Investigation of turbulent convective heat transfer and

International Communications in Heat and Mass Transfer 38 (2011) 1474–1478

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International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t

Investigation of turbulent convective heat transfer and pressure drop of TiO2/water nanofluid in circular tube☆ A.R. Sajadi, M.H. Kazemi ⁎ School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

a r t i c l e

i n f o

Available online 19 July 2011 Keywords: Turbulent flow Nanofluid Convective heat transfer Convection correlation

a b s t r a c t Turbulent heat transfer behavior of titanium dioxide/water nanofluid in a circular pipe was investigated experimentally where the volume fraction of nanoparticles in the base fluid was less than 0.25%. The experimental measurements have been carried out in the fully-developed turbulent regime for various volumetric concentrations. The results indicated that addition of small amounts of nanoparticles to the base fluid augmented heat transfer remarkably. There was no much effect on heat transfer enhancement with increasing the volume fraction of nanoparticles. The measurements also showed that the pressure drop of nanofluid was slightly higher than that of the base fluid and increased with increasing the volume concentration. In this paper, experimental results have been compared with the existing correlations for nanofluid convective heat transfer coefficient in turbulent regime. Finally, a new correlation of the Nusselt number will be presented using the results of the experiments with titanium dioxide nanoparticles dispersed in water. © 2011 Elsevier Ltd. All rights reserved.

1. Introduction The poor thermal properties of fluids act as a main barrier to the growth of energy-efficient heat exchanger. During the past decades, many efforts have been devoted to the enhancement of heat transfer. One of the possible techniques for improving heat transfer is adding millimeter- or micrometer-sized particles in fluids. In recent years, nanofluids have been introduced as an ideal candidate for enhancing heat transfer [1,2]. As a result of the small size of nanoparticles, a little pressure drop is observed in the fluid. In this situation the fluid behaves like a pure fluid or single phase liquid [1]. Various studies have been conducted on the performances of nanofluids convective heat transfer in laminar flow [3–5]. They concluded that nanofluids provide heat transfer enhancement in comparison with their corresponding base fluids. Mansour et al. [6] experimentally studied the mixed convection of water–Al2O3 mixture inside an inclined tube. Their results indicated that a higher particle volume concentration clearly induced a decrease of the Nusselt number for the horizontal inclination. On the other hand, they showed that for the vertical one, the Nusselt number remains nearly constant with an increase of particle volume concentration from 0 to 4%. Nanofluids have valuable industrial applications including heating systems through the hydronic coils, cooling automotive engines through ☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (M.H. Kazemi). 0735-1933/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2011.07.007

the radiators and in heat exchangers. In all of these applications, the regime of fluid flow is generally turbulent in which higher heat transfer is achievable. Based on numerical or experimental analyses of previous studies, with increasing the particle volume concentration of nanofluids the turbolant heat transfer improved [7–10]. On the other hand, Fotukian and Nasr [8] studied turbulent convective heat transfer performance of very dilute (less than 0.24% volume) CuO/water nanofluid. In their study, increasing the volume fraction of CuO particles in nanofluid had negligible effect on the heat transfer enhancement. A few studies have reported the influence of TiO2 on the heat transfer of nanofluids. Duangthongsuck and Wongwises [12,13] showed that using different predictive thermophysical models for nanofluid has no effect on the predicted values of the convective heat transfer coefficient of TiO2/water nanofluids. Murshed et al. [14] measured the thermal conductivity of suspended TiO2 nanoparticles in deionized water. The results showed that the thermal conductivity of nanofluid increased remarkably with increasing the volume fraction of nanoparticles. He et al. [15] studied static thermal conductivity, heat transfer and flow behavior of stable aqueous TiO2 nanofluid with different particle sizes and concentrations. They found that the convective heat transfer coefficient increased with increasing nanoparticle concentration. They showed that the heat transfer improvement was more significant in turbulent flow regime. The previous work of the authors did not examine the effect of the dilute particle concentration on heat transfer and pressure drop of TiO2/water based nanofluids. Since this behavior has not been already reported, experiments with very dilute TiO2 nanoparticles were planned to see if the same behavior was observed. As a result, this

A.R. Sajadi, M.H. Kazemi / International Communications in Heat and Mass Transfer 38 (2011) 1474–1478

nanoparticles were mixed with distilled water by a mixer for ten minutes. Then, ultrasonic cleaner (model UP400S-Hielcher) was used to disperse nanoparticles for thirty minutes.

Nomenclature A Cp D h k L Nu Pe Pr Re T u

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tube cross section area, m 2 specific heat capacity, kJ/kgK diameter of the tube, m heat transfer coefficient, W/m 2K thermal conductivity, W/mK length of the tube, m Nusselt number Peclet number Prandtl number Reynolds number temperature, K mean fluid velocity, m 2/s

2.2. Experimental apparatus and procedure An experimental apparatus was built to study the flow and convective heat transfer features in a tube. As shown schematically in Fig. 1, the experimental system mainly includes a reservoir tank, a pump, a flow loop, a test section, a cooler and a steam supplier tank. The transparent plastic reservoir tank with capacity of 6 L was manufactured to reserve the nanofluid and monitor the sedimentation rate and the height of nanofluid. The test section is a straight copper tube with the inner diameter, thickness and length of about 5, 0.675 and 1800 mm, respectively. Five K-type thermocouples were mounted on the copper tube wall at equal intervals to measure the wall temperature. Two other K-type thermocouples were inserted at the entrance and exit of the test section to measure the bulk temperature. The first 50 cm of the copper tube was thermally isolated from its begining using fiberglass to minimize the heat loss and to guarantee hydrodynamically fully-developed condition. The flow rate was controlled with two adjusting valves, one at the end of the test section and the other at the by-pass line. The cooler includes a shell and tube heat exchanger which was used to reduce the temperature of the nanofluid at the inlet of the test section. The 50-liter steam supplier tank contains water as well as a 8 KW element heater to generate fully saturated vapor. The next 120 cm of test section is surrounded by saturated vapor to reach constant water temperature. In order to minimize the heat loss from the steam tank supplier to the surrounding area, the whole tank was thermally isolated with a fiberglass cover. A differential pressure transducer (manufactured by Endress Hauser) with an uncertainty of ±1 Pa was employed for measuring the pressure loss along the test section tube. A 1-liter glass vessel with a drain valve was utilized to calculate the flow rate. A stopwatch with accuracy of ±0.01 s was employed to measure the time required for filling the vessel.

Greek symbols α thermal diffusivity, m 2/s ε roughness, m μ viscosity, Pa s ρ density, kg/m 3 υ kinematics viscosity, m 2/s ϕ nanoparticle volume fraction

Subscripts b bulk nf nanofluid w water p solid nanoparticle exp. obtained experimentally ν laminar sublayer in inlet out outlet

2.3. Data reduction paper aims at studying the heat transfer of TiO2 water-based nanofluids flow inside the tubes with constant wall temperature and developing heat transfer correlation based on the experimental results. The effect of the dilute particles concentration on heat transfer and pressure drop of TiO2/water based nanofluids will be investigated.

The heat transfer performance of nanofluid was defined in terms of the convective heat transfer coefficient as follows:

hnf ð exp:Þ =

2. Experimental procedures

ρCp ⋅ A⋅ u Tbout −Tbin nf

π⋅ D⋅ LðTw −Tb ÞLMTD

ð1Þ

where (Tw − Tb)LMTD is the logarithmic mean temperature difference, and Tw is the wall temperature that is the average of six measured

2.1. Nanofluid preparation Preparing stable suspension of nanoparticles in the base liquid was the first step in applying nanofluids for the heat transfer enhancement. In this study, TiO2 nanoparticles with an average diameter of about 30 nm were prepared at Sharif University Physics laboratory. Thermophysical properties of these nanoparticles calculated at 65 °C are shown in Table 1. Nanofluid was obtained by dispersing TiO2 nanoparticles in deionized water as a base fluid. The nanofluid with five different nanoparticle volume concentrations (0.05%, 0.1%, 0.15%, 0.20%, and 0.25%) was prepared and utilized to study the heat transfer enhancement. The proper amount of TiO2

Table 1 Thermophysical properties of TiO2 nanoparticles. Mean diameter nm

Density kg/m3

Thermal conductivity kJ/kgK

Specific heat W/mK

30

4170

11.8

711

Fig. 1. Schematic diagram of experimental set-up.

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Fig. 2. Comparison of experimental Nusselt number with data obtained by Dittus– Boelter equation vs Reynolds number. Fig. 4. Nusselt number for water and TiO2/water nanofluid vs Reynolds number at different volume concentration.

temperatures on tube wall at different positions. The convective heat transfer coefficient is usually expressed in the form of Nusselt number (Nu) as: Nunf ð exp:Þ =

hnf ð exp:Þ⋅ D knf

ð2Þ

where D is the tube diameter, and knf is the nanofluid thermal conductivity. Traditionally, Nu is related to the Reynolds number and the Prandtl number defined as: Renf

The viscosity of nanofluid could be estimated with the existing relations for the two-phase mixture: μnf = μw ð1 + 2:5ϕÞ:

ð8Þ

The effective thermal conductivity of solid–liquid mixtures was introduced by Yu and Choi [16] according to the following equation: 2 3 kp + 2kw + 2 kp −kw ð1 + βÞ3 ϕ 4 5kw = kp + 2kw −2 kp −kw ð1 + βÞ3 ϕ

uD = υnf

ð3Þ

Knf

υnf αnf

ð4Þ

where β is the ratio of the nanolayer thickness to the original particle radius and kp is the equivalent thermal conductivity of the equivalent particle. The rheological and physical properties of the nanofluid were calculated at the mean fluid temperature. Then, the Nusselt number and convective heat transfer coefficient at different concentrations were calculated.

Prnf =

knf αnf = ρCp

ð5Þ

nf

where υnf is the nanofluid kinematic viscosity and αnf is the nanofluid thermal diffusivity. Three main parameters involved in calculating heat transfer rate of the nanofluid are heat capacity, viscosity, and thermal conductivity, which may be quite different from those of the pure fluid. (ρCp)nf for nanofluids is defined as follows: ρCp

nf

= ð1−ϕÞ ρCp + ϕ ρCp p

ρnf = ϕρp + ð1−ϕÞρw :

w

ð6Þ ð7Þ

Fig. 3. The ratio of heat transfer coefficient of nanofluid to that of pure water vs Reynolds number at different concentration of nanoparticles.

ð9Þ

3. Result and discussion 3.1. Heat transfer results Before measuring the convective heat transfer coefficient of nanofluids, the reliability and accuracy of the experimental system was investigated using water as the working fluid. The results of this study are compared with the calculated values obtained from the well-known Dittus–Boelter equation. As can be seen in Fig. 2, a good coincidence between the experimental results and the calculated values for water revealed that the experimental data were in a good agreement (within ±10%) with the prediction of the correlation. Fig. 3 presents the ratio of convective heat transfer coefficient in nanofluid to that of pure water as a function of Reynolds number. As can be seen, a significant augmentation of heat transfer could be obtained by suspending a small amount of nanoparticles in water. The suspended particles increased the thermal conductivity of the twophase mixture. Furthermore, chaotic movement of these particles accelerated energy exchange process in the fluid. As can be seen in Fig. 3, at higher concentration levels, no sensible increase in the heat transfer of nanofluid was obtained. As an example, at Reynolds number around 5000, the value of hnf/hw was 1.19 and 1.22 for 0.05% and 0.25% concentrations, respectively, which showed 3% improvement for 0.20% increase in the concentration. It is worth to notice that the concentration of 0.05% and 0.25% was the lowest and the highest amount of volume fraction in this experiment, respectively. In addition, by increasing Reynolds number for all concentrations, the


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Fig. 5. Comparison of experimental Nusselt number with existing convective heat transfer correlations at 0.2% volume fraction.

ratio of heat transfer coefficient of nanofluid to that of the base fluid decreased. Fig. 4 depicts Nusselt number variations versus Reynolds number for different volume fractions of nanoparticles. Based on this figure, Nu for nanofluid was greater than that of water. This result confirms the claim by Xuan and Li [8] that Dittus–Boelter correlation underestimates the heat transfer coefficients of nanofluids. Increasing the concentration of nanoparticles in a small range studied in this work had no influence on the heat transfer enhancement. The latter fact was against the observation of Xuan and Li [8] who reported a large increase in the heat transfer of a nanofluid with augmentation of the nanoparticles volume fraction. However, the result of our study was consistent with the experimental results reported by Fotukian and Nasr [11]. 3.2. Comparison of results with proposed correlations Nusselt number for the fully developed turbulent flow for TiO2/ water is compared with the correlation proposed by Dittus–Boelter, Pack and Cho, Maiga et al., and Xuan and Li.,which are shown here respectively:

0:71

Nu = 0:085Re

Pr

0:35

0:6886 0:001 0:9238 0:4 Pep Prnf : Nu = 0:0059 1:0 + 7:6286ϕ Renf

ð12Þ ð13Þ

Pak and Cho [7] and Maiga et al. [10] showed that for nanofluids, Nu is a function of Reynolds number and Prandtl number, and the use of a correlation of the Dittus was adequate to represent the forced convection heat transfer in nanofluids. However, in their correlations any dependence on the particle volumetric concentration was not considered. Xuan and Li [8] presented a correlation in which Nu was a function of concentration, particle size (through a particle Peclet number), Reynolds number and Prandtl number. In Fig. 5, a comparison between the experimental data and the proposed correlations is shown for 0.2% volume fraction of TiO2 dispersed in water. From this figure, it is clearly observed that except Maiga et al. correlation, which overestimates the Nusselt number, the other correlations underestimate the Nusselt number of nanofluids. This behavior was observed for all volume fractions of nanofluids investigated in this work. 3.3. New Nusselt number correlation

0:23

Nu = 0:023Re

Pr

0:4

ð10Þ ð11Þ

From our experimental observation, we noticed that increasing the nanoparticles concentration had no influence on the heat transfer enhancement in turbulent regime in the range of concentrations studied. Therefore, the Nu was not a function of ϕ. In the present work, a new correlation was derived by careful analyzing of the data

Fig. 6. Comparison of the experimental values with the values obtained from the proposed correlation, Eq. (14).

Fig. 7. The ratio of experimental pressure drop of nanofluid to that of pure water along the test tube versus Reynolds number at different volume concentrations.

0:8

Nu = 0:021Re

Pr

0:5

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6. Conclusion

Table 2 The experimental data for convective heat transfer and pressure drop. ϕ(%)

Re

hw

hnf

hnf/hw

dPnf/dPw

0.05 0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.25

5547 10308 15943 19821 26004 30411 5933 11076 14730 20352 25271 30007 5329 9852 15333 19948 25541 30242 5281 12324 15308 20463 25631 30031 5579 9736 17409 20359 24472 29312

4568.51 7453.6 10439.2 12318.3 15451.7 17498.2 4802.2 7869.8 9850.8 12575.2 1511.4 17312 4436.4 7177.5 10143 12380 15236 17420 4408 8545.9 10131 12629 15278 17322 4587.9 7107.1 11149 12575 14739 16988

5436.9 8795.25 12631.42 14289.23 17305.12 18723.07 5762.64 9286.36 11722.45 14209.98 16622.1 18349.66 5368.04 8541.11 11664.45 14608.4 16759.6 18291 5377.76 10255.1 11650.66 14144.48 16805.8 18534.54 5597.24 8386.38 12821.35 14587 16507.68 18347

1.19 1.18 1.21 1.16 1.12 1.07 1.20 1.18 1.19 1.13 1.10 1.06 1.21 1.19 1.15 1.18 1.11 1.05 1.22 1.20 1.15 1.12 1.1 1.07 1.22 1.18 1.15 1.16 1.12 1.08

1.13 1.11 1.08 1.09 1.08 1.07 1.2 1.18 1.17 1.19 1.16 1.14 1.26 1.23 1.22 1.20 1.18 1.20 1.31 1.28 1.30 1.28 1.26 1.26 1.37 1.35 1.36 1.31 1.33 1.30

1. By suspending a small amount of TiO2 nanoparticles, heat transfer coefficient of nanofluids increased. At a Reynolds number of 5000, for 0.25% volume fraction of TiO2, an increase of about 22% in the heat transfer coefficient was occurred in comparison with pure water. 2. Increasing the nanoparticles concentration had not considerable effect on the heat transfer enhancement in the range of concentration studied in this work. 3. The rate of the heat transfer coefficient enhancement of nanofluid to that of pure water decreased with increasing the Reynolds number. 4. The pressure drop of nanofluid increased with increasing the volume fraction of nanoparticles. The maximum pressure drop was about 25% greater than that of pure water which was occurred in the highest volume fraction of nanofluid (0.25%) at Reynolds number of 5000. 5. The experimental data were in disagreement with existing correlations for Nu of nanofluids developed in previous studies. Therefore, a new Nu correlation for single phase liquid was developed. This new equation was a function of the Reynolds number and Prandtl number. References

obtained for all volume fractions of nanofluids illustrated in Fig. 6. This correlation is a function of Re and Pr numbers as follows: 0:71

Nu = 0:067Re

Pr

0:35

+ :0005Re:

The following conclusions have been drawn from the present study:

ð14Þ

The above equation was obtained by curve fitting of all the experimental data for nanofluids. The results showed a good relation between the experimental values and the calculated ones by the above equation. As can be seen, the majority of the data was fallen within ±8% of the proposed equation. This equation can be used for predicting the heat transfer coefficient of nanofluids with a volume concentraiton of ≤0.25% and a Reynolds number range between 5000 and 30000. Morover, it is very important to note that this equation was only established with respect to the data of TiO2/water nanofluids. 3.4. Pressure drop results It is necessary to measure the pressure drop of nanofluids beside the heat transfer performance in order to apply nanofluids in practical applications. In this study, nanofluids with 0.05, 0.1, 0.15 and 0.2 vol.% suspended nanoparticles were used in the pressure drop test under the turbulent flow condtion. The pressure drop of nanofluids along the test section was measured by a Differntial pressure transducer with an uncertainty of ±1 Pa. Fig. 7 shows the ratio of pressure drop of nanofluids to that of pure water as a function of Reynolds number. The experimental data are reported in Table 2. As shown in Fig. 7, addition of nanoparticles to the base fluid increased the pressure drop. This means that using the nanofluids at higher particle volume fraction may create a small penalty in pressure drop.

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