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Heat transfer and pressure drop of nanofluids containing carbon nanotubes in laminar flows
Experimental Thermal and Fluid Science 44 (2013) 716–721
Contents lists available at SciVerse ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Heat transfer and pressure drop of nanofluids containing carbon nanotubes in laminar flows Jianli Wang a,b, Jianjun Zhu b, Xing Zhang b,⇑, Yunfei Chen a a b
School of Mechanical Engineering and Jiangsu Key Laboratory for Design and Manufacture of Micro Nano Biomedical Instruments, Southeast University, Nanjing 210096, China Key Laboratory for Thermal Science and Power Engineering of Education Ministry, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 9 February 2012 Received in revised form 30 August 2012 Accepted 10 September 2012 Available online 21 September 2012 Keywords: Carbon nanotube Convective heat transfer Nanofluid Pressure drop
a b s t r a c t The heat transfer and pressure drop of nanofluids containing carbon nanotubes in a horizontal circular tube are experimentally investigated. The friction factor of the dilute nanofluids shows a good agreement with the prediction from the Hagen-Poiseuille flow theory. A considerable enhancement in the average convective heat transfer is also observed compared with the distilled water. For the nanofluids with volumetric concentration of 0.05% and 0.24%, the heat transfer enhancement are 70% and 190% at Reynolds number of about 120 respectively, while the enhancement of thermal conductivity is less than 10%, therefore, the large heat transfer increase cannot be solely attributed to the enhanced thermal conductivity. By measuring the pump power supply and the thermal conductance of the test tube, our results suggest that the nanofluids at low concentration enhance the heat transfer with little extra penalty in pump power, thus have great potential for applications in the heat transfer systems. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction With the increasing requirement of high removal capacity of the heat dissipation in microelectronic devices, such as microelectromechanical systems and microflow devices, many efforts have been devoted to the study of heat transfer and flow resistance in microchannels. The fluids dispersed with nanoparticles (nanofluids) have been demonstrated to give a large increase in thermal conductivity [1], thus show great potential for improving the heat transfer performance. In the past decade, many attempts have been made to characterize the heat transfer and pressure drop of nanofluids. For turbulent flow, Pak and Cho [2] measured the friction factor and heat transfer behaviors of Al2O3/water and TiO2/water nanofluids, the heat transfer coefficient was found to be smaller than that of pure water at a given flow rate. Nevertheless, Xuan and Li [3] reported an enhancement of about 60% in the heat transfer coefficient with the use of 2 vol.% Cu/water nanofluids, and no extra augmentation in pressure drop was observed with the addition of nanoparticles. Williams et al. [4] showed no abnormal heat transfer enhancement for Al2O3/water and ZrO2/water nanofluids. For laminar flow, Heris et al. [5] reported an enhancement of about 29% in the heat transfer coefficient using Al2O3/water nanofluids, and concluded that the heat transfer coefficient of Al2O3/water was higher than that of CuO/water. Xie et al. [6] investigated the heat transfer enhance⇑ Corresponding author. Tel.: +86 010 62772668; fax: +86 010 62781610. E-mail address: [email protected] (X. Zhang). 0894-1777/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2012.09.013
ment of nanofluids using four different nanoparticles, and the highest enhancement up to 252% for MgO/water nanofluids was observed. Compared with these oxide nanoparticles, the carbon nanotubes (CNTs) have significantly high thermal conductivities [7,8], thus show great potential to be used as additives in nanofluids. Ding et al. [9] measured the convective heat transfer of multiwalled carbon nanotube (MWNT) nanofluids, and found an increase of about 350%. Ko et al. [10] reported that the friction factor of MWNT/water nanofluid dispersed with CNTs using surfactants was larger than that prepared by the acid treatment, and the latter gave only a slight increase in friction factor compared with the prediction from the Hagen-Poiseuille flow theory. Liao and Liu [11] measured the heat transfer and flow drag characteristics of MWNT/water nanofluids under both laminar and turbulent flow conditions, and showed that the enhancement ratio of heat transfer coefficient and that of thermal conductivity were almost the same. Recently, by measuring the viscosity and heat transfer coefficient, Lee et al. [12] evaluated the heat transfer performance with different nanofluids, and concluded that only the MWNT/ water nanofluid was promising for microfludic heat transfer. The inconsistent or even controversial results in the above reports may arise from the sample preparation (including particle shape, aspect ratio, volume fraction, aggregation, surfactant, and base fluid), measurement accuracy, and data processing, as a consequence, detailed investigations on both heat transfer and pressure drop for nanofluid flow are needed to reach a consensus. In the present study, mixed surfactants were used to make homogeneous nanofluids containing MWNTs. Since the fluid
J. Wang et al. / Experimental Thermal and Fluid Science 44 (2013) 716–721
717
Nomenclature Cp dp D f G h lp L Nu P Q Re Si T u
specific heat, J/kg K diameter of nanoparticle, m diameter of test tube, m friction factor mass flow rate, kg/s convective heat transfer coefficient, W/m2 K length of nanoparticle, m length of test tube, m Nusselt number, hDi/k pump power, W heat transfer rate, W Reynolds number, quDi/l inner surface area of test tube, m2 temperature, °C flow velocity, m/s
DT
u k
g l q
temperature difference, °C volume fraction, % thermal conductivity, W m1 K1 heat transfer rate per pump power and per temperature difference, K1 dynamic viscosity, Pa s density, kg/m3
Subscripts b base fluid eff effective i inner surface in inlet m mean out outlet p nanoparticle
Greek symbols DP pressure drop, Pa
temperature changes with flow rate in the heat transfer experiment, the effective thermal conductivity of nanofluids was determined beforehand, and the viscosity was obtained as a function of temperature. Afterwards, a heat transfer system was established, and the average convective heat transfer coefficient and pressure drop for the laminar flow of nanofluids in a circular tube were measured, compared with those of distilled (DI) water. 2. Experimental 2.1. Nanofluids preparation DI water and the Carboxyl MWNTs were used to produce the nanofluids. The carboxyle MWNTs were provided by Chengdu Organic Chemicals Co. Ltd., with length ranging from 5 to 30 lm, outer diameter from 20 to 30 nm and density of about 2.1 g cm3. Since MWNTs were prone to aggregate in DI water, a binary mixture of TritonX-100 (nonionic surfactant) and sodium dodecyl benzene sulfonate (SDBS, anionic surfactant) was used to accomplish better stability. The mass ratios of TritonX-100/SDBS and mixture/MWNT were about 20:1 and 3:20, respectively. Then, the MWNT and surfactant mixtures were dispersed into a preset amount of DI water, and the agglomerated MWNTs were separated by a high-shear mixer. Finally, a black homogeneous ink-like suspension with different concentrations was obtained.
erated joule heat and produced a temperature oscillation at 2x, its electrical resistance was also modulated at 2x, thus the voltage drop across the strip contained a modulated component at 3x, which related to the thermal properties of the surrounding materials. In order to prevent the electrical leakage from the heater to the surrounding liquid, a 100 nm dielectric film (silicon nitride) was deposited on the substrate by chemical vapor deposition. The schematic of the measuring device for 3x method is shown in Fig. 1. The experimental system was similar to that for measuring the thermal effusivity of microwires [13,16]. The deposited Au strip was firstly loaded into a high vacuum chamber, by measuring the third harmonic voltages of the strip at frequency ranges from 5 to 100 Hz, the thermal conductivity of substrate was obtained by the slope of the curve in the real part of the temperature oscillation versus a logarithm of frequency. Afterward, the device was immersed in a bath of the test fluids (DI water or nanofluid), and the sum of the thermal conductivities of the two media (i.e., substrate and test fluid) was determined by the similar approach at room temperature. Using this two-step experiment, the thermal conductivities of DI water and nanofluids with different concentrations were derived.
2.2. Measurement of viscosity and thermal conductivity The viscosity of nanofluids was measured by a rheometer (Physica-MCR300, Germany) with the same rotor. The measurements were done on nanofluids with different concentrations at shear rate in the range from 1 to 120 s1. The temperature-dependent behavior of viscosity was also obtained at a given shear rate (30 s1) from 20 to 50 °C. The thermal conductivity was measured by using the 3x method [13–15]. In this experiment, a 200 nm thick Au film was deposited on a 0.7 mm thick substrate (Pyrex glass) along with a 10 nm thick Cr film as an adhesion layer. The Au film was patterned by the standard photolithographic technique, and the Au strip with length of 5 mm and width of 20 lm was fabricated, which served both as a heater and a senor to detect the temperature response. Driven by an alternating current at an angular frequency x, the Au strip gen-
Fig. 1. Enhancement ratio of thermal conductivity of nanofluids. Insert: Schematic of measuring device for 3x measurement.
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J. Wang et al. / Experimental Thermal and Fluid Science 44 (2013) 716–721
Fig. 2. Experimental setup. Insert: Scanning electron microscopy image of cross section of test tube.
2.3. Measurement of heat transfer and pressure drop The experimental setup for measuring the convective heat transfer and pressure drop mainly consisted of a pump, a test section, a storage tank, a reservoir, which is shown schematically in Fig. 2. The test fluid was pumped through a reservoir, then entered the test section, and finally collected by a collection tank. The flow rate was regulated by a peristaltic type pump, which was calibrated by collecting liquid in a specified time interval, and the maximum flow rate the pump could deliver was 20 mL per minute. A stainless tube with 952 lm inner diameter, 2243 lm outer diameter and 949.5 mm length was used as the test section, and the peak-valley roughness of its inner surface was measured by a Talysurf-120 tester, giving a relative roughness less than 1%. The test tube was electrically heated by a power supply with constant current, and was insulated thermally by a thick blanket to minimize the heat loss from the tube to the ambient. Ten thermocouples (T-type) were mounted evenly along the tube to measure the wall temperatures, and another two armored thermocouples (K-type) were located at the inlet and outlet of the tube to measure the fluid temperature. The pressure drop along the tube was measured by a pressure transducer, which was installed at the inlet, and the outlet was approximately equal to the atmospheric pressure. The readings of twelve thermocouples and the pressure transducer were automatically recorded by the data acquisition system (Agilent 34970). From the collected data of temperatures and mass flow rates (G), the average Nusselt number (Nu) can be calculated from
Nu ¼
hDi QDi ¼ k kDT m S
ð1Þ
where h is the convective heat transfer coefficient, S is the inner surface area of the test tube, i.e., S = pDiL, Q is the heat transfer rate, which is calculated by Q = GCp(ToutTin), Di and L are the inner diameter and length of the tube, Cp and k are the specific heat and thermal conductivity of liquids at (Tin + Tout)/2, DTm is the mean temperature difference between the wall and the flow fluid, which is estimated by
DT m ¼
10 X j¼1
Tj
T in þ T out 2
ð2Þ
Tj represents the temperature measured by the T-type thermocouple, Tin and Tout denote inlet and outlet temperatures, respectively. The Reynolds number (Re) is defined by
Re ¼
quDi l
ð3Þ
where q and l are density and viscosity of fluid at (Tin + Tout)/2, u is the mean flow velocity, which is determined by u ¼ 4G=ðqpD2i Þ. With the obtained pressure drop (DP) and mean flow velocity, the friction factor is given by
f ¼
Di 2DP L qu2
ð4Þ
In the absence of the available experimental data, the density and specific heat of the dilute nanofluids are determined by the correlations in [17], which is close to those of DI water. The enhancement of the heat transfer is usually at the expense of the pump power. Considering the two factors, the performance of heat transfer system with different fluids can be evaluated by the heat transfer rate per pump power and per temperature difference [18]
g¼
hS P
ð5Þ
Here, hS denotes the thermal conductance of the tube, and P is the required pump power to drive liquid through the tube
P ¼ DP
G
q
ð6Þ
Obviously, the fluids with large g are preferred to be used in the heat transfer systems. 2.4. Uncertainty analysis The uncertainty of thermal conductivity measured by the 3x method mainly comes from the reading errors of third harmonic voltage (2%), fitting errors (less than 0.5%), and the uncertainty of alternating current (less than 0.2%), thus is estimated to be about 2%. The measurement uncertainties of viscosity and pressure drop are about 4% and 5%, respectively. According to Eq. (1), the uncertainty of Nu can be calculated by
dNu ¼ Nu
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 2 dQ dDi dk dDT m dS þ þ þ þ Q k S Di DT m
ð7Þ
The errors associated with the inner diameter and surface area can be ignored. The flow rate controlled by the rotational rate is calibrated by a weighing method, the uncertainty is less than 1%. The accuracy of the thermocouple is found to be within 0.1 °C, excluding the one installed in the outlet of the test section, which is about 0.2 °C. The temperature difference between the inlet and outlet fluid is larger than 10 °C, so the uncertainty of heat transfer rate Q is less than 2%. The mean temperature difference between the wall and the test fluid decreases when the flow rate increases, in this
J. Wang et al. / Experimental Thermal and Fluid Science 44 (2013) 716–721
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experiment the mean temperature difference ranges from 1 to 5 °C, giving an uncertainty of about 7%. Therefore, the uncertainty of Nu is found to be about 7.5% from Eq. (7). Using the similar approach, according to Eq. (4), the uncertainty of the friction factor can be determined to be about 5.2%. 3. Results and discussion Fig. 3 shows the viscosity of nanofluids as a function of shear rate at room temperature. Although the data at low shear rate (below 10 s1) is scattering, a clear shear thinning behavior is observed for MWNT nanofluids especially at high concentration, similar results were reported by [9,10,12,19]. If the shear rate is above 10 s1, the viscosity of the dilute nanofluids reaches a Newtonian plateau, which has a similar value to that of DI water, confirming the measurement accuracy. Comparatively, the viscosity of nanofluid at 1.27 vol.% is about five times larger than that of DI water, and decreases with increasing shear rate even above 100 s1. Fig. 4 presents the temperature-dependent behavior of viscosity of MWNT nanofluids. For the dilute nanofluids, the viscosity decreases with increasing temperature, and the data in Fig. 4 are used to interpolate the viscosity at specific fluid temperature in the heat transfer experiment. The experimental procedure presented in previous section for the 3x measurement is verified by measuring the thermal conductivity of DI water. The sum of thermal conductivities of DI water and substrate is determined to be 1.619 W m1 K1, subtracting the thermal conductivity of Pyrex glass of 1.022 W m1 K1, the thermal conductivity of DI water is calculated to be 0.597 W m1 K1, which is closed to the literature value of 0.60 W m1 K1at room temperature [20]. Fig. 1 shows the effective thermal conductivity of nanofluids as a function of volume fraction at room temperature, where the data are normalized with respect to the thermal conductivity of DI water, and are compared with the results in [9,21–23]. The effective thermal conductivity is compared with that obtained by the measuring device without depositing the dielectric film. It is found that the dielectric film has a negligible effect on the thermal conductivity measurement of nanofluids, and the enhancement is less than 13% for the nanofluid at 1.27 vol.%. The effective thermal conductivity increases with increasing CNT concentration. At low concentration, the data can be predicted reasonably well by the Hamilton-Crosser (H-C) model [23]
keff ¼ kb
kp þ ðn 1Þkb ðn 1Þðkb kp Þuv kp þ ðn 1Þkb þ ðkb kp Þuv
ð8Þ
Fig. 3. Viscosity as a function of shear rate for nanofluids at different concentrations.
Fig. 4. Effect of temperature on viscosity of nanofluids.
where uv is the volume fraction, keff, kb and kp are the thermal conductivity of CNT nanofluid, DI water and MWNT, respectively. The parameter n is defined by
1=3 lp n ¼ 12 dp
ð9Þ
with CNT length lp and diameter dp. In this calculation, the length, diameter and thermal conductivity of MWNT are taken to be 5 lm, 30 nm and 200 W m1 K1 [8], respectively. To evaluate the measurement accuracy, the experiments on the convective heat transfer and pressure drop of each fluid are repeated twice, and Nu of nanofluids at different concentrations is shown in Fig. 5, compared with that of DI water. At a given power supply, the mean fluid temperature decreases as the flow rate increases. Taken into account the temperature effect, the viscosity presented in Fig. 3 is used for the data reduction process, and the effective thermal conductivity is predicted from the H-C model with the aid of the temperature-dependent behavior of thermal conductivity of DI water [20]. Fig. 5 shows that Nu increases with increasing Re, and is not limited in between 4.36 and 3.66 which correspond to constant heat flux and constant temperature boundary condition, respectively. The deviation from the classical theory can be possibly explained by the axial heat conduction [24]. A considerable increase in the convective heat transfer of nanofluids at Re > 100 is observed in comparison with that of DI water, and the enhancement becomes more obvious for nanofluids at high concentration. For example, Re 120, the heat transfer coefficient in-
Fig. 5. Nusselt numbers as a function of Reynolds numbers.
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J. Wang et al. / Experimental Thermal and Fluid Science 44 (2013) 716–721
creases up to about 70% and 190% with concentrations of 0.05 vol.% and 0.24 vol.%, respectively. At (Tin + Tout)/2 50 °C, the increase of thermal conductivity is predicted to be less than 10% for suspension at 0.24 vol.%, therefore, the enhancement in heat transfer cannot be purely attributed to the increase of thermal conductivity. Since the heat transfer coefficient can be approximately treated as the ratio of the thermal conductivity to the thermal boundary layer thickness, the reduction in the thermal boundary layer can be another reason for the significant enhancement in the heat transfer. Several mechanisms will incur the thermal boundary reduction. One possible explanation is the early transition from laminar to turbulent flow [25], which can be clarified by the flow resistance pattern. The pressure drop for different fluids in the horizontal tube is shown in Fig. 6, which is found to vary linearly with Re, therefore, the present flow pattern is confirmed to be laminar. The corresponding friction factor is well predicted by the HagenPoiseuille flow theory, as shown in Fig. 7, similar findings were reported by [3,11,26–28]. The particle migration offers another explanation to the thermal boundary reduction. The following mechanisms [26,29], such as inertia, Brownian diffusion, thermophoresis, and diffusiophoresis are likely to induce the particle migration. Using the order of magnitude analysis, Buongiorno [29] proposed that the Brownian diffusion and thermophoresis were the dominate effects, which was confirmed by [26]. Due to the particle migration, the concentration near the tube centerline will be larger than that at the wall, thus the relatively large viscosity and thermal conductivity are predicted at the centerline, leading to the flattening of velocity profile and the increasing temperature gradient at the wall region [26,30]. Recently, using a micro-particle image velocimetry, Walsh et al. [31] found that the shear rate at the wall region increased up to 100% above that predicted by the Hagen-Poiseuille flow theory. The high shear rate at the wall region will further reduce the viscosity and enhance the particle migration, which is possibly responsible for the notable enhancement in the heat transfer. The merits of CNT nanofluids depend on the trade-off between the desired heat transfer enhancement and the pump power consumption. Fig. 8 shows the relationship between the heat transfer rate per pump power and per temperature difference, g, and Re for different fluids. Although the data appear somewhat scattering, it can be found that, g of DI water is nearly Re independent, while g for nanofluid flow increases monotonously with increasing Re, and the effect of CNT concentration on g is not obvious. At relatively high flow rate, i.e., Re > 100, g of nanofluids is much larger than that of DI water due to the considerable enhancement in the heat transfer rate. The present result indicates that the CNT nanofluids at low concentration will increase the heat transfer
Fig. 7. Comparison of friction factor correlation with experimental data for different fluids.
Fig. 8. Heat transfer rate per pump power and per temperature difference for different fluids.
with little extra penalty in pump power, thus are the promising heat transfer media. 4. Conclusions The convective heat transfer and pressure drop of dilute nanofluids containing MWNTs in a horizontal circular tube are experimentally investigated. The effective thermal conductivity of the nanofluids can be reasonably well predicted by the H-C model, and a shear thinning behavior is also observed. The suspended MWNTs remarkably enhance the convective heat transfer compared with that of DI water at Re > 100, indicating that the enhancement in the convective heat transfer is not solely attributed to the effective thermal conductivity enhancement. The pressure drop is found to increase linearly with increasing Re, confirming the laminar flow condition. The corresponding friction factor for the dilute nanofluids is approximately the same as that of DI water, and can be well predicted by the Hagen-Poiseuille flow theory. Our results suggest that the CNT nanofluids at low concentration have great potential for applications in the heat transfer systems. Acknowledgements
Fig. 6. Pressure drops as a function of Reynolds numbers.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 50730006, 50925519, 51106029) and
J. Wang et al. / Experimental Thermal and Fluid Science 44 (2013) 716–721
the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20110092120006). References [1] S.U.S. Choi, Developments, applications of non-Newtonian flows vol 3, in: D.A. Siginer, H.P. Wang (Eds.), Springer, New York, 1995, p. 99. [2] B.C. Pak, Y. Cho, Exp. Heat Transfer 11 (1998) 151. [3] Y.M. Xuan, Q. Li, J. Heat Transfer 125 (2003) 151. [4] W. Williams, J. Buongiorno, L.W. Hu, J. Heat Transfer 130 (2008) 042412. [5] S.Z. Heris, M.N. Esfahany, S.Gh. Etemad, Int. Commun. Heat Mass Transfer 33 (2006) 529. [6] H.Q. Xie, Y. Li, W. Yu, Phys. Lett. A 374 (2010) 2566. [7] C.H. Yu, L. Shi, Z. Yao, D.Y. Li, A. Majumdar, Nano Lett. 5 (2005) 1842. [8] M. Fujii, X. Zhang, H.Q. Xie, H. Ago, K. Takahashi, T. Ikuta, H. Abe, T. Shimizu, Phys. Rev. Lett. 95 (2005) 065502. [9] Y.L. Ding, H. Alias, D.S. Wen, R.A. Williams, Int. J. Heat Mass Transfer 49 (2006) 240. [10] G.W. Ko, K. Heo, K. Lee, D.S. Kim, C. Kim, Y. Sohn, M. Choi, Int. J. Heat Mass Transfer 50 (2007) 4749. [11] L. Liao, Z.H. Liu, Heat Mass Transfer 45 (2009) 1129. [12] J. Lee, P.E. Charagozloo, B. Kolade, J.K. Eaton, K.E. Goodson, J. Heat Transfer 132 (2010) 092401. [13] S.R. Choi, J. Kim, D. Kim, Rev. Sci. Instrum. 78 (2007) 084902.
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Contents lists available at SciVerse ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Heat transfer and pressure drop of nanofluids containing carbon nanotubes in laminar flows Jianli Wang a,b, Jianjun Zhu b, Xing Zhang b,⇑, Yunfei Chen a a b
School of Mechanical Engineering and Jiangsu Key Laboratory for Design and Manufacture of Micro Nano Biomedical Instruments, Southeast University, Nanjing 210096, China Key Laboratory for Thermal Science and Power Engineering of Education Ministry, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 9 February 2012 Received in revised form 30 August 2012 Accepted 10 September 2012 Available online 21 September 2012 Keywords: Carbon nanotube Convective heat transfer Nanofluid Pressure drop
a b s t r a c t The heat transfer and pressure drop of nanofluids containing carbon nanotubes in a horizontal circular tube are experimentally investigated. The friction factor of the dilute nanofluids shows a good agreement with the prediction from the Hagen-Poiseuille flow theory. A considerable enhancement in the average convective heat transfer is also observed compared with the distilled water. For the nanofluids with volumetric concentration of 0.05% and 0.24%, the heat transfer enhancement are 70% and 190% at Reynolds number of about 120 respectively, while the enhancement of thermal conductivity is less than 10%, therefore, the large heat transfer increase cannot be solely attributed to the enhanced thermal conductivity. By measuring the pump power supply and the thermal conductance of the test tube, our results suggest that the nanofluids at low concentration enhance the heat transfer with little extra penalty in pump power, thus have great potential for applications in the heat transfer systems. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction With the increasing requirement of high removal capacity of the heat dissipation in microelectronic devices, such as microelectromechanical systems and microflow devices, many efforts have been devoted to the study of heat transfer and flow resistance in microchannels. The fluids dispersed with nanoparticles (nanofluids) have been demonstrated to give a large increase in thermal conductivity [1], thus show great potential for improving the heat transfer performance. In the past decade, many attempts have been made to characterize the heat transfer and pressure drop of nanofluids. For turbulent flow, Pak and Cho [2] measured the friction factor and heat transfer behaviors of Al2O3/water and TiO2/water nanofluids, the heat transfer coefficient was found to be smaller than that of pure water at a given flow rate. Nevertheless, Xuan and Li [3] reported an enhancement of about 60% in the heat transfer coefficient with the use of 2 vol.% Cu/water nanofluids, and no extra augmentation in pressure drop was observed with the addition of nanoparticles. Williams et al. [4] showed no abnormal heat transfer enhancement for Al2O3/water and ZrO2/water nanofluids. For laminar flow, Heris et al. [5] reported an enhancement of about 29% in the heat transfer coefficient using Al2O3/water nanofluids, and concluded that the heat transfer coefficient of Al2O3/water was higher than that of CuO/water. Xie et al. [6] investigated the heat transfer enhance⇑ Corresponding author. Tel.: +86 010 62772668; fax: +86 010 62781610. E-mail address: [email protected] (X. Zhang). 0894-1777/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2012.09.013
ment of nanofluids using four different nanoparticles, and the highest enhancement up to 252% for MgO/water nanofluids was observed. Compared with these oxide nanoparticles, the carbon nanotubes (CNTs) have significantly high thermal conductivities [7,8], thus show great potential to be used as additives in nanofluids. Ding et al. [9] measured the convective heat transfer of multiwalled carbon nanotube (MWNT) nanofluids, and found an increase of about 350%. Ko et al. [10] reported that the friction factor of MWNT/water nanofluid dispersed with CNTs using surfactants was larger than that prepared by the acid treatment, and the latter gave only a slight increase in friction factor compared with the prediction from the Hagen-Poiseuille flow theory. Liao and Liu [11] measured the heat transfer and flow drag characteristics of MWNT/water nanofluids under both laminar and turbulent flow conditions, and showed that the enhancement ratio of heat transfer coefficient and that of thermal conductivity were almost the same. Recently, by measuring the viscosity and heat transfer coefficient, Lee et al. [12] evaluated the heat transfer performance with different nanofluids, and concluded that only the MWNT/ water nanofluid was promising for microfludic heat transfer. The inconsistent or even controversial results in the above reports may arise from the sample preparation (including particle shape, aspect ratio, volume fraction, aggregation, surfactant, and base fluid), measurement accuracy, and data processing, as a consequence, detailed investigations on both heat transfer and pressure drop for nanofluid flow are needed to reach a consensus. In the present study, mixed surfactants were used to make homogeneous nanofluids containing MWNTs. Since the fluid
J. Wang et al. / Experimental Thermal and Fluid Science 44 (2013) 716–721
717
Nomenclature Cp dp D f G h lp L Nu P Q Re Si T u
specific heat, J/kg K diameter of nanoparticle, m diameter of test tube, m friction factor mass flow rate, kg/s convective heat transfer coefficient, W/m2 K length of nanoparticle, m length of test tube, m Nusselt number, hDi/k pump power, W heat transfer rate, W Reynolds number, quDi/l inner surface area of test tube, m2 temperature, °C flow velocity, m/s
DT
u k
g l q
temperature difference, °C volume fraction, % thermal conductivity, W m1 K1 heat transfer rate per pump power and per temperature difference, K1 dynamic viscosity, Pa s density, kg/m3
Subscripts b base fluid eff effective i inner surface in inlet m mean out outlet p nanoparticle
Greek symbols DP pressure drop, Pa
temperature changes with flow rate in the heat transfer experiment, the effective thermal conductivity of nanofluids was determined beforehand, and the viscosity was obtained as a function of temperature. Afterwards, a heat transfer system was established, and the average convective heat transfer coefficient and pressure drop for the laminar flow of nanofluids in a circular tube were measured, compared with those of distilled (DI) water. 2. Experimental 2.1. Nanofluids preparation DI water and the Carboxyl MWNTs were used to produce the nanofluids. The carboxyle MWNTs were provided by Chengdu Organic Chemicals Co. Ltd., with length ranging from 5 to 30 lm, outer diameter from 20 to 30 nm and density of about 2.1 g cm3. Since MWNTs were prone to aggregate in DI water, a binary mixture of TritonX-100 (nonionic surfactant) and sodium dodecyl benzene sulfonate (SDBS, anionic surfactant) was used to accomplish better stability. The mass ratios of TritonX-100/SDBS and mixture/MWNT were about 20:1 and 3:20, respectively. Then, the MWNT and surfactant mixtures were dispersed into a preset amount of DI water, and the agglomerated MWNTs were separated by a high-shear mixer. Finally, a black homogeneous ink-like suspension with different concentrations was obtained.
erated joule heat and produced a temperature oscillation at 2x, its electrical resistance was also modulated at 2x, thus the voltage drop across the strip contained a modulated component at 3x, which related to the thermal properties of the surrounding materials. In order to prevent the electrical leakage from the heater to the surrounding liquid, a 100 nm dielectric film (silicon nitride) was deposited on the substrate by chemical vapor deposition. The schematic of the measuring device for 3x method is shown in Fig. 1. The experimental system was similar to that for measuring the thermal effusivity of microwires [13,16]. The deposited Au strip was firstly loaded into a high vacuum chamber, by measuring the third harmonic voltages of the strip at frequency ranges from 5 to 100 Hz, the thermal conductivity of substrate was obtained by the slope of the curve in the real part of the temperature oscillation versus a logarithm of frequency. Afterward, the device was immersed in a bath of the test fluids (DI water or nanofluid), and the sum of the thermal conductivities of the two media (i.e., substrate and test fluid) was determined by the similar approach at room temperature. Using this two-step experiment, the thermal conductivities of DI water and nanofluids with different concentrations were derived.
2.2. Measurement of viscosity and thermal conductivity The viscosity of nanofluids was measured by a rheometer (Physica-MCR300, Germany) with the same rotor. The measurements were done on nanofluids with different concentrations at shear rate in the range from 1 to 120 s1. The temperature-dependent behavior of viscosity was also obtained at a given shear rate (30 s1) from 20 to 50 °C. The thermal conductivity was measured by using the 3x method [13–15]. In this experiment, a 200 nm thick Au film was deposited on a 0.7 mm thick substrate (Pyrex glass) along with a 10 nm thick Cr film as an adhesion layer. The Au film was patterned by the standard photolithographic technique, and the Au strip with length of 5 mm and width of 20 lm was fabricated, which served both as a heater and a senor to detect the temperature response. Driven by an alternating current at an angular frequency x, the Au strip gen-
Fig. 1. Enhancement ratio of thermal conductivity of nanofluids. Insert: Schematic of measuring device for 3x measurement.
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Fig. 2. Experimental setup. Insert: Scanning electron microscopy image of cross section of test tube.
2.3. Measurement of heat transfer and pressure drop The experimental setup for measuring the convective heat transfer and pressure drop mainly consisted of a pump, a test section, a storage tank, a reservoir, which is shown schematically in Fig. 2. The test fluid was pumped through a reservoir, then entered the test section, and finally collected by a collection tank. The flow rate was regulated by a peristaltic type pump, which was calibrated by collecting liquid in a specified time interval, and the maximum flow rate the pump could deliver was 20 mL per minute. A stainless tube with 952 lm inner diameter, 2243 lm outer diameter and 949.5 mm length was used as the test section, and the peak-valley roughness of its inner surface was measured by a Talysurf-120 tester, giving a relative roughness less than 1%. The test tube was electrically heated by a power supply with constant current, and was insulated thermally by a thick blanket to minimize the heat loss from the tube to the ambient. Ten thermocouples (T-type) were mounted evenly along the tube to measure the wall temperatures, and another two armored thermocouples (K-type) were located at the inlet and outlet of the tube to measure the fluid temperature. The pressure drop along the tube was measured by a pressure transducer, which was installed at the inlet, and the outlet was approximately equal to the atmospheric pressure. The readings of twelve thermocouples and the pressure transducer were automatically recorded by the data acquisition system (Agilent 34970). From the collected data of temperatures and mass flow rates (G), the average Nusselt number (Nu) can be calculated from
Nu ¼
hDi QDi ¼ k kDT m S
ð1Þ
where h is the convective heat transfer coefficient, S is the inner surface area of the test tube, i.e., S = pDiL, Q is the heat transfer rate, which is calculated by Q = GCp(ToutTin), Di and L are the inner diameter and length of the tube, Cp and k are the specific heat and thermal conductivity of liquids at (Tin + Tout)/2, DTm is the mean temperature difference between the wall and the flow fluid, which is estimated by
DT m ¼
10 X j¼1
Tj
T in þ T out 2
ð2Þ
Tj represents the temperature measured by the T-type thermocouple, Tin and Tout denote inlet and outlet temperatures, respectively. The Reynolds number (Re) is defined by
Re ¼
quDi l
ð3Þ
where q and l are density and viscosity of fluid at (Tin + Tout)/2, u is the mean flow velocity, which is determined by u ¼ 4G=ðqpD2i Þ. With the obtained pressure drop (DP) and mean flow velocity, the friction factor is given by
f ¼
Di 2DP L qu2
ð4Þ
In the absence of the available experimental data, the density and specific heat of the dilute nanofluids are determined by the correlations in [17], which is close to those of DI water. The enhancement of the heat transfer is usually at the expense of the pump power. Considering the two factors, the performance of heat transfer system with different fluids can be evaluated by the heat transfer rate per pump power and per temperature difference [18]
g¼
hS P
ð5Þ
Here, hS denotes the thermal conductance of the tube, and P is the required pump power to drive liquid through the tube
P ¼ DP
G
q
ð6Þ
Obviously, the fluids with large g are preferred to be used in the heat transfer systems. 2.4. Uncertainty analysis The uncertainty of thermal conductivity measured by the 3x method mainly comes from the reading errors of third harmonic voltage (2%), fitting errors (less than 0.5%), and the uncertainty of alternating current (less than 0.2%), thus is estimated to be about 2%. The measurement uncertainties of viscosity and pressure drop are about 4% and 5%, respectively. According to Eq. (1), the uncertainty of Nu can be calculated by
dNu ¼ Nu
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 2 dQ dDi dk dDT m dS þ þ þ þ Q k S Di DT m
ð7Þ
The errors associated with the inner diameter and surface area can be ignored. The flow rate controlled by the rotational rate is calibrated by a weighing method, the uncertainty is less than 1%. The accuracy of the thermocouple is found to be within 0.1 °C, excluding the one installed in the outlet of the test section, which is about 0.2 °C. The temperature difference between the inlet and outlet fluid is larger than 10 °C, so the uncertainty of heat transfer rate Q is less than 2%. The mean temperature difference between the wall and the test fluid decreases when the flow rate increases, in this
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experiment the mean temperature difference ranges from 1 to 5 °C, giving an uncertainty of about 7%. Therefore, the uncertainty of Nu is found to be about 7.5% from Eq. (7). Using the similar approach, according to Eq. (4), the uncertainty of the friction factor can be determined to be about 5.2%. 3. Results and discussion Fig. 3 shows the viscosity of nanofluids as a function of shear rate at room temperature. Although the data at low shear rate (below 10 s1) is scattering, a clear shear thinning behavior is observed for MWNT nanofluids especially at high concentration, similar results were reported by [9,10,12,19]. If the shear rate is above 10 s1, the viscosity of the dilute nanofluids reaches a Newtonian plateau, which has a similar value to that of DI water, confirming the measurement accuracy. Comparatively, the viscosity of nanofluid at 1.27 vol.% is about five times larger than that of DI water, and decreases with increasing shear rate even above 100 s1. Fig. 4 presents the temperature-dependent behavior of viscosity of MWNT nanofluids. For the dilute nanofluids, the viscosity decreases with increasing temperature, and the data in Fig. 4 are used to interpolate the viscosity at specific fluid temperature in the heat transfer experiment. The experimental procedure presented in previous section for the 3x measurement is verified by measuring the thermal conductivity of DI water. The sum of thermal conductivities of DI water and substrate is determined to be 1.619 W m1 K1, subtracting the thermal conductivity of Pyrex glass of 1.022 W m1 K1, the thermal conductivity of DI water is calculated to be 0.597 W m1 K1, which is closed to the literature value of 0.60 W m1 K1at room temperature [20]. Fig. 1 shows the effective thermal conductivity of nanofluids as a function of volume fraction at room temperature, where the data are normalized with respect to the thermal conductivity of DI water, and are compared with the results in [9,21–23]. The effective thermal conductivity is compared with that obtained by the measuring device without depositing the dielectric film. It is found that the dielectric film has a negligible effect on the thermal conductivity measurement of nanofluids, and the enhancement is less than 13% for the nanofluid at 1.27 vol.%. The effective thermal conductivity increases with increasing CNT concentration. At low concentration, the data can be predicted reasonably well by the Hamilton-Crosser (H-C) model [23]
keff ¼ kb
kp þ ðn 1Þkb ðn 1Þðkb kp Þuv kp þ ðn 1Þkb þ ðkb kp Þuv
ð8Þ
Fig. 3. Viscosity as a function of shear rate for nanofluids at different concentrations.
Fig. 4. Effect of temperature on viscosity of nanofluids.
where uv is the volume fraction, keff, kb and kp are the thermal conductivity of CNT nanofluid, DI water and MWNT, respectively. The parameter n is defined by
1=3 lp n ¼ 12 dp
ð9Þ
with CNT length lp and diameter dp. In this calculation, the length, diameter and thermal conductivity of MWNT are taken to be 5 lm, 30 nm and 200 W m1 K1 [8], respectively. To evaluate the measurement accuracy, the experiments on the convective heat transfer and pressure drop of each fluid are repeated twice, and Nu of nanofluids at different concentrations is shown in Fig. 5, compared with that of DI water. At a given power supply, the mean fluid temperature decreases as the flow rate increases. Taken into account the temperature effect, the viscosity presented in Fig. 3 is used for the data reduction process, and the effective thermal conductivity is predicted from the H-C model with the aid of the temperature-dependent behavior of thermal conductivity of DI water [20]. Fig. 5 shows that Nu increases with increasing Re, and is not limited in between 4.36 and 3.66 which correspond to constant heat flux and constant temperature boundary condition, respectively. The deviation from the classical theory can be possibly explained by the axial heat conduction [24]. A considerable increase in the convective heat transfer of nanofluids at Re > 100 is observed in comparison with that of DI water, and the enhancement becomes more obvious for nanofluids at high concentration. For example, Re 120, the heat transfer coefficient in-
Fig. 5. Nusselt numbers as a function of Reynolds numbers.
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creases up to about 70% and 190% with concentrations of 0.05 vol.% and 0.24 vol.%, respectively. At (Tin + Tout)/2 50 °C, the increase of thermal conductivity is predicted to be less than 10% for suspension at 0.24 vol.%, therefore, the enhancement in heat transfer cannot be purely attributed to the increase of thermal conductivity. Since the heat transfer coefficient can be approximately treated as the ratio of the thermal conductivity to the thermal boundary layer thickness, the reduction in the thermal boundary layer can be another reason for the significant enhancement in the heat transfer. Several mechanisms will incur the thermal boundary reduction. One possible explanation is the early transition from laminar to turbulent flow [25], which can be clarified by the flow resistance pattern. The pressure drop for different fluids in the horizontal tube is shown in Fig. 6, which is found to vary linearly with Re, therefore, the present flow pattern is confirmed to be laminar. The corresponding friction factor is well predicted by the HagenPoiseuille flow theory, as shown in Fig. 7, similar findings were reported by [3,11,26–28]. The particle migration offers another explanation to the thermal boundary reduction. The following mechanisms [26,29], such as inertia, Brownian diffusion, thermophoresis, and diffusiophoresis are likely to induce the particle migration. Using the order of magnitude analysis, Buongiorno [29] proposed that the Brownian diffusion and thermophoresis were the dominate effects, which was confirmed by [26]. Due to the particle migration, the concentration near the tube centerline will be larger than that at the wall, thus the relatively large viscosity and thermal conductivity are predicted at the centerline, leading to the flattening of velocity profile and the increasing temperature gradient at the wall region [26,30]. Recently, using a micro-particle image velocimetry, Walsh et al. [31] found that the shear rate at the wall region increased up to 100% above that predicted by the Hagen-Poiseuille flow theory. The high shear rate at the wall region will further reduce the viscosity and enhance the particle migration, which is possibly responsible for the notable enhancement in the heat transfer. The merits of CNT nanofluids depend on the trade-off between the desired heat transfer enhancement and the pump power consumption. Fig. 8 shows the relationship between the heat transfer rate per pump power and per temperature difference, g, and Re for different fluids. Although the data appear somewhat scattering, it can be found that, g of DI water is nearly Re independent, while g for nanofluid flow increases monotonously with increasing Re, and the effect of CNT concentration on g is not obvious. At relatively high flow rate, i.e., Re > 100, g of nanofluids is much larger than that of DI water due to the considerable enhancement in the heat transfer rate. The present result indicates that the CNT nanofluids at low concentration will increase the heat transfer
Fig. 7. Comparison of friction factor correlation with experimental data for different fluids.
Fig. 8. Heat transfer rate per pump power and per temperature difference for different fluids.
with little extra penalty in pump power, thus are the promising heat transfer media. 4. Conclusions The convective heat transfer and pressure drop of dilute nanofluids containing MWNTs in a horizontal circular tube are experimentally investigated. The effective thermal conductivity of the nanofluids can be reasonably well predicted by the H-C model, and a shear thinning behavior is also observed. The suspended MWNTs remarkably enhance the convective heat transfer compared with that of DI water at Re > 100, indicating that the enhancement in the convective heat transfer is not solely attributed to the effective thermal conductivity enhancement. The pressure drop is found to increase linearly with increasing Re, confirming the laminar flow condition. The corresponding friction factor for the dilute nanofluids is approximately the same as that of DI water, and can be well predicted by the Hagen-Poiseuille flow theory. Our results suggest that the CNT nanofluids at low concentration have great potential for applications in the heat transfer systems. Acknowledgements
Fig. 6. Pressure drops as a function of Reynolds numbers.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 50730006, 50925519, 51106029) and
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