- Email: [email protected]
Pressure drop of TiO2 nanofluid in circular pipes
Particuology 9 (2011) 486–491
Contents lists available at ScienceDirect
Particuology journal homepage: www.elsevier.com/locate/partic
Pressure drop of TiO2 nanofluid in circular pipes Tun-Ping Teng a,∗ , Yi-Hsuan Hung a , Ching-Song Jwo b , Chien-Chih Chen c , Lung-Yue Jeng c a
Department of Industrial Education, National Taiwan Normal University, Taipei City 10610, Taiwan, China Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei City 10608, Taiwan, China c Graduate Institute of Mechanical and Electrical Engineering, National Taipei University of Technology, Taipei City 10608, Taiwan, China b
a r t i c l e
i n f o
Article history: Received 22 September 2009 Received in revised form 14 January 2011 Accepted 3 May 2011 Keywords: Titania (TiO2 ) Nanofluid Laminar flow Turbulent flow
a b s t r a c t This paper discusses the pressure drop in circular pipes of TiO2 /water nanofluid for both laminar and turbulent flows at different temperatures and TiO2 weight fractions. This study shows that TiO2 /water nanofluid causes enhancement, but temperature rise reduces pressure drop. The proportional increase in pressure drop for turbulent flow is lower than that for laminar flow. The traditional equation for pressure drop fails to accurately estimate the pressure drop for laminar and turbulent flows. Accordingly, this study developed new empirical equations for the friction factor for both laminar and turbulent flows, and the maximum deviations between calculated and experimental results were reduced to within the ranges of −6.17% to 3.55% and −3.08% to 3.81%, respectively, that is, for TiO2 /water nanofluid, the correlations apply better to turbulent than to laminar flow. © 2011 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
1. Introduction Research has shown that adding nanoparticles to a liquid can enhance its thermal conductivity, which, however, does not necessarily lead to increase heat exchange in real practice. Recent research has focused on the benefits of nanofluid in heat convection (Buongiorno, Venerus, Prabhat, McKrell, Townsend, & Christianson, 2009; Godson, Raja, Mohan Lal, & Wongwises, 2010; Heris, Etemad, & Esfahany, 2006; Khanafer, Vafai, & Lightstone, 2003; Nguyen, Roy, Gauthier, & Galanis, 2007; Tsai et al., 2004; Wang & Mujumdar, 2007; Wu et al., 2010; Xuan & Li, 2003). However, others suggested the opposite results (Putra, Roetzel, & Das, 2003; Wen & Ding, 2006) and believed that the performance of the whole system would deteriorate if the benefits of increased performance in heat exchange were less than the damage caused by increased pressure drop due to increased viscosity by the solid–liquid mixture. Many empirical equations have been proposed to predict viscosity of nanofluids, yet no consensus has been reached because of differences caused by materials, particle sizes, and manufacturing methods (Das, Putra, & Roetzel, 2003; Jwo, Teng, Wu, Chang, & Chen, 2009; Li, Li, & Wang, 2002; Rao, 2010; Tseng & Lin, 2003; Wang, Xu, & Choi, 1999; Wierenga & Philipse, 1998). He et al. (2007) studied both heat transfer and flow behavior of TiO2 /distilled water nanofluids flowing upward through a ver-
∗ Corresponding author. Tel.: +866 2 7734 3358; fax: +866 2 2392 9449. E-mail address: [email protected] (T.-P. Teng).
tical pipe, both laminar and turbulent, under a constant heat flux around the tube, finding that the pressure drop of the nanofluids was not much different from that of the base fluid. Rea, McKrell, Hu, and Buongiorno (2009) studied laminar convective heat transfer and viscous pressure loss for alumina/water and zirconia/water nanofluids flowing in a vertical heated tube, showing that the heat transfer coefficient was increased by the nanofluids, and that the measured pressure loss for the nanofluids was much higher than that for pure water. The pressure loss of the 6 vol.% alumina nanofluid was approximately 7.2 times higher than that of water. Duangthongsuk and Wongwises (2009) studied experimentally the forced convective heat transfer and flow characteristics of a nanofluid consisting of water and 0.2 vol.% TiO2 nanoparticles. The results showed that use of a nanofluid had hardly any penalty in pressure drop. Pantzali, Kanaris, Antoniadis, Mouza, and Paras (2009) presented the effects of using a nanofluid (CuO/water, 4 vol.%) in a miniature plate heat exchanger (PHE) with a modulated surface, showing that the pressure drop increased by less than 10%. Sundar and Sharma (2010) studied the heat transfer coefficient and friction factor in a plain tube with a twisted tape insert at different volume concentrations of Al2 O3 nanofluids under Re of 10,000–22,000 (turbulent flow) with tapes of different twist ratios, showing that the friction factor of 0.5 vol.% of Al2 O3 nanofluid with a twist ratio of five was 1.096 times higher as compared to the flow of water in a circular tube. This research focuses on TiO2 /water nanofluids with low nanoparticle concentrations (0–1.5 wt%), aiming at measuring the effect of nanoparticle concentration and temperatures (10–40 ◦ C)
1674-2001/$ – see front matter © 2011 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
doi:10.1016/j.partic.2011.05.001
T.-P. Teng et al. / Particuology 9 (2011) 486–491
487
on the density, viscosity, and pressure drop, in order to compare the difference in pressure drop between the nanofluid and pure water in a circular pipe. Finally, the experimental data are analyzed using traditional equations for friction factor, to formulate empirical equations suitable for calculating pressure drop of TiO2 /water nanofluids. 2. Calculation of pressure drop The measured or calculated results of friction factor, density, flow rate, and pipe size were substituted into the following equation, for both laminar flow and turbulent flow conditions, for a circular pipe, to yield the pressure drop (White, 1991): P = f
L V2 , d 2 f
(1)
with the following friction factor for laminar flow: flami.
64 = . Re
Fig. 1. SEM image of TiO2 nanoparticles as purchased.
(2)
For turbulent flow, Swamee and Jain (1976) proposed a formula which leads to calculated results extremely close to the turbulent flow region in the Moody chart, as could be written as follows: fturb. =
0.25 [log((1/(3.7(d/ε))) + (5.74/Re0.9 ))]
2
.
(3)
The Reynolds number (Re) in Eqs. (2) and (3) could be shown as: Re =
Vdf , f
(4)
where f is the friction factor, d is the inner diameter of pipe (m), L is the length of pipe (m), V is the velocity of fluid (m/s), f is the density of fluid (kg/m3 ), ε is the roughness (m), and f is the viscosity of fluid (Pa s). The value of Re represents the flow condition: for laminar flow Re < 2000 and for turbulent flow Re > 4000. 3. Experimental and data analysis 3.1. Preparation of TiO2 /water nanofluid Fig. 2. TEM image of TiO2 nanoparticles.
The TiO2 /water nanofluid produced from a direct synthesis method was used as the experimental sample, and mechanical agitations were used for dispersing the nanoparticles into three weight fractions (0.5, 1.0, 1.5 wt%). The solid volume was determined by calculating the equivalent weight of the solid based on its true density (approximately 3840 kg/m3 ). The nanoparticles, purchased from Yong-Zhen Technomaterial Co. Ltd., generally form loose agglomerates as shown in Fig. 1. Fig. 2, the TEM photograph of TiO2 nanoparticles with nominal particle sizes of 20–30 nm, shows that the shapes of nanoparticles are mainly rectangular, and the particle size closely meets the nominal particle size of the supplier. Fig. 3 shows the XRD pattern of TiO2 nanoparticles, confirming the main component to be anatase. The nanoparticles can be successfully dispersed in deionized water using a homogenizer with electromagnetic agitation and ultrasonic vibration, to form a TiO2 /water nanofluid without addition of any dispersant or surfactant. 3.2. Experimental procedure Fig. 4 shows this experiment used a thermostatic bath (Firsteck B403L) to stabilize the temperature of the sample until it reached the expected temperature of ±0.5 ◦ C. A density meter and a rheometer were then used to measure the density and viscosity
Fig. 3. XRD pattern of TiO2 nanoparticles.
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T.-P. Teng et al. / Particuology 9 (2011) 486–491
um =
2 +
2 +
V V
2 +
P P
2 +
W W
2 +
T T
2 .
(5) The accuracy of the density meter is ±0.001 g, that of the rheometer is ±1.0%, that of the flow meter is ±2.0%, that of the pressure meter is ±2.0%, that of the precise electric balance is ±0.01 g, and that of the RTD is ±0.5 ◦ C. Therefore, the uncertainty of the experiment was less than ±6.0%. 3.4. Data analysis Regarding the margin of deviation between experimental data (DExp. ) and data calculated by the traditional equation (DCal. ) and empirical equations (DReg. ): this study used experimental data as a benchmark for results of empirical equations, and the deviation between experimental results and calculated data of the traditional equation and empirical equations can be calculated as follows:
DevCal. (%) =
Fig. 4. Experimental setup for measuring pressure drop.
DevReg. (%) = of the nanofluids of various weight fractions and sample temperatures. In pressure drop experiments in a circular pipe, after 1800 cm3 of nanofluid was poured into a 2-l stainless steel bucket, and the bucket was placed in a thermostatic bath, the nanofluid was pumped to the measurement pipe for circulation. The pressure drop of nanofluid in the pipe was measured. The test pipe consisted of a circular steel tube (ε = 4.6 × 10−5 m) with the length (L) of 0.6 m and the internal diameter (d) of 0.0035 m. To avoid entrance effect, L/d 100. To avoid drastic temperature change, the pipe was wrapped by thermal insulation material at a thickness of 2 cm. Nanofluid flow rate was controlled at a region between turbulent and laminar flow. The temperature of the sample was stabilized at ±0.5 ◦ C of the expected value. The pressure was then measured of the nanofluid of various weight fractions, and sample temperatures were taken at the inlet and outlet of the pipe. To guarantee accuracy, all controlled factors were measured ten times, and the most concentrated five test results were selected as average values of the experimental results. Experimental results of density and viscosity were inserted into Eqs. (1)–(4) to calculate their effects on pressure drop in the circular pipe, in order to compare calculated results with experimental data. Finally, the experimental and calculated results were used to perform multiple regression analysis to acquire a new empirical equation.
DCal. − DExp. DExp.
DReg. − DExp. DExp.
× 100,
(6)
× 100.
(7)
For easy comparison of experimental data of pressure drop before and after changing the TiO2 /water nanofluid, all data obtained with the water were used as baseline values; that is, experimental data obtained after the TiO2 /water nanofluid were used to compare with baseline values. The differences before and after changing the TiO2 /water nanofluid are presented as proportions, and can be calculated as follows: RP (%) =
P − P water nf Pwater
× 100.
4. Results and discussion Fig. 5 shows the measured results of the weight fractions of TiO2 /water nanofluid with the change of density under different temperatures. The increase in added concentration enhances the density of nanofluid, whereas temperature rise reduces the density
3.3. Uncertainty analysis Uncertainty of experimental results was determined by measurement deviation of the parameters, including density, viscosity, flow rate, pressure drop, weight, and temperature. In pressure drop experiment on nanofluid, density () was measured by a density meter (DA-130, KYOTO); viscosity () was measured by a rheometer (DVIII+, Brookfield); flow rate (V) was measured by a flow meter (NF05, Aichi Tokei); pressure (P) drop was measured by a pressure meter (PS-9302, LUTRON); the weight (W) of nanoparticles was measured by a precision electric balance (XT620M, Precisa); and temperature was determined using a resistance temperature (T) detector (RTD, pt-100) of the thermostatic bath. The uncertainty of experimental results could be expressed as follows:
(8)
Fig. 5. Experimental results of density measurement.
T.-P. Teng et al. / Particuology 9 (2011) 486–491
489
Fig. 6. Experimental results of viscosity measurement.
Fig. 8. Experimental data and calculated results of pressure drop in laminar flow (V = 0.57 m/s).
of nanofluid. The influence of weight fractions on density change appears to be approximately linear. However, the density presented a non-linear trend under different temperatures; the main reason is that the added nanoparticles and bulk liquid have a great difference in the coefficient of thermal expansion. Fig. 6 shows the measured effect of the weight fractions of TiO2 /water nanofluid on the change of viscosity under different temperatures. Temperature rise reduces the viscosity of nanofluid, whereas increased weight fraction increases the viscosity of nanofluid, and for the different temperatures, the effect of weight fraction on viscosity appears nearly linear. Fig. 7 shows the enhancement ratio of pressure drop by increasing the solids content of the TiO2 /water nanofluid. For solids content of 0–1.5 wt% and temperature of 10–40 ◦ C, the enhancement ratio of pressure drop is 25.0–63.3% and 5.7–15.3% for laminar and turbulent flow, respectively, the enhancement ratio of pressure drop being larger for laminar flow than for turbulent flow. The results compare well with literature data (Jwo et al., 2009; Rea et al., 2009; Sundar & Sharma, 2010).
Fig. 8 compares calculated pressure drop with experimental results for TiO2 /water nanofluid in laminar flow (V = 0.57 m/s), showing rather great deviation between calculated and experimental results. To consider the impact of pressure drop when the TiO2 nanoparticles were added, in the concentration range of 0–1.5 wt% and temperature range of 10–40 ◦ C, the margin of deviation is 0.01% to −52.36%. It is found that the higher the temperature, the greater the deviation between the calculated and experimental values. Fig. 9 compares calculated and experimental pressure drops for TiO2 /water nanofluid in turbulent flow (V = 1.53 m/s), showing that the deviation between the two is within 20%. For concentration range of 0–1.5 wt% and temperature of 10–40 ◦ C, the margin of deviation is 3.20–19.48%, showing that calculation tends toward overestimation. Comparison between calculation and experiment for pressure drop shows that the deviation between the two is extremely large, reaching −52.36% of the maximum for laminar flow (Jwo et al., 2009), thus showing that the traditional equation for calculating pressure drop calls for amendment. To apply the empirical
Fig. 7. Enhancement ratio of experimental data of pressure drop.
Fig. 9. Experimental data and calculated results of pressure drop in turbulent flow (V = 1.53 m/s).
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T.-P. Teng et al. / Particuology 9 (2011) 486–491
fturb.Reg. = 0.001 + 0.871fturb. + 0.003ω − 1.438 × 10−6 T 2 .
(10)
5. Conclusions Nanofluid is a novel suspension with a wide scope of applications. This study focuses on the effect of TiO2 /water nanofluid on pressure drop under different weight fractions and temperatures, and conducts related experimental research, leading to the following conclusions.
Fig. 10. Pressure drop in laminar flow: comparison between experiments and estimates by regression.
equation developed in this study to a wider range, this paper uses multiple regression analysis for the friction factor under both laminar and turbulent flow, to estimate the influence of temperature, weight fraction, and calculated friction factor (flami. and fturb. ) on friction factor (fExp. ) from examining pressure drop under laminar and turbulent flow respectively. The new equations for the friction factor (flamiReg. and fturbReg. ) were respectively Eqs. (9) and (10) with R2 = 0.970 and 0.910, and the pressure drop was calculated by using Eq. (1). Figs. 10 and 11 compare the pressure drops estimated by regression of the friction factor with weight fraction, temperature, and calculated friction factor. The deviation of the empirical friction factor equation is much lower than that produced by the use of the traditional friction factor equation for pressure drop under laminar and turbulent flow: the margin of deviation is respectively in the ranges of −6.17% to 3.55% and −3.08% to 3.81%. Thus, multiple regression of the friction factor could accurately estimate the result in this investigation. flami.Reg. = 0.041 + 0.079flami. + 0.014ω − 3.516 × 10−6 T 2 ,
(9)
Fig. 11. Pressure drop in turbulent flow: comparison between experiments and estimates by regression.
(1) Increase in its solids content will enhance both the density and viscosity of a nanofluid, whereas temperature rise tends to reduce both the density and viscosity. (2) Enhancement of pressure drop for a nanofluid is lower under turbulent flow in a circular pipe, but higher under laminar flow condition, thus helping to reduce the delivery loss of pumping. (3) Traditional equations of friction factor cannot accurately calculate the TiO2 /water nanofluid flow through circular pipes, especially in the range of laminar flow. (4) New empirical equations for friction factor are proposed in this study. The traditional equation of pressure drop can thus calculate the pressure drop more accurately for the TiO2 /water nanofluid flow through the circular pipe under laminar and turbulent flow using the friction factor from newly proposed empirical equations. (5) The deviation of the empirical friction factor equation is much lower than that produced by the use of the traditional friction factor equation for the pressure drop under laminar and turbulent flow; the margin of deviation was in the ranges of −6.17% to 3.55% and −3.08% to 3.81%. Acknowledgement The authors would like to thank National Science Council of the Republic of China, Taiwan, for financial support under Contract Nos. NSC 98-2221-E-003-018 and 99-2221-E-003-008. References Buongiorno, J., Venerus, D. C., Prabhat, N., McKrell, T., Townsend, J., Christianson, R., et al. (2009). A benchmark study on the thermal conductivity of nanofluids. Journal of Applied Physics, 106, 094312. Das, S. K., Putra, N., & Roetzel, W. (2003). Pool boiling characteristics of nano-fluids. International Journal of Heat and Mass Transfer, 46(5), 851–862. Duangthongsuk, W., & Wongwises, S. (2009). Heat transfer enhancement and pressure drop characteristics of TiO2 -water nanofluid in a double-tube counter flow heat exchanger. International Journal of Heat and Mass Transfer, 52, 2059–2067. Godson, L., Raja, B., Mohan Lal, D., & Wongwises, S. (2010). Enhancement of heat transfer using nanofluids – An overview. Renewable and Sustainable Energy Reviews, 14, 629–641. He, Y., Jin, Y., Chen, H., Ding, Y., Cang, D., & Lu, H. (2007). Heat transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe. International Journal of Heat and Mass Transfer, 50, 2272–2282. Heris, S. Z., Etemad, S., & Esfahany, Gh. M. N. (2006). Experimental investigation of oxide nanofluids laminar flow convective heat transfer. International Communications in Heat and Mass Transfer, 33(4), 529–535. Jwo, C. C., Teng, T. P., Wu, D. J., Chang, H., & Chen, S. L. (2009). Research on pressure loss of alumina nanofluid flow in a pipe. Journal of the Chinese Society of Mechanical Engineers, 30(6), 511–517. Khanafer, K., Vafai, K., & Lightstone, M. (2003). Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. International Journal of Heat and Mass Transfer, 46, 3639–3653. Li, J. M., Li, Z. L., & Wang, B. X. (2002). Experimental viscosity measurements for copper oxide nanoparticle suspensions. Tsinghua Science & Technology, 7(2), 198–201. Nguyen, C. T., Roy, G., Gauthier, C., & Galanis, N. (2007). Heat transfer enhancement using Al2 O3 -water nanofluid for an electronic liquid cooling system. Applied Thermal Engineering, 27, 1501–1506. Pantzali, M. N., Kanaris, A. G., Antoniadis, K. D., Mouza, A. A., & Paras, S. V. (2009). Effect of nanofluids on the performance of a miniature plate heat exchanger with modulated surface. International Journal of Heat and Fluid Flow, 30, 691–699.
T.-P. Teng et al. / Particuology 9 (2011) 486–491 Putra, N., Roetzel, W., & Das, S. K. (2003). Natural convection of nano-fluids. Heat and Mass Transfer, 39(8–9), 775–784. Rao, Y. (2010). Nanofluids: Stability, phase diagram, rheology and applications. Particuology, 8, 549–555. Rea, U., McKrell, T., Hu, L. W., & Buongiorno, J. (2009). Laminar convective heat transfer and viscous pressure loss of alumina-water and zirconia-water nanofluids. International Journal of Heat and Mass Transfer, 52, 2042–2048. Sundar, L. S., & Sharma, K. V. (2010). Turbulent heat transfer and friction factor of Al2 O3 nanofluid in circular tube with twisted tape inserts. International Journal of Heat and Mass Transfer, 53, 1409–1416. Swamee, P. K., & Jain, A. K. (1976). Explicit equation for pipe-flow problem. Journal of the hydraulics division, 102(HY5), 657–664. Tsai, C. Y., Chien, H. T., Ding, P. P., Chan, B., Luh, T. Y., & Chen, P. H. (2004). Effect of structural character of gold nanoparticles in nanofluid on heat pipe thermal performance. Materials Letters, 58, 1461–1465. Tseng, W. J., & Lin, K. C. (2003). Rheology and colloidal structure of aqueous TiO2 nanoparticle suspensions. Materials Science and Engineering A, 355, 186–192.
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Wang, X. Q., & Mujumdar, A. S. (2007). Heat transfer characteristics of nanofluids: A review. International Journal of Thermal Sciences, 46, 1–19. Wang, X. W., Xu, X. F., & Choi, S. U. S. (1999). Thermal conductivity of nanoparticle-fluid mixture. Journal of Thermophysics and Heat Transfer, 13(4), 474–480. Wen, D., & Ding, Y. (2006). Natural convective heat transfer of suspensions of titanium dioxide nanoparticles (nanofluids). IEEE Transactions on nanotechnology, 5(3), 220–227. White, F. M. (1991). Viscous fluid flow. New York: McGraw Hill, Inc. Wierenga, A. M., & Philipse, A. P. (1998). Low-shear viscosity of isotropic dispersions of (Brownian) rods and fibres: A review of theory and experiments. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 137, 355–372. Wu, C., Cho, T. J., Xu, J., Lee, D., Yang, B., & Zachariah, M. Z. (2010). Effect of nanoparticle clustering on the effective thermal conductivity of concentrated silica colloids. Physical Review E, 81, 011406. Xuan, Y., & Li, Q. (2003). Investigation on convective heat transfer and flow features of nanofluids. ASME Journal of Heat Transfer, 125, 151–155.
Contents lists available at ScienceDirect
Particuology journal homepage: www.elsevier.com/locate/partic
Pressure drop of TiO2 nanofluid in circular pipes Tun-Ping Teng a,∗ , Yi-Hsuan Hung a , Ching-Song Jwo b , Chien-Chih Chen c , Lung-Yue Jeng c a
Department of Industrial Education, National Taiwan Normal University, Taipei City 10610, Taiwan, China Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei City 10608, Taiwan, China c Graduate Institute of Mechanical and Electrical Engineering, National Taipei University of Technology, Taipei City 10608, Taiwan, China b
a r t i c l e
i n f o
Article history: Received 22 September 2009 Received in revised form 14 January 2011 Accepted 3 May 2011 Keywords: Titania (TiO2 ) Nanofluid Laminar flow Turbulent flow
a b s t r a c t This paper discusses the pressure drop in circular pipes of TiO2 /water nanofluid for both laminar and turbulent flows at different temperatures and TiO2 weight fractions. This study shows that TiO2 /water nanofluid causes enhancement, but temperature rise reduces pressure drop. The proportional increase in pressure drop for turbulent flow is lower than that for laminar flow. The traditional equation for pressure drop fails to accurately estimate the pressure drop for laminar and turbulent flows. Accordingly, this study developed new empirical equations for the friction factor for both laminar and turbulent flows, and the maximum deviations between calculated and experimental results were reduced to within the ranges of −6.17% to 3.55% and −3.08% to 3.81%, respectively, that is, for TiO2 /water nanofluid, the correlations apply better to turbulent than to laminar flow. © 2011 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
1. Introduction Research has shown that adding nanoparticles to a liquid can enhance its thermal conductivity, which, however, does not necessarily lead to increase heat exchange in real practice. Recent research has focused on the benefits of nanofluid in heat convection (Buongiorno, Venerus, Prabhat, McKrell, Townsend, & Christianson, 2009; Godson, Raja, Mohan Lal, & Wongwises, 2010; Heris, Etemad, & Esfahany, 2006; Khanafer, Vafai, & Lightstone, 2003; Nguyen, Roy, Gauthier, & Galanis, 2007; Tsai et al., 2004; Wang & Mujumdar, 2007; Wu et al., 2010; Xuan & Li, 2003). However, others suggested the opposite results (Putra, Roetzel, & Das, 2003; Wen & Ding, 2006) and believed that the performance of the whole system would deteriorate if the benefits of increased performance in heat exchange were less than the damage caused by increased pressure drop due to increased viscosity by the solid–liquid mixture. Many empirical equations have been proposed to predict viscosity of nanofluids, yet no consensus has been reached because of differences caused by materials, particle sizes, and manufacturing methods (Das, Putra, & Roetzel, 2003; Jwo, Teng, Wu, Chang, & Chen, 2009; Li, Li, & Wang, 2002; Rao, 2010; Tseng & Lin, 2003; Wang, Xu, & Choi, 1999; Wierenga & Philipse, 1998). He et al. (2007) studied both heat transfer and flow behavior of TiO2 /distilled water nanofluids flowing upward through a ver-
∗ Corresponding author. Tel.: +866 2 7734 3358; fax: +866 2 2392 9449. E-mail address: [email protected] (T.-P. Teng).
tical pipe, both laminar and turbulent, under a constant heat flux around the tube, finding that the pressure drop of the nanofluids was not much different from that of the base fluid. Rea, McKrell, Hu, and Buongiorno (2009) studied laminar convective heat transfer and viscous pressure loss for alumina/water and zirconia/water nanofluids flowing in a vertical heated tube, showing that the heat transfer coefficient was increased by the nanofluids, and that the measured pressure loss for the nanofluids was much higher than that for pure water. The pressure loss of the 6 vol.% alumina nanofluid was approximately 7.2 times higher than that of water. Duangthongsuk and Wongwises (2009) studied experimentally the forced convective heat transfer and flow characteristics of a nanofluid consisting of water and 0.2 vol.% TiO2 nanoparticles. The results showed that use of a nanofluid had hardly any penalty in pressure drop. Pantzali, Kanaris, Antoniadis, Mouza, and Paras (2009) presented the effects of using a nanofluid (CuO/water, 4 vol.%) in a miniature plate heat exchanger (PHE) with a modulated surface, showing that the pressure drop increased by less than 10%. Sundar and Sharma (2010) studied the heat transfer coefficient and friction factor in a plain tube with a twisted tape insert at different volume concentrations of Al2 O3 nanofluids under Re of 10,000–22,000 (turbulent flow) with tapes of different twist ratios, showing that the friction factor of 0.5 vol.% of Al2 O3 nanofluid with a twist ratio of five was 1.096 times higher as compared to the flow of water in a circular tube. This research focuses on TiO2 /water nanofluids with low nanoparticle concentrations (0–1.5 wt%), aiming at measuring the effect of nanoparticle concentration and temperatures (10–40 ◦ C)
1674-2001/$ – see front matter © 2011 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
doi:10.1016/j.partic.2011.05.001
T.-P. Teng et al. / Particuology 9 (2011) 486–491
487
on the density, viscosity, and pressure drop, in order to compare the difference in pressure drop between the nanofluid and pure water in a circular pipe. Finally, the experimental data are analyzed using traditional equations for friction factor, to formulate empirical equations suitable for calculating pressure drop of TiO2 /water nanofluids. 2. Calculation of pressure drop The measured or calculated results of friction factor, density, flow rate, and pipe size were substituted into the following equation, for both laminar flow and turbulent flow conditions, for a circular pipe, to yield the pressure drop (White, 1991): P = f
L V2 , d 2 f
(1)
with the following friction factor for laminar flow: flami.
64 = . Re
Fig. 1. SEM image of TiO2 nanoparticles as purchased.
(2)
For turbulent flow, Swamee and Jain (1976) proposed a formula which leads to calculated results extremely close to the turbulent flow region in the Moody chart, as could be written as follows: fturb. =
0.25 [log((1/(3.7(d/ε))) + (5.74/Re0.9 ))]
2
.
(3)
The Reynolds number (Re) in Eqs. (2) and (3) could be shown as: Re =
Vdf , f
(4)
where f is the friction factor, d is the inner diameter of pipe (m), L is the length of pipe (m), V is the velocity of fluid (m/s), f is the density of fluid (kg/m3 ), ε is the roughness (m), and f is the viscosity of fluid (Pa s). The value of Re represents the flow condition: for laminar flow Re < 2000 and for turbulent flow Re > 4000. 3. Experimental and data analysis 3.1. Preparation of TiO2 /water nanofluid Fig. 2. TEM image of TiO2 nanoparticles.
The TiO2 /water nanofluid produced from a direct synthesis method was used as the experimental sample, and mechanical agitations were used for dispersing the nanoparticles into three weight fractions (0.5, 1.0, 1.5 wt%). The solid volume was determined by calculating the equivalent weight of the solid based on its true density (approximately 3840 kg/m3 ). The nanoparticles, purchased from Yong-Zhen Technomaterial Co. Ltd., generally form loose agglomerates as shown in Fig. 1. Fig. 2, the TEM photograph of TiO2 nanoparticles with nominal particle sizes of 20–30 nm, shows that the shapes of nanoparticles are mainly rectangular, and the particle size closely meets the nominal particle size of the supplier. Fig. 3 shows the XRD pattern of TiO2 nanoparticles, confirming the main component to be anatase. The nanoparticles can be successfully dispersed in deionized water using a homogenizer with electromagnetic agitation and ultrasonic vibration, to form a TiO2 /water nanofluid without addition of any dispersant or surfactant. 3.2. Experimental procedure Fig. 4 shows this experiment used a thermostatic bath (Firsteck B403L) to stabilize the temperature of the sample until it reached the expected temperature of ±0.5 ◦ C. A density meter and a rheometer were then used to measure the density and viscosity
Fig. 3. XRD pattern of TiO2 nanoparticles.
488
T.-P. Teng et al. / Particuology 9 (2011) 486–491
um =
2 +
2 +
V V
2 +
P P
2 +
W W
2 +
T T
2 .
(5) The accuracy of the density meter is ±0.001 g, that of the rheometer is ±1.0%, that of the flow meter is ±2.0%, that of the pressure meter is ±2.0%, that of the precise electric balance is ±0.01 g, and that of the RTD is ±0.5 ◦ C. Therefore, the uncertainty of the experiment was less than ±6.0%. 3.4. Data analysis Regarding the margin of deviation between experimental data (DExp. ) and data calculated by the traditional equation (DCal. ) and empirical equations (DReg. ): this study used experimental data as a benchmark for results of empirical equations, and the deviation between experimental results and calculated data of the traditional equation and empirical equations can be calculated as follows:
DevCal. (%) =
Fig. 4. Experimental setup for measuring pressure drop.
DevReg. (%) = of the nanofluids of various weight fractions and sample temperatures. In pressure drop experiments in a circular pipe, after 1800 cm3 of nanofluid was poured into a 2-l stainless steel bucket, and the bucket was placed in a thermostatic bath, the nanofluid was pumped to the measurement pipe for circulation. The pressure drop of nanofluid in the pipe was measured. The test pipe consisted of a circular steel tube (ε = 4.6 × 10−5 m) with the length (L) of 0.6 m and the internal diameter (d) of 0.0035 m. To avoid entrance effect, L/d 100. To avoid drastic temperature change, the pipe was wrapped by thermal insulation material at a thickness of 2 cm. Nanofluid flow rate was controlled at a region between turbulent and laminar flow. The temperature of the sample was stabilized at ±0.5 ◦ C of the expected value. The pressure was then measured of the nanofluid of various weight fractions, and sample temperatures were taken at the inlet and outlet of the pipe. To guarantee accuracy, all controlled factors were measured ten times, and the most concentrated five test results were selected as average values of the experimental results. Experimental results of density and viscosity were inserted into Eqs. (1)–(4) to calculate their effects on pressure drop in the circular pipe, in order to compare calculated results with experimental data. Finally, the experimental and calculated results were used to perform multiple regression analysis to acquire a new empirical equation.
DCal. − DExp. DExp.
DReg. − DExp. DExp.
× 100,
(6)
× 100.
(7)
For easy comparison of experimental data of pressure drop before and after changing the TiO2 /water nanofluid, all data obtained with the water were used as baseline values; that is, experimental data obtained after the TiO2 /water nanofluid were used to compare with baseline values. The differences before and after changing the TiO2 /water nanofluid are presented as proportions, and can be calculated as follows: RP (%) =
P − P water nf Pwater
× 100.
4. Results and discussion Fig. 5 shows the measured results of the weight fractions of TiO2 /water nanofluid with the change of density under different temperatures. The increase in added concentration enhances the density of nanofluid, whereas temperature rise reduces the density
3.3. Uncertainty analysis Uncertainty of experimental results was determined by measurement deviation of the parameters, including density, viscosity, flow rate, pressure drop, weight, and temperature. In pressure drop experiment on nanofluid, density () was measured by a density meter (DA-130, KYOTO); viscosity () was measured by a rheometer (DVIII+, Brookfield); flow rate (V) was measured by a flow meter (NF05, Aichi Tokei); pressure (P) drop was measured by a pressure meter (PS-9302, LUTRON); the weight (W) of nanoparticles was measured by a precision electric balance (XT620M, Precisa); and temperature was determined using a resistance temperature (T) detector (RTD, pt-100) of the thermostatic bath. The uncertainty of experimental results could be expressed as follows:
(8)
Fig. 5. Experimental results of density measurement.
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Fig. 6. Experimental results of viscosity measurement.
Fig. 8. Experimental data and calculated results of pressure drop in laminar flow (V = 0.57 m/s).
of nanofluid. The influence of weight fractions on density change appears to be approximately linear. However, the density presented a non-linear trend under different temperatures; the main reason is that the added nanoparticles and bulk liquid have a great difference in the coefficient of thermal expansion. Fig. 6 shows the measured effect of the weight fractions of TiO2 /water nanofluid on the change of viscosity under different temperatures. Temperature rise reduces the viscosity of nanofluid, whereas increased weight fraction increases the viscosity of nanofluid, and for the different temperatures, the effect of weight fraction on viscosity appears nearly linear. Fig. 7 shows the enhancement ratio of pressure drop by increasing the solids content of the TiO2 /water nanofluid. For solids content of 0–1.5 wt% and temperature of 10–40 ◦ C, the enhancement ratio of pressure drop is 25.0–63.3% and 5.7–15.3% for laminar and turbulent flow, respectively, the enhancement ratio of pressure drop being larger for laminar flow than for turbulent flow. The results compare well with literature data (Jwo et al., 2009; Rea et al., 2009; Sundar & Sharma, 2010).
Fig. 8 compares calculated pressure drop with experimental results for TiO2 /water nanofluid in laminar flow (V = 0.57 m/s), showing rather great deviation between calculated and experimental results. To consider the impact of pressure drop when the TiO2 nanoparticles were added, in the concentration range of 0–1.5 wt% and temperature range of 10–40 ◦ C, the margin of deviation is 0.01% to −52.36%. It is found that the higher the temperature, the greater the deviation between the calculated and experimental values. Fig. 9 compares calculated and experimental pressure drops for TiO2 /water nanofluid in turbulent flow (V = 1.53 m/s), showing that the deviation between the two is within 20%. For concentration range of 0–1.5 wt% and temperature of 10–40 ◦ C, the margin of deviation is 3.20–19.48%, showing that calculation tends toward overestimation. Comparison between calculation and experiment for pressure drop shows that the deviation between the two is extremely large, reaching −52.36% of the maximum for laminar flow (Jwo et al., 2009), thus showing that the traditional equation for calculating pressure drop calls for amendment. To apply the empirical
Fig. 7. Enhancement ratio of experimental data of pressure drop.
Fig. 9. Experimental data and calculated results of pressure drop in turbulent flow (V = 1.53 m/s).
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fturb.Reg. = 0.001 + 0.871fturb. + 0.003ω − 1.438 × 10−6 T 2 .
(10)
5. Conclusions Nanofluid is a novel suspension with a wide scope of applications. This study focuses on the effect of TiO2 /water nanofluid on pressure drop under different weight fractions and temperatures, and conducts related experimental research, leading to the following conclusions.
Fig. 10. Pressure drop in laminar flow: comparison between experiments and estimates by regression.
equation developed in this study to a wider range, this paper uses multiple regression analysis for the friction factor under both laminar and turbulent flow, to estimate the influence of temperature, weight fraction, and calculated friction factor (flami. and fturb. ) on friction factor (fExp. ) from examining pressure drop under laminar and turbulent flow respectively. The new equations for the friction factor (flamiReg. and fturbReg. ) were respectively Eqs. (9) and (10) with R2 = 0.970 and 0.910, and the pressure drop was calculated by using Eq. (1). Figs. 10 and 11 compare the pressure drops estimated by regression of the friction factor with weight fraction, temperature, and calculated friction factor. The deviation of the empirical friction factor equation is much lower than that produced by the use of the traditional friction factor equation for pressure drop under laminar and turbulent flow: the margin of deviation is respectively in the ranges of −6.17% to 3.55% and −3.08% to 3.81%. Thus, multiple regression of the friction factor could accurately estimate the result in this investigation. flami.Reg. = 0.041 + 0.079flami. + 0.014ω − 3.516 × 10−6 T 2 ,
(9)
Fig. 11. Pressure drop in turbulent flow: comparison between experiments and estimates by regression.
(1) Increase in its solids content will enhance both the density and viscosity of a nanofluid, whereas temperature rise tends to reduce both the density and viscosity. (2) Enhancement of pressure drop for a nanofluid is lower under turbulent flow in a circular pipe, but higher under laminar flow condition, thus helping to reduce the delivery loss of pumping. (3) Traditional equations of friction factor cannot accurately calculate the TiO2 /water nanofluid flow through circular pipes, especially in the range of laminar flow. (4) New empirical equations for friction factor are proposed in this study. The traditional equation of pressure drop can thus calculate the pressure drop more accurately for the TiO2 /water nanofluid flow through the circular pipe under laminar and turbulent flow using the friction factor from newly proposed empirical equations. (5) The deviation of the empirical friction factor equation is much lower than that produced by the use of the traditional friction factor equation for the pressure drop under laminar and turbulent flow; the margin of deviation was in the ranges of −6.17% to 3.55% and −3.08% to 3.81%. Acknowledgement The authors would like to thank National Science Council of the Republic of China, Taiwan, for financial support under Contract Nos. NSC 98-2221-E-003-018 and 99-2221-E-003-008. References Buongiorno, J., Venerus, D. C., Prabhat, N., McKrell, T., Townsend, J., Christianson, R., et al. (2009). A benchmark study on the thermal conductivity of nanofluids. Journal of Applied Physics, 106, 094312. Das, S. K., Putra, N., & Roetzel, W. (2003). Pool boiling characteristics of nano-fluids. International Journal of Heat and Mass Transfer, 46(5), 851–862. Duangthongsuk, W., & Wongwises, S. (2009). Heat transfer enhancement and pressure drop characteristics of TiO2 -water nanofluid in a double-tube counter flow heat exchanger. International Journal of Heat and Mass Transfer, 52, 2059–2067. Godson, L., Raja, B., Mohan Lal, D., & Wongwises, S. (2010). Enhancement of heat transfer using nanofluids – An overview. Renewable and Sustainable Energy Reviews, 14, 629–641. He, Y., Jin, Y., Chen, H., Ding, Y., Cang, D., & Lu, H. (2007). Heat transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe. International Journal of Heat and Mass Transfer, 50, 2272–2282. Heris, S. Z., Etemad, S., & Esfahany, Gh. M. N. (2006). Experimental investigation of oxide nanofluids laminar flow convective heat transfer. International Communications in Heat and Mass Transfer, 33(4), 529–535. Jwo, C. C., Teng, T. P., Wu, D. J., Chang, H., & Chen, S. L. (2009). Research on pressure loss of alumina nanofluid flow in a pipe. Journal of the Chinese Society of Mechanical Engineers, 30(6), 511–517. Khanafer, K., Vafai, K., & Lightstone, M. (2003). Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. International Journal of Heat and Mass Transfer, 46, 3639–3653. Li, J. M., Li, Z. L., & Wang, B. X. (2002). Experimental viscosity measurements for copper oxide nanoparticle suspensions. Tsinghua Science & Technology, 7(2), 198–201. Nguyen, C. T., Roy, G., Gauthier, C., & Galanis, N. (2007). Heat transfer enhancement using Al2 O3 -water nanofluid for an electronic liquid cooling system. Applied Thermal Engineering, 27, 1501–1506. Pantzali, M. N., Kanaris, A. G., Antoniadis, K. D., Mouza, A. A., & Paras, S. V. (2009). Effect of nanofluids on the performance of a miniature plate heat exchanger with modulated surface. International Journal of Heat and Fluid Flow, 30, 691–699.
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