Reynolds number of 10,000 was observed. Sajadi and Kazemi [11] studied the turbulent heat transfer behavior of titanium dioxide/water nanofluid in a circular pipe under the constant wall temperature condition, experimentally. The volume fraction of nanoparticles in the base fluid was less than 0.25%. Their results showed that the heat transfer coefficient increased about 22% at a Reynolds number of 5000, for 0.25% volume fraction of TiO2, while the pressure drop was about 25% greater than that of pure water. Other several experimental studies have been carried out on turbulent convective heat transfer and pressure drop of nanofluids (for example see [12–14]). The aim of the present experimental work is to have a better fundamental understanding of the pressure drop and convective heat transfer behavior of nanofluids. The focus is on the fully developed region under the turbulent flow and constant wall temperature conditions for relatively concentrated nanofluids, for which no previous studies have been found in the literature. Water based nanofluids containing γ-Al2O3 nanoparticles with volume fractions between 0.001 and 0.02 are tested and the results are compared with conventional theories. All physical properties of the Al2O3–water nanofluids needed to calculate the pressure drop and the convective heat transfer coefficient are measured.
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Table 1 Thermophysical properties of Al2O3 nanoparticles. dp (nm)
ρ (kg/m3)
k (W/m.K)
Cp (J/kg.K)
40
3900
42.34
880
(PlasmaChem GmbH) with a nominal average particle diameter of 40 nm and the density 3.9 g/cm3 to distilled water. Thermophysical properties of alumina nanoparticles are shown in Table 1. The process of preparation of Al2O3–water nanofluids is as follows: (1) weigh the mass of Al2O3 nanoparticles by a digital electronic balance; (2) put Al2O3 nanoparticles into the weighed distilled water gradually and agitate the Al2O3–water mixture; (3) sonicate the mixture continuously for 1 h with an ultrasonic probe (UP400S, Hielscher GmbH) at 400 W and 24 kHz to produce uniform dispersion of nanoparticles in distilled water. The nanofluids were made in different volume fractions (0.1, 0.5, 1, 1.5, and 2%) and no surfactant or pH changes were used as they may have some influence on the thermophysical properties of nanofluids. Fig. 1 shows the field emission scanning electron microscope (FESEM) image of the nanoparticles after dispersing in water. Moreover, the Zeta potential of Al2O3–water nanofluids used in this work is about 30 mV. Therefore the nanofluids are physically stable [15]. All physical properties of the Al2O3–water nanofluids needed to calculate the pressure drop and the convective heat transfer coefficient are measured as follows: the specific heat capacity (Cp) was measured with a differential scanning calorimeter (DSC) (NETZSCH DSC 200F3-Maia), the density (ρ) is measured using a SVM 3000 Stabinger Viscometer (Anton Paar GmbH), the kinematic viscosity is measured using a U-tube (reverse-flow) capillary viscometer (Petrotest® Instruments GmbH & Co. KG) and then converted to the dynamic viscosity by multiplying the measured kinematic viscosity by the density of the nanofluid and the thermal conductivity (k) is measured using a KD2 Pro thermal properties analyzer (Decagon devices, Inc., USA), which is based on the transient hot wire method. The thermophysical properties are collected for temperatures ranging from 20 to 60 °C and for the nanoparticle volume fractions ranging from 0.1% to 2.0%. Fig. 2 shows that the measured density of nanofluids in various temperatures and volume fractions of nanoparticle are in good agreement with the values calculated from the mixing theory, i.e. ρnf ¼ φρn þ ð1−φÞρbf :
There are two models that have been extensively applied for determining the specific heat capacity in the experimental and numerical nanofluid investigations. The first model (Model I) assumes that the
2. Experiments 2.1. Preparation and properties of nanofluids In the present work, a two-step method was used to produce uniform and stable nanofluids by adding the spherical γ-Al2O3 nanoparticles
ð1Þ
Fig. 1. FESEM image of dispersed Al2O3 nanoparticles.
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Fig. 4. Thermal conductivity enhancement of Al2O3 nanofluids in different temperatures and volume fractions.
Fig. 2. Density of Al2O3 nanofluids.
base fluid and the nanoparticles are in thermal equilibrium. Therefore the nanofluid specific heat capacity Cp is expressed as
C p;nf ¼
φ ρC p þ ð1−φÞ ρC p n
φρn þ ð1−φÞρbf
bf
:
ð2Þ
The second model (Model II) is similar to the mixing theory for ideal gas mixtures. In this model the specific heat capacity of a nanofluid is given as C p;nf ¼ φC p;n þ ð1−φÞC p;bf :
ð3Þ
We measured the specific heat capacity for nanoparticle volume fractions of 0.1, 0.5, 1, 1.5, and 2.0% but because of the same behavior of the results and regarding brevity only the result for 0.5% is presented here. As shown in Fig. 3, the obtained results are close to the prediction of the first model which is based on the thermal equilibrium. Therefore, we use Eq. (2) to calculate the nanofluid specific heat capacity.
Fig. 3. Comparison of the specific heat capacity of Al2O3 nanofluids with two models (φ = 0.005).
The thermal conductivity enhancement of Al2O3–water nanofluids in different temperatures and particle volume fractions has been shown in Fig. 4. The results illustrate that the thermal conductivity of nanofluids considerably increases with increasing nanofluid temperature and particle volume fraction. However, depending on temperature in each volume fraction is low. As can be seen, the enhancement of the thermal conductivity is approximately between 2 and 18%. Curve fit was created for the thermal conductivity data and the following empirical correlation has been derived for the thermal conductivity of nanofluids: knf ¼ 1 þ 8:733φ: kbf ðT Þ
ð4Þ
Fig. 4 shows that this equation predicts the experimental data well. Fig. 5 illustrates the dynamic viscosity ratio of Al2O3–water nanofluids in different temperatures and volume fractions. The measured kinematic viscosities of the nanofluids have been converted to the dynamic viscosity by multiplying them by the density of the nanofluids. Results indicate that the dynamic viscosity ratio of nanofluids significantly increases with increasing nanofluid volume fraction. Moreover, it can be seen that, interestingly, the dynamic viscosity ratio of nanofluids is nearly independent of temperature. Based on these experimental data the
Fig. 5. Dynamic viscosity ratio of Al2O3 nanofluids in different temperatures and volume fractions.
M.M. Heyhat et al. / International Communications in Heat and Mass Transfer 39 (2012) 1272–1278
following correlation has been derived for calculating the dynamic viscosity of nanofluids. μ nf 5:989φ : ¼ exp 0:278−φ μ bf ðT Þ
ð5Þ
Fig. 5 displays that the above equation predicts the experimental data well. It can be seen that the viscosity and the thermal conductivity correlations are multipliers utilizing only the temperature dependence of the base fluid water as found in this experiment. The form of the above equations is similar to the empirical equations of Williams et al. [14] but with different coefficients. It should be noted that these equations have been extracted based on the experimental data for Al2O3–water nanofluids. The restrictions of these equations are the temperature range between 20 °C and 60 °C and volume fraction range between 0.1 vol.% and 2.0 vol.%. 2.2. Experimental setup An experimental apparatus was built to study the turbulent convective heat transfer and flow characteristics of Al2O3–water nanofluids flowing through a tube. Fig. 6 shows the experimental system schematically. It consists of a pump, a bypass valve for controlling the flow rate, a shell and tube heat exchanger as cooling unit, a test section, several temperature indicators, a flow measuring unit, a differential pressure transmitter and a reservoir tank. The test section made of a steam bath which a straight copper tube with 5 mm inner diameter, 0.5 mm thickness and 2 m length is run through it. Steam at atmospheric pressure is generated by using four electrical heaters that are submerged in water contained in the steam bath tank. The tank has a small opening that allows the steam to escape when the heaters are on to ensure that steam remains at atmospheric pressure. Ten K-type thermocouples
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were mounted on the copper tube wall at equal intervals to measure the wall temperature. Two K-type thermocouples were inserted into the flow at the inlet and outlet of the test section to measure bulk temperatures of nanofluids. The uncertainty in temperature measurement was ±0.1 °C. First the flow passed a horizontal isolated copper tube with 50 cm length to guarantee the hydrodynamically fully-developed condition at the entrance of flow to the test section. The flow rate was controlled with two adjusting valves, one at the end of the test section and the other at the by-pass line. The cooling unit includes a shell and tube heat exchanger which water is used to reduce the temperature of the nanofluid. The pressure drop is measured by a differential pressure transmitter (Smar-LD 301) with an accuracy of ±50 Pa. The flow rate was calculated by determining the time required to collect into a certain volume. This was typically repeated three times with the help of a precise measuring vessel and stop watch. 3. Data reduction The Al2O3 nanoparticles dispersed in pure water with volume concentrations of 0.1%, 0.5%, 1.0%, 1.5% and 2.0% were used to investigate the turbulent convective heat transfer coefficient and pressure drop of the nanofluids. The convective heat transfer coefficient and Nusselt number of nanofluids are calculated as follows: h nf ðexpÞ ¼
C pnf :ρnf :u:AðT bo −T bi Þ π:D:L:LMTD
Nu nf ð expÞ ¼
h nf :D knf
ð6Þ
ð7Þ
where D is the inner diameter of the test tube, and Tbo and Tbi are the outlet and inlet bulk temperatures of the nanofluids, respectively.
Fig. 6. Schematic of the experimental setup.
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Moreover, LMTD is the logarithmic mean temperature difference and calculated as: LMTD ¼
ðT W −T bi Þ−ðT W −T bo Þ : ln½ðT W −T bi Þ=ðT W −T bo Þ
ð8Þ
Tw is the wall temperature that is the average of ten measured temperatures on tube wall at different positions. Similarly to the heat transfer coefficient, the friction factor of the nanofluid is calculated from: f nf ¼
2DΔP nf
ð9Þ
u2m Lρnf
where fnf is the friction factor of the nanofluid, ΔPnf is the measured pressure drop of the nanofluid, L is the length of the tube, D is the inner diameter of the tube, ρnf is the density of the nanofluid, and um is the mean velocity of the nanofluid. 4. Results and discussion Fig. 8. Comparison between theoretical and experimental data for the pressure drop of water.
4.1. Validation of the experimental system Initially the experimental apparatus was run with distilled water to investigate the reliability and accuracy of the experiments. The Nusselt numbers calculated using the experimental data were compared with the Nusselt numbers obtained from the Gnielinski equation [16] for the turbulent flow, given by the following equation: NuD ¼
ðf =8ÞðReD −1000ÞPr : 1 þ 12:7ðf =8Þ1=2 Pr2=3 −1
ð10Þ
The friction factor, f, in the above equation can be calculated as follows [17]: −2
f ¼ ð0:79 lnReD −1:64Þ
:
ð11Þ
Moreover, in order to evaluate the accuracy of fluid flow measurements inside the tube the measured pressure drop was compared with the Darcy–Weisbach equation. ΔP ¼ f
L u2m ρ D 2
ð12Þ
Figs. 7 and 8 display the comparison of the experimental data with the Nusselt number and pressure drop of the pure water as a function
Fig. 7. Comparison between theoretical and experimental data for the Nusselt number of water.
of Reynolds number. As can be seen, there is a good agreement between experimental and theoretical results. 4.2. Convective heat transfer coefficient of nanofluid The turbulent convective heat transfer coefficient of Al2O3–water nanofluids flowing through a circular tube for a constant wall temperature is experimentally measured. Al2O3–water nanofluids with nanoparticle concentrations of 0.1%, 0.5%, 1%, 1.5% and 2% were used in this study. The Reynolds number of flow varied in the approximate range of 3000–13,500. Fig. 9 presents the average convective heat transfer coefficient in nanofluid at different volume fractions as a function of Reynolds number. Moreover, the average convective heat transfer coefficient for pure water has been plotted in this figure. As can be seen, the heat transfer coefficient of the nanofluids is higher than those of the pure water. Similar observations were reported by previous researches [9–12]. The convective heat transfer coefficent ratio of the nanofluids to that of pure water is shown in Fig. 10. It is obvious that adding nanoparticles to the pure water increases the heat transfer. The heat transfer enhancement is higher at high particle volume fraction, however, the Reynolds number has a little effect on the heat transfer augmentation for a fixed
Fig. 9. The heat transfer coefficient for Al2O3–water nanofluids and pure water versus Reynolds number at various volume concentrations.
M.M. Heyhat et al. / International Communications in Heat and Mass Transfer 39 (2012) 1272–1278
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Fig. 10. The ratio of heat transfer coefficient for Al2O3–water nanofluids versus Reynolds number at various volume concentrations. Fig. 12. Comparison of measured and predicted pressure losses for nanofluid tests.
volume concentration of nanoparticles. The heat transfer enhancement is approximately 1.5% and 23% for nanofluids with volume fractions of 0.001 and 0.02, respectively. One of the main reasons which can explain the significant heat transfer enhancement in nanofluids is augmentation of the thermal conductivity of nanofluids. Another mechanism which can effect the heat transfer enhancement of nanofluids is the acceleration of energy exchange process in the fluid because of chaotic movement of nanoparticles. This chaotic movement can flatten temperature distribution in nanofluid and result in a steeper temperature gradient between the nanofluid and wall. Therefore, the heat transfer rate between the nanofluid and wall will be increased. The experimental Nusselt number of water-based Al2O3 nanofluids is compared with results obtained by the Eq. (10). In this comparison, the measured physical properties such as thermal conductivity, viscosity and heat capacity of nanofluids are applied to the Reynolds number and the Prandtl number for calculating the Nusselt number by Eq. (10). Fig. 11 displays this comparison. As can be seen, Eq. (10) can predict the experimental data well (within ±15%). This observation is in agreement with the results of Williams et al. [14], but is in contrast with the results of Fotukian and Nasr Esfahany [9,10].
4.3. Viscous pressure loss of nanofluid In order to apply the nanofluids for practical applications, it is necessary to find out the flow features of the nanofluids besides the heat transfer measurements. Therefore, the viscous pressure loss was measured by a differential pressure transmitter in the test section of the loop for water and alumina nanofluids with 0.001, 0.005, 0.01, 0.015 and 0.02 volume fractions of nanoparticles. The comparison of measured and predicted pressure losses for nanofluid tests is shown in Fig. 12. The predicted pressure losses are calculated by inserting the nanofluid properties in Eq. (12) at the same Reynolds number. As can be seen, the measured and predicted pressure losses with traditional correlation are in good agreement (within ±16%) if the nanofluid mixture properties are utilized. This observation is in agreement with the results of Williams et al. [14]. 5. Conclusion This paper is concerned with the convective heat transfer and pressure drop of Al2O3–water nanofluids. All physical properties of the Al2O3–water nanofluids needed to calculate the pressure drop and the convective heat transfer coefficient have been measured. Experiments were carried out in the fully developed turbulent flow regime in a circular tube under the constant wall temperature condition. The turbulent convective heat transfer coefficient of the nanofluids increases with increasing the particle volume concentrations. However, increasing in the Reynolds number did not show much effect on the heat transfer enhancement in a fixed volume fraction. The heat transfer coefficient of Al2O3–water nanofluids is increased by 23% at 2 vol.% compared with that of pure water. Comparison of the experimental data with the traditional correlations, i.e. Eqs. (10) and (12), revealed that the convective heat transfer and pressure drop of the Al2O3– water nanofluids tested in fully developed turbulent flow region can be predicted with the help of the traditional correlations and models, provided that the effective nanofluid properties are used in calculating the dimensionless numbers. References
Fig. 11. Comparison of measured and predicted Nusselt numbers for nanofluids.
[1] R. Saidur, K.Y. Leong, H.A. Mohammad, A review on applications and challenges of nanofluids, Renewable and Sustainable Energy Reviews 15 (2011) 1646–1668. [2] D. Wen, Y. Ding, Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions, International Journal of Heat and Mass Transfer 47 (2004) 5181–5188.
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[3] S. Zeinali Heris, S.Gh. Etemad, M. Nasr Esfahany, Experimental investigation of oxide nanofluids laminar flow convective heat transfer, International Communications in Heat and Mass Transfer 33 (2006) 529–535. [4] S. Zeinali Heris, S. Gh Etemad, M.N. Esfahany, Convective heat transfer of a Cu/water nanofluid flowing through a circular tube, Experimental Heat Transfer 22 (2009) 217–227. [5] U. Rea, T. McKrell, L.w. Hu, J. Buongiorno, Laminar convective heat transfer and viscous pressure loss of alumina–water and zirconia–water nanofluids, International Journal of Heat and Mass Transfer 52 (2009) 2042–2048. [6] K.S. Hwang, S.P. Jang, S.U.S. Choi, Flow and convective heat transfer characteristics of water-based Al2O3 nanofluids in fully developed laminar flow regime, International Journal of Heat and Mass Transfer 52 (2009) 193–199. [7] B.C. Pak, Y.I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Experimental Heat Transfer 11 (1998) 151–170. [8] Y. Xuan, Q. Li, Investigation on convective heat transfer and flow features of nanofluids, ASME Journal of Heat Transfer 125 (2003) 151–155. [9] S.M. Fotukian, M. Nasr Esfahany, Experimental study of turbulent convective heat transfer and pressure drop of dilute CuO/water nanofluid inside a circular tube, International Communications in Heat and Mass Transfer 37 (2010) 214–219. [10] S.M. Fotukian, M. Nasr Esfahany, Experimental investigation of turbulent convective heat transfer of dilute γ-Al2O3/water nanofluid inside a circular tube, International Journal of Heat and Fluid Flow 31 (2010) 606–612.
[11] A.R. Sajadi, M.H. Kazemi, Investigation of turbulent convective heat transfer and pressure drop of TiO2/water nanofluid in circular tube, International Communications in Heat and Mass Transfer 38 (2011) 1474–1478. [12] W. Duangthongsuk, S. Wongwises, An experimental study on the heat transfer performance and pressure drop of TiO2–water nanofluids flowing under a turbulent flow regime, International Journal of Heat and Mass Transfer 53 (2010) 334–344. [13] D.P. Kulkarni, P.K. Namburu, H.E. Bargar, D.K. Das, Convective heat transfer and fluid dynamic characteristics of SiO2–ethylene glycol/water nanofluid, Heat Transfer Engineering 29 (2008) 1027–1035. [14] W. Williams, J. Buongiorno, L.W. Hu, Experimental investigation of turbulent convective heat transfer and pressure loss of alumina/water and zirconia/water nanoparticle colloids (nanofluids) in horizontal tubes, ASME Journal of Heat Transfer 130 (2008) 042412. [15] J.H. Lee, K.S. Hwang, S.P. Jang, B.H. Lee, J.H. Kim, S.U.S. Choi, C.J. Choi, Effective viscosities and thermal conductivities of aqueous nanofluids containing low volume concentrations of Al2O3 nanoparticles, International Journal of Heat and Mass Transfer 51 (2008) 2651–2656. [16] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, International Chemical Engineering 16 (1976) 359–368. [17] F.P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, 1996.
Contents lists available at SciVerse ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Experimental investigation of turbulent flow and convective heat transfer characteristics of alumina water nanofluids in fully developed flow regime☆ M.M. Heyhat a,⁎, F. Kowsary a, A.M. Rashidi b, S. Alem Varzane Esfehani a, A. Amrollahi b a b
Mechanical Engineering Department, University College of Engineering, University of Tehran, Tehran, Iran Nanotechnology Research Center, Institute of Petroleum Industry (RIPI), Azadi Complex, Tehran, Iran
a r t i c l e
i n f o
Available online 27 June 2012 Keywords: Nanofluids Convective heat transfer Pressure drop Turbulent flow Fully developed
a b s t r a c t In this paper the convective heat transfer and friction factor of the nanofluids in a circular tube with constant wall temperature under turbulent flow conditions were investigated experimentally. Al2O3 nanoparticles with diameters of 40 nm dispersed in distilled water with volume concentrations of 0.1–2 vol.% were used as the test fluid. All physical properties of the Al2O3–water nanofluids needed to calculate the pressure drop and the convective heat transfer coefficient were measured. The results show that the heat transfer coefficient of nanofluid is higher than that of the base fluid and increased with increasing the particle concentrations. Moreover, the Reynolds number has a little effect on heat transfer enhancement. The experimental data were compared with traditional convective heat transfer and viscous pressure drop correlations for fully developed turbulent flow. It was found that if the measured thermal conductivities and viscosities of the nanofluids were used in calculating the Reynolds, Prandtl, and Nusselt numbers, the existing correlations perfectly predict the convective heat transfer and viscous pressure drop in tubes. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Nanofluids are a new class of nanotechnology-based heat transfer fluids produced by dispersing nanoparticles with sizes typically smaller than 100 nm into traditional heat transfer fluids such as water, ethylene glycol, and engine oil. Due to small sizes and very large specific surface areas of the nanoparticles, nanofluids have novel properties like high thermal conductivity, superior critical heat flux (CHF), minimal clogging in flow, and improved heat transfer coefficient. These characteristics of nanofluids make them potentially useful in a plethora of engineering applications ranging from use in the automotive industry to the medical field to use in power plant cooling systems. A comprehensive literature review on the applications and challenges of nanofluids has been provided by Saidur et al. [1]. Various experimental investigations have been performed on the performance of convective heat transfer of nanofluids in laminar flow [2–6]. It is found that adding nanoparticles to the base liquid can improve the heat transfer and there is a pressure drop augmentation as a penalty. However, compared with the traditional techniques for improving heat transfer by adding millimeter and/or micrometersized particles in fluids, nanofluids incur little penalty in pressure drop because the nanoparticles are so small that the nanofluid behaves like a pure fluid.
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (M.M. Heyhat). 0735-1933/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2012.06.024
Most of fluid flow regime in practical situations such as heating or cooling systems is turbulent. Because of the existence of chaotic and unsteady vortexes, the turbulent flow has more potential to remove heat. Therefore, the investigations on turbulent flow of nanofluids can be more useful for practical applications. Pak and Cho [7] investigated the convective heat transfer performance of alumina–water and titania–water nanofluids in a horizontal tube with a constant heat flux under turbulent flow conditions experimentally. Their results showed that the Nusselt number of nanofluids increased with increasing Reynolds number and the volume concentration. However, they found that the convective heat transfer coefficient of the nanofluids with 3 vol.% nanoparticles was 12% lower than that of pure water at a given condition. Xuan and Li [8] built an experimental system to investigate the turbulent flow and convective heat transfer of the Cu–water nanofluids in a tube. Their results showed that the ratio of the Nusselt number of the Cu–water nanofluid to that of water varies from 1.06 to 1.39 while the volume fraction of the Cu nanoparticles increased from 0.5% to 2.0% under the same Reynolds number. Fotukian and Nasr Esfahany [9] investigated the turbulent convective heat transfer and pressure drop of very dilute CuO/water nanofluid flowing through a circular tube, experimentally. Their results showed that the convective heat transfer increased by 25% while the pressure drop was 20% higher than that of pure water. In a similar work [10] they conducted an experimental investigation to study a turbulent forced convection heat transfer of dilute Al2O3–water nanofluid inside a circular tube with constant wall temperature. Results indicated that addition of small amounts of nanoparticles to the base
M.M. Heyhat et al. / International Communications in Heat and Mass Transfer 39 (2012) 1272–1278
Nomenclature C D dp h k L Nu Pr Re T u
specific heat capacity (J/kg.K) diameter of tube (m) nanoparticle diameter, (m) heat transfer coefficient, (W/m 2.K) thermal conductivity (W/m.K) length of the tube, (m) Nusselt number Prandtl number Reynolds number temperature (K) fluid velocity, (m 2/s)
Greek Symbols φ nanoparticle volumetric fraction μ dynamic viscosity (Pa.s) ρ density (kg/m 3) ν kinematic viscosity (m 2/s)
Superscript _ average
Subscripts bf base fluid nf nanofluid m mean n nanoparticle
fluid augmented heat transfer remarkably while the pressure drop for the dilute nanofluid was much greater than that of the base fluid. The maximum value of 48% increase in heat transfer coefficient compared to pure water for 0.054% volume concentration at Reynolds number of 10,000 was observed. Sajadi and Kazemi [11] studied the turbulent heat transfer behavior of titanium dioxide/water nanofluid in a circular pipe under the constant wall temperature condition, experimentally. The volume fraction of nanoparticles in the base fluid was less than 0.25%. Their results showed that the heat transfer coefficient increased about 22% at a Reynolds number of 5000, for 0.25% volume fraction of TiO2, while the pressure drop was about 25% greater than that of pure water. Other several experimental studies have been carried out on turbulent convective heat transfer and pressure drop of nanofluids (for example see [12–14]). The aim of the present experimental work is to have a better fundamental understanding of the pressure drop and convective heat transfer behavior of nanofluids. The focus is on the fully developed region under the turbulent flow and constant wall temperature conditions for relatively concentrated nanofluids, for which no previous studies have been found in the literature. Water based nanofluids containing γ-Al2O3 nanoparticles with volume fractions between 0.001 and 0.02 are tested and the results are compared with conventional theories. All physical properties of the Al2O3–water nanofluids needed to calculate the pressure drop and the convective heat transfer coefficient are measured.
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Table 1 Thermophysical properties of Al2O3 nanoparticles. dp (nm)
ρ (kg/m3)
k (W/m.K)
Cp (J/kg.K)
40
3900
42.34
880
(PlasmaChem GmbH) with a nominal average particle diameter of 40 nm and the density 3.9 g/cm3 to distilled water. Thermophysical properties of alumina nanoparticles are shown in Table 1. The process of preparation of Al2O3–water nanofluids is as follows: (1) weigh the mass of Al2O3 nanoparticles by a digital electronic balance; (2) put Al2O3 nanoparticles into the weighed distilled water gradually and agitate the Al2O3–water mixture; (3) sonicate the mixture continuously for 1 h with an ultrasonic probe (UP400S, Hielscher GmbH) at 400 W and 24 kHz to produce uniform dispersion of nanoparticles in distilled water. The nanofluids were made in different volume fractions (0.1, 0.5, 1, 1.5, and 2%) and no surfactant or pH changes were used as they may have some influence on the thermophysical properties of nanofluids. Fig. 1 shows the field emission scanning electron microscope (FESEM) image of the nanoparticles after dispersing in water. Moreover, the Zeta potential of Al2O3–water nanofluids used in this work is about 30 mV. Therefore the nanofluids are physically stable [15]. All physical properties of the Al2O3–water nanofluids needed to calculate the pressure drop and the convective heat transfer coefficient are measured as follows: the specific heat capacity (Cp) was measured with a differential scanning calorimeter (DSC) (NETZSCH DSC 200F3-Maia), the density (ρ) is measured using a SVM 3000 Stabinger Viscometer (Anton Paar GmbH), the kinematic viscosity is measured using a U-tube (reverse-flow) capillary viscometer (Petrotest® Instruments GmbH & Co. KG) and then converted to the dynamic viscosity by multiplying the measured kinematic viscosity by the density of the nanofluid and the thermal conductivity (k) is measured using a KD2 Pro thermal properties analyzer (Decagon devices, Inc., USA), which is based on the transient hot wire method. The thermophysical properties are collected for temperatures ranging from 20 to 60 °C and for the nanoparticle volume fractions ranging from 0.1% to 2.0%. Fig. 2 shows that the measured density of nanofluids in various temperatures and volume fractions of nanoparticle are in good agreement with the values calculated from the mixing theory, i.e. ρnf ¼ φρn þ ð1−φÞρbf :
There are two models that have been extensively applied for determining the specific heat capacity in the experimental and numerical nanofluid investigations. The first model (Model I) assumes that the
2. Experiments 2.1. Preparation and properties of nanofluids In the present work, a two-step method was used to produce uniform and stable nanofluids by adding the spherical γ-Al2O3 nanoparticles
ð1Þ
Fig. 1. FESEM image of dispersed Al2O3 nanoparticles.
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Fig. 4. Thermal conductivity enhancement of Al2O3 nanofluids in different temperatures and volume fractions.
Fig. 2. Density of Al2O3 nanofluids.
base fluid and the nanoparticles are in thermal equilibrium. Therefore the nanofluid specific heat capacity Cp is expressed as
C p;nf ¼
φ ρC p þ ð1−φÞ ρC p n
φρn þ ð1−φÞρbf
bf
:
ð2Þ
The second model (Model II) is similar to the mixing theory for ideal gas mixtures. In this model the specific heat capacity of a nanofluid is given as C p;nf ¼ φC p;n þ ð1−φÞC p;bf :
ð3Þ
We measured the specific heat capacity for nanoparticle volume fractions of 0.1, 0.5, 1, 1.5, and 2.0% but because of the same behavior of the results and regarding brevity only the result for 0.5% is presented here. As shown in Fig. 3, the obtained results are close to the prediction of the first model which is based on the thermal equilibrium. Therefore, we use Eq. (2) to calculate the nanofluid specific heat capacity.
Fig. 3. Comparison of the specific heat capacity of Al2O3 nanofluids with two models (φ = 0.005).
The thermal conductivity enhancement of Al2O3–water nanofluids in different temperatures and particle volume fractions has been shown in Fig. 4. The results illustrate that the thermal conductivity of nanofluids considerably increases with increasing nanofluid temperature and particle volume fraction. However, depending on temperature in each volume fraction is low. As can be seen, the enhancement of the thermal conductivity is approximately between 2 and 18%. Curve fit was created for the thermal conductivity data and the following empirical correlation has been derived for the thermal conductivity of nanofluids: knf ¼ 1 þ 8:733φ: kbf ðT Þ
ð4Þ
Fig. 4 shows that this equation predicts the experimental data well. Fig. 5 illustrates the dynamic viscosity ratio of Al2O3–water nanofluids in different temperatures and volume fractions. The measured kinematic viscosities of the nanofluids have been converted to the dynamic viscosity by multiplying them by the density of the nanofluids. Results indicate that the dynamic viscosity ratio of nanofluids significantly increases with increasing nanofluid volume fraction. Moreover, it can be seen that, interestingly, the dynamic viscosity ratio of nanofluids is nearly independent of temperature. Based on these experimental data the
Fig. 5. Dynamic viscosity ratio of Al2O3 nanofluids in different temperatures and volume fractions.
M.M. Heyhat et al. / International Communications in Heat and Mass Transfer 39 (2012) 1272–1278
following correlation has been derived for calculating the dynamic viscosity of nanofluids. μ nf 5:989φ : ¼ exp 0:278−φ μ bf ðT Þ
ð5Þ
Fig. 5 displays that the above equation predicts the experimental data well. It can be seen that the viscosity and the thermal conductivity correlations are multipliers utilizing only the temperature dependence of the base fluid water as found in this experiment. The form of the above equations is similar to the empirical equations of Williams et al. [14] but with different coefficients. It should be noted that these equations have been extracted based on the experimental data for Al2O3–water nanofluids. The restrictions of these equations are the temperature range between 20 °C and 60 °C and volume fraction range between 0.1 vol.% and 2.0 vol.%. 2.2. Experimental setup An experimental apparatus was built to study the turbulent convective heat transfer and flow characteristics of Al2O3–water nanofluids flowing through a tube. Fig. 6 shows the experimental system schematically. It consists of a pump, a bypass valve for controlling the flow rate, a shell and tube heat exchanger as cooling unit, a test section, several temperature indicators, a flow measuring unit, a differential pressure transmitter and a reservoir tank. The test section made of a steam bath which a straight copper tube with 5 mm inner diameter, 0.5 mm thickness and 2 m length is run through it. Steam at atmospheric pressure is generated by using four electrical heaters that are submerged in water contained in the steam bath tank. The tank has a small opening that allows the steam to escape when the heaters are on to ensure that steam remains at atmospheric pressure. Ten K-type thermocouples
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were mounted on the copper tube wall at equal intervals to measure the wall temperature. Two K-type thermocouples were inserted into the flow at the inlet and outlet of the test section to measure bulk temperatures of nanofluids. The uncertainty in temperature measurement was ±0.1 °C. First the flow passed a horizontal isolated copper tube with 50 cm length to guarantee the hydrodynamically fully-developed condition at the entrance of flow to the test section. The flow rate was controlled with two adjusting valves, one at the end of the test section and the other at the by-pass line. The cooling unit includes a shell and tube heat exchanger which water is used to reduce the temperature of the nanofluid. The pressure drop is measured by a differential pressure transmitter (Smar-LD 301) with an accuracy of ±50 Pa. The flow rate was calculated by determining the time required to collect into a certain volume. This was typically repeated three times with the help of a precise measuring vessel and stop watch. 3. Data reduction The Al2O3 nanoparticles dispersed in pure water with volume concentrations of 0.1%, 0.5%, 1.0%, 1.5% and 2.0% were used to investigate the turbulent convective heat transfer coefficient and pressure drop of the nanofluids. The convective heat transfer coefficient and Nusselt number of nanofluids are calculated as follows: h nf ðexpÞ ¼
C pnf :ρnf :u:AðT bo −T bi Þ π:D:L:LMTD
Nu nf ð expÞ ¼
h nf :D knf
ð6Þ
ð7Þ
where D is the inner diameter of the test tube, and Tbo and Tbi are the outlet and inlet bulk temperatures of the nanofluids, respectively.
Fig. 6. Schematic of the experimental setup.
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Moreover, LMTD is the logarithmic mean temperature difference and calculated as: LMTD ¼
ðT W −T bi Þ−ðT W −T bo Þ : ln½ðT W −T bi Þ=ðT W −T bo Þ
ð8Þ
Tw is the wall temperature that is the average of ten measured temperatures on tube wall at different positions. Similarly to the heat transfer coefficient, the friction factor of the nanofluid is calculated from: f nf ¼
2DΔP nf
ð9Þ
u2m Lρnf
where fnf is the friction factor of the nanofluid, ΔPnf is the measured pressure drop of the nanofluid, L is the length of the tube, D is the inner diameter of the tube, ρnf is the density of the nanofluid, and um is the mean velocity of the nanofluid. 4. Results and discussion Fig. 8. Comparison between theoretical and experimental data for the pressure drop of water.
4.1. Validation of the experimental system Initially the experimental apparatus was run with distilled water to investigate the reliability and accuracy of the experiments. The Nusselt numbers calculated using the experimental data were compared with the Nusselt numbers obtained from the Gnielinski equation [16] for the turbulent flow, given by the following equation: NuD ¼
ðf =8ÞðReD −1000ÞPr : 1 þ 12:7ðf =8Þ1=2 Pr2=3 −1
ð10Þ
The friction factor, f, in the above equation can be calculated as follows [17]: −2
f ¼ ð0:79 lnReD −1:64Þ
:
ð11Þ
Moreover, in order to evaluate the accuracy of fluid flow measurements inside the tube the measured pressure drop was compared with the Darcy–Weisbach equation. ΔP ¼ f
L u2m ρ D 2
ð12Þ
Figs. 7 and 8 display the comparison of the experimental data with the Nusselt number and pressure drop of the pure water as a function
Fig. 7. Comparison between theoretical and experimental data for the Nusselt number of water.
of Reynolds number. As can be seen, there is a good agreement between experimental and theoretical results. 4.2. Convective heat transfer coefficient of nanofluid The turbulent convective heat transfer coefficient of Al2O3–water nanofluids flowing through a circular tube for a constant wall temperature is experimentally measured. Al2O3–water nanofluids with nanoparticle concentrations of 0.1%, 0.5%, 1%, 1.5% and 2% were used in this study. The Reynolds number of flow varied in the approximate range of 3000–13,500. Fig. 9 presents the average convective heat transfer coefficient in nanofluid at different volume fractions as a function of Reynolds number. Moreover, the average convective heat transfer coefficient for pure water has been plotted in this figure. As can be seen, the heat transfer coefficient of the nanofluids is higher than those of the pure water. Similar observations were reported by previous researches [9–12]. The convective heat transfer coefficent ratio of the nanofluids to that of pure water is shown in Fig. 10. It is obvious that adding nanoparticles to the pure water increases the heat transfer. The heat transfer enhancement is higher at high particle volume fraction, however, the Reynolds number has a little effect on the heat transfer augmentation for a fixed
Fig. 9. The heat transfer coefficient for Al2O3–water nanofluids and pure water versus Reynolds number at various volume concentrations.
M.M. Heyhat et al. / International Communications in Heat and Mass Transfer 39 (2012) 1272–1278
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Fig. 10. The ratio of heat transfer coefficient for Al2O3–water nanofluids versus Reynolds number at various volume concentrations. Fig. 12. Comparison of measured and predicted pressure losses for nanofluid tests.
volume concentration of nanoparticles. The heat transfer enhancement is approximately 1.5% and 23% for nanofluids with volume fractions of 0.001 and 0.02, respectively. One of the main reasons which can explain the significant heat transfer enhancement in nanofluids is augmentation of the thermal conductivity of nanofluids. Another mechanism which can effect the heat transfer enhancement of nanofluids is the acceleration of energy exchange process in the fluid because of chaotic movement of nanoparticles. This chaotic movement can flatten temperature distribution in nanofluid and result in a steeper temperature gradient between the nanofluid and wall. Therefore, the heat transfer rate between the nanofluid and wall will be increased. The experimental Nusselt number of water-based Al2O3 nanofluids is compared with results obtained by the Eq. (10). In this comparison, the measured physical properties such as thermal conductivity, viscosity and heat capacity of nanofluids are applied to the Reynolds number and the Prandtl number for calculating the Nusselt number by Eq. (10). Fig. 11 displays this comparison. As can be seen, Eq. (10) can predict the experimental data well (within ±15%). This observation is in agreement with the results of Williams et al. [14], but is in contrast with the results of Fotukian and Nasr Esfahany [9,10].
4.3. Viscous pressure loss of nanofluid In order to apply the nanofluids for practical applications, it is necessary to find out the flow features of the nanofluids besides the heat transfer measurements. Therefore, the viscous pressure loss was measured by a differential pressure transmitter in the test section of the loop for water and alumina nanofluids with 0.001, 0.005, 0.01, 0.015 and 0.02 volume fractions of nanoparticles. The comparison of measured and predicted pressure losses for nanofluid tests is shown in Fig. 12. The predicted pressure losses are calculated by inserting the nanofluid properties in Eq. (12) at the same Reynolds number. As can be seen, the measured and predicted pressure losses with traditional correlation are in good agreement (within ±16%) if the nanofluid mixture properties are utilized. This observation is in agreement with the results of Williams et al. [14]. 5. Conclusion This paper is concerned with the convective heat transfer and pressure drop of Al2O3–water nanofluids. All physical properties of the Al2O3–water nanofluids needed to calculate the pressure drop and the convective heat transfer coefficient have been measured. Experiments were carried out in the fully developed turbulent flow regime in a circular tube under the constant wall temperature condition. The turbulent convective heat transfer coefficient of the nanofluids increases with increasing the particle volume concentrations. However, increasing in the Reynolds number did not show much effect on the heat transfer enhancement in a fixed volume fraction. The heat transfer coefficient of Al2O3–water nanofluids is increased by 23% at 2 vol.% compared with that of pure water. Comparison of the experimental data with the traditional correlations, i.e. Eqs. (10) and (12), revealed that the convective heat transfer and pressure drop of the Al2O3– water nanofluids tested in fully developed turbulent flow region can be predicted with the help of the traditional correlations and models, provided that the effective nanofluid properties are used in calculating the dimensionless numbers. References
Fig. 11. Comparison of measured and predicted Nusselt numbers for nanofluids.
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