Turbulent Heat Transfer Behavior of Nanofluid in a Circular Tube Heated under Constant Heat Flux

Abstract

The aim of the present study is to disclose the forced convective heat transport phenomenon of nanofluids inside a horizontal circular tube subject to a constant and uniform heat flux at the wall. Consideration is given to the effect of the inclusion of nanoparticles on heat transfer enhancement, thermal conductivity, viscosity, and pressure loss in the turbulent flow region. It is found that (i) heat transfer enhancement is caused by suspending nanoparticles and becomes more pronounced with the increase of the particle volume fraction, (ii) its augmentation is affected by three different nanofluids employed here, and (iii) the presence of particles produces adverse effects on viscosity and pressure loss that also increases with the particle volume fraction.

1. Introduction

In general, the working fluid such as water, oil, and ethylene glycol is used for various industrial fields, namely, power generation and air conditioner. However, those fluids with low thermal conductivity suppress development of compact and higher-performance heat exchangers. Fluid including nanoparticles is referred to as nanofluid, which is a term proposed by Choi [1]. The term “nanofluid” refers to a two-phase mixture with its continuous phase being generally a liquid and the dispersed phase constituted of “nanoparticles,” that is, extremely fine metallic particles of size below 100 nm. In other words, the large surface-area-to-volume ratio also increases the stability of the suspensions. Thus, the nanofluid becomes a new promising heat transfer fluid in a variety of application cases. For example, the thermal properties of such a nanofluid appear to be well above those of the base-fluid and, particularly, the suspended nanoparticles remarkably increase the thermal conductivity of the mixture [2, 3] and improve its capability of energy exchange.

With the nanofluids as the coolant, Lee and Choi [4] proposed that the nanofluids dramatically enhance cooling rates of microchannel heat exchanger compared with the cases of conventional water and liquid-nitrogen coolant. Li and Xuan [5] studied experimentally convective heat transfer performances of nanofluids for laminar and turbulent flow inside a tube. They disclosed that a remarkable increase in heat transfer performances of nanofluids causes for the same Reynolds numbers. Heat transfer enhancement using copper nanoparticles is also proposed by Xuan and Roetzel [6]. Xuan and Li [7] measured convective heat transfer coefficient of Cu/water nanofluids from 0.3 in volume fraction to $2.0 %$ under constant heat flux condition and reported that the suspended nanoparticles remarkably enhance heat transfer process with smaller volume fraction of nanoparticles. Ding et al. [8] investigated the heat transfer performance of CNT nanofluids in a tube with 4.5 mm inner diameter. They found that the observed enhancement of heat transfer coefficient is much higher than the increase in the effective thermal conductivity.

Meanwhile, there are some inconsistent reports on nanofluid behavior in forced convection. For example, Pak and Cho [9] studied convective heat transfer performance in tube using nanofluids, that is, $γ − {Al}_{2} O_{3}$ and TiO₂ water and found that for fixed average fluid velocity, the convective heat transfer coefficient of the nanofluids is lower than that of pure water. They postulated that the suspensions have higher viscosity than that of pure water, especially at high particle volume fractions. Using nanofluid including the discshape nanoparticle, Yang et al. [10] measured much lower increase of convective heat transfer coefficient with respect to the effective thermal conductivity and concluded that the particle shape or aspect ratio of the particle is a significant parameter to affect the thermal performance of nanofluids.

Throughout the existing reports, Wang and Mujumdar [11] described that (i) the application of nanofluids for heat transfer enhancement should not be decided only by their effective thermal conductivity, and (ii) many other factors such as particle size, shape and distribution, microconvection, pH value, and the particle-fluid interactions should have important influence on the heat transfer performance of the nanofluids.

The purpose of this study is to disclose the thermal fluid flow transport phenomenon of nanofluid in a circular tube by measuring thermal conductivity, effective viscosity, the pressure drop, and the convective heat transfer performance for various concentrations of three different nanofluids. Here aqueous-based nanofluids containing diamond, alumina, and copper oxide, that is, diamond/water, ${Al}_{2} O_{3}$ /water, and CuO/water nanofluids are used as the working fluid and are tested under the constant heat flux boundary.

2. Experimental Apparatus and Measure Method

The nanoparticles used in this study are diamond, alumina ( ${Al}_{2} O_{3}$ ), and copper oxide in which alumina and copper oxide are the most common and inexpensive nanoparticles used by many researchers in their experimental investigations. Figure 1 shows TEM image of three different nanoparticles and the corresponding physical properties are summarized in Table 1. The diamond nanoparticle has the highest thermal conductivity among three different particles used here, as is seen in Table 1. Deionized water is used as the base liquid. Figure 2 depicts pictures of 1 vol.% nanofluids after 60 days later. Here, 1 vol.% implies a nanofluid of $1 %$ volume fraction of particles. The corresponding pH for three nanofluids is 6.62, 6.66, and 6.35, respectively. Since no concentration gradient appears in three different nanofluids, the nanofluids employed here maintain stability for several weeks. Figure 3 depicts the relationship between the average particle size and the zeta potential in three different nanofluids measured with the use of ELSZ-2 zeta potential and particle size analyzer (Otsuka Electronics Co., Ltd. Japan). In general, the relationship between zeta potential and average particle size of nanoparticles in suspension implies the particle dispersion state in nanofluid and in other words a large zeta potential corresponds to homogeneous dispersion. Zeta potential of ${Al}_{2} O_{3}$ is the highest in three different nanofluids, as is seen in Figure 3. One observes that diamond- and CuO-nanofluids form large aggregation, and in particular CuO nanofluids include several micro-order particles in diameter. Small particle has large zeta potential, as expected.

Table 1:

Physical property of nanoparticles.

Nanoparticle	Particle diameter (nm)	Thermal conductivity (W/mk)	Shape

Diamond	2∼10	2000	Sphere
${Al}_{2} O_{3}$	33	36	Sphere
CuO	47	20	Polyhedron

TEM images of three different nanoparticles.

Nanofluids at 1 vol.% of particle volume fraction after 60 days.

Zeta potential and average particle diameter in nanofluids for various volume fractions.

The effective thermal conductivity of nanofluids is measured with the aid of a KD2 thermal property meter (Labcell Ltd, UK), which is based on the transient hot wire method. Here the thermal conductivities of the nanofluids and base liquid (water) are measured at 293 K. The KD2 meter is calibrated using distilled water before any set of measurements.

The viscosity of nanofluids is measured with the use of a rotary viscometer (BROOKFIELD Co. DV-II+ProCP). The measurement is carried out at 293 K for the nanofluids of different concentrations and containing particles of three different materials. At least the viscosity for each nanofluid is measured three times and the mean value is applied as an effective viscosity of the nanofluid.

Figure 4 illustrates the experimental apparatus for measuring the convective heat transfer coefficient which consists of a closed flow loop, a heating unit, a cooling part, and a measuring and control unit. A straight stainless tube with 1000 mm in length, 3.96 mm in inner diameter, and 0.17 mm in thickness is employed as the test section and electrodes for the direct electric current heating are connected at both ends. The DC power supply (TOKYO SEIDEN CVS1-5 K) is employed and its voltage is adjustable with the aid of the voltmeter (YOKOGAWA 2011). The test tube is surrounded by a thick thermal insulation material to suppress heat loss from the test section. The six thermocouples (100 μm in diameter), which are welded on the outer surface of the test tube, are used to measure the local wall temperature along the heated surface of the tube, and the other thermocouples are inserted into the flow at the inlet (T_in) and outlet (T_out) of the test section to measure the bulk temperature of a working fluid. Here, axial positions are 150 mm, 290 mm, 430 mm, 570 mm, 710 mm, and 850 mm from the inlet of the test section, whose locations are named as T1, T2, T3, T4, T5, and T6, respectively. The working fluid in the test loop is circulated by a magnet pump (IWAKI MD-100 RM). Here the maximum flow rate that the pump can deliver is 8 L/minute and is measured by an electromagnetic flowmeter (KYENCE FD-81SO). The pressure loss between the inlet of the test section and the outlet is measured with the aid of the differential pressure instrument (NAGANO-KEIKI NR-250). Notice that the test loop is cleaned up between runs even with the same nanofluid.

Figure 4

Experimental apparatus.

The measured local wall temperature and heat flux are used to calculate the local Nusselt number ${Nu}_{x}$ defined by the following formula:

N u_{x} = \frac{h_{x} D}{k},

(1)

where D is the diameter of test tube, h_x is the local heat transfer coefficient, and k is the thermal conductivity of working fluid. Note that the thermal conductivity in (1) employs the value measured here. The local heat transfer coefficient is defined as

h_{x} = \frac{q}{(T_{w x} - T_{m x})} .

(2)

Here the subscriptx represents axial distance from the entrance of the test section, q is the heat flux, T_w,x is the measured local wall temperature, and T_m,x is the mixed mean temperature. The mixed mean temperature is determined by the following energy balance equation;

T_{m x} = T_{in} + \frac{q S x}{ρ C p A U},

(3)

where T_in, ρ, and cp are, respectively, the inlet temperature, the density, and the specific heat of fluid, S and A are, respectively, the outer surface area of test tube and the cross sectional area, and U is the averaged flow velocity.

Three volumetric fractions of $0.1 %$ , $1.0 %$ , and $5.0 %$ are tested for diamond/water, ${Al}_{2} O_{3}$ /water, and CuO/water nanofluids in the present study. The Reynolds number is ranged from 3000 to 10 000. An uncertainty analysis (Kline and McClintock [12]) yields the following results: the uncertainty in nanofluid flowrate is estimated to be $\pm 1.5 %$ , the uncertainty in the physical properties is less than $1 %$ , and the uncertainty in the temperature measurement is estimated to be $\pm 1.5 %$ . The uncertainty of the measurements was within $3 %$ under the conditions of this work.

3. Results and Discussions

The measured effective thermal conductivity k_n,f, for three difference nanofluids, is illustrated in Figure 5 in the form of volume fraction versus dimensionless thermal conductivity where k_n,f is divided by that of the base liquid (water), k_f. As a comparison, the prediction is superimposed in the figure as straight lines. Here the Hamilton and Crosser equation [13] (H-C equation) is employed. This equation is a classical formula to predict thermal conductivity of solid-liquid mixture;

k_{n f} = k_{L} [\frac{k_{S} + (n - 1) k_{L} - (n - 1) ϕ (k_{L} - k_{S})}{k_{S} + (n - 1) k_{L} + ϕ (k_{L} - k_{S})}],

(4)

where ϕ shows volume fraction, and the subscript nf, S, and L indicate nanofluid, solid particles, and liquid, respectively, and n is sphere coefficient. Note that n = 3is used in (4). The density ρ_n,f and specific heat ${C p}_{n f}$ of nanofluid are estimated from the physical properties of both nanoparticles and deionized water using the following correlations obtained at mean bulk temperature:

\begin{gathered} ρ_{n f} = ϕ ρ_{S} + (1 - ϕ) ρ_{L}, \end{gathered}

(5)

\begin{gathered} C p_{n f} = \frac{ϕ (ρ_{S} C p_{n f}) + (1 - ϕ) (ρ_{L} C p_{n f})}{ρ_{n f}} . \end{gathered}

(6)

Note that the density and specific heat of the nanofluid in (3) are determined by (5) and (6), respectively. It is observed that the effective thermal conductivity increases with increasing the volume fraction and its trend is different for each nanofluid. In other words, the thermal conductivity of CuO-nalfluid is predicted by the correlation equation, while the corresponding values for diamond/water and CuO/water nanofluids become larger than that of the pure water in the low-volume fraction region and increases slightly in the higher volume fraction.

Figure 5

Measured thermal conductivity of nanofluids under different volume fractions.

The viscosities for three different nanofluids, which are normalized by that of the pure water, are illustrated in Figure 6. For comparison, the prediction by Batchelor equation [14] is superimposed in Figure 6 as a solid line;

Figure 6

Relative viscosity for different nanofluids.

\frac{μ_{n f}}{μ_{f}} = 6.2 ϕ^{2} + 2.5 ϕ + 1,

(7)

where μ_n,f is viscosity of suspension and μ_f is that of a pure fluid. One observes that the measured viscosities of nanofluids are much higher than that of prediction, the viscosity of nanofluids increases with an increase in the particle concentration, and this trend is different for three nanoparticles. The effective particle volume fraction including cluster in a nanofluid becomes higher than that in the ideal suspension fluid in which each particle is independently and homogeneously dispersed in a fluid. In other words, the cluster including a fluid is considered as a particle, resulting in attenuation in the fluid volume fraction. Thus, the viscosity of diamond nanofluid is the highest, because diamond particles are strongly aggregated, as is seen in Figure 3(c), and cluster restricts a large amount of pure water. On the contrary, the viscosity of CuO nanofluid is relatively low because the CuO nanoparticles had already aggregated in the state of the powder.

The pressure loss between the test sections, for three different nanofluids, is illustrated in Figure 7 in the form of pressure drop versus flow rate at 5 vol% of volume fraction. The following equation for pure water is superimposed in the figure as lines for comparison;

Δ p = λ \frac{l}{D} \frac{ρ U^{2}}{2},

(8)

where l is the length of test tube and ρ is the density of nanofluid. The friction coefficient of the pipe λ is given by the Blasius equation, $λ = 0.3164 R e^{- 1 / 4}$ . Here, the thermal properties in the Reynolds number (Re) are estimated using the density determined by (5) and the viscosity measured here. The pressure loss of the nanofluids is slightly increased compared with that of the pure water, because an increase in the friction loss is caused by suspension of nanoparticles in the pure fluid. Note that no substantial discrepancy for pressure loss appears in three different nanofluids and the pressure drop for each nanofluid is reasonably predicted by (8).

Figure 7

Pressure drop for different nanofluids at 5 vol.%.

Next task is to consider the effect of suspension of nanoparticles on enhancement heat transfer. Figure 8 depicts the relationship between Nusselt number Nu and Reynolds number Re with different volume fractions, as a parameter. Figures 8(a), 8(b), and 8(c) correspond to the results for ${Al}_{2} O_{3}$ /water, CuO/water, and diamond/water nanofluids, respectively. Here the heat transfer coefficient in (1) is measured at $x / D = 200$ , which corresponds to the hydrodynamically and thermally fully developed region based on the pre-experimental result. The following classical Gnielinski equation [15] in the turbulent flow is superimposed in Figure 8 as a solid line for reference;

Nu = \frac{(f / 8) (Re - 1000) Pr}{1.07 + 12.7 \sqrt{f / 8} ({Pr}^{2 / 3} - 1)} .

(9)

Here, the friction coefficient f is calculated by

f = {[1.82 lo g_{10} (Re) - 1.64]}^{- 2} .

(10)

One observes that the Nusselt numbers for each nanofluid are higher than those for pure water. In other words, the Nusselt numbers for 1 vol.% diamond, CuO, and ${Al}_{2} O_{3}$ nanofluids, at $Re = 6000 \pm 100$ , show an enhancement of up to $9.8 %$ , $6.6 %$ , and $5.4 %$ , respectively. In particular, heat transfer performance, for ${Al}_{2} O_{3}$ nanofluid, is intensified with an increase in the volume fraction of nanoparticles and this trend becomes larger in the higher Reynolds number region. The heat transfer surface area of ${Al}_{2} O_{3}$ nanoparticles is the largest among three different nanoparticles because average diameter of the aggregated ${Al}_{2} O_{3}$ nanoparticles is the smallest, as is seen in Figure 3.

Nusselt numbers for each nanofluid.

In other words, lower enhancement of heat transfer for diamond and CuO nanofluids is attributed to substantial aggregation of nanoparticles, which plays an important role in heat transfer performance. This is because average diameter of the aggregated diamond nanoparticles is increased with an increase in volume fraction, as is seen in Figure 3(c) so that the Nusselt number of 1.0 vol.% is almost the same as that of 5 vol.%, as is seen in Figure 8(c).

Throughout the experimental results, as the volume fraction of nanoparticles is increased, the viscosity of nanofluids with cluster and the pressure drop are amplified, but the latter is slightly affected by the different nanofluids. Heat transfer enhancement is caused by the suspension of particles and its trend is intensified with an increase in the volume fraction of particles and is attributed to average diameter of the aggregated nanoparticles. In order to suppress aggregation of nanoparticles, the absolute value of zeta potential for the particle in suspension has to be intensified.

4. Conclusions

Experimental study has been performed to investigate heat transfer performance of aqueous suspensions of nanoparticles, that is, ${Al}_{2} O_{3}$ , CuO, and diamond. The results are summarized as follows.

The relative viscosity of nanofluids increases with an increase in concentration of nanoparticles, and the increase rate of the viscosity for nanofluid is different by the particle.

The pressure loss of the nanofluids tends to increase slightly compared with that of pure water.

Heat transfer performance in the circular tube flow is amplified by suspension of nanoparticles in comparison with that of pure water.

Heat transfer enhancement is affected by the occurrence of particle aggregation, that is, zeta potential of nanoparticles in suspension.

Footnotes

Nomenclature

Acknowledgments

This study was supported by the Grants-in-Aid for Scientific Research (C) (no. 16560153) from Japan Society for the Promotion of Science (JSPS). The author would like to express his thanks to Mr. Satoh of Graduate School of Science and Technology, Kumamoto University, for the heat transfer experiment.

References

Choi

S. U. S.

, “Enhancing thermal conductivity of fluids with nanoparticles,” in Developments Applications of Non-Newtonian Flows, Siginer

D. A.

and Wang

H. P.

, Eds., FED-vol. 231/MD-vol. 66, pp. 99–105, ASME, New York, NY, USA, 1995.

Khanafer

Vafai

, and Lightstone

, “Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids,” International Journal of Heat and Mass Transfer, vol. 46, no. 19, pp. 3639–3653, 2003.

Lee

Choi

S. U. S.

, and Eastman

J. A.

, “Measuring thermal conductivity of fluids containing oxide nanoparticles,” Journal of Heat Transfer, vol. 121, no. 2, pp. 280–289, 1999.

Lee

S. P.

and Choi

U. S.

, “Application of metallic nanoparticles suspensions in advanced cooling system,” in Recent Advances in Solid/Structures and Application of Metallic Materials, Kwon

Davis

, and Chung

, Eds., PVP-Vol.342/MD-Vol.72, pp. 227–234, ASME, New York, NY, USA, 1996.

and Xuan

, “Convective heat transfer performances of fluids with nanoparticles,” in Proceedings of the 12th International Heat Transfer Conference, pp. 483–488, 2002.

Xuan

and Roetzel

, “Conceptions for heat transfer correlation of nanofluids,” International Journal of Heat and Mass Transfer, vol. 43, no. 19, pp. 3701–3707, 2000.

Xuan

and Li

, “Investigation on convective heat transfer and flow features of nanofluids,” Journal of Heat Transfer, vol. 125, no. 1, pp. 151–155, 2003.

Ding

Alias

Wen

, and Williams

R. A.

, “Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids),” International Journal of Heat and Mass Transfer, vol. 49, no. 1–2, pp. 240–250, 2006.

Pak

B. C.

and Cho

Y. I.

, “Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles,” Experimental Heat Transfer, vol. 11, no. 2, pp. 151–170, 1998.

10.

Yang

Zhang

Z. G.

Grulke

E. A.

Anderson

W. B.

, and Wu

, “Heat transfer properties of nanoparticle-in-fluid dispersions (nanofluids) in laminar flow,” International Journal of Heat and Mass Transfer, vol. 48, no. 6, pp. 1107–1116, 2005.

11.

Wang

X.-Q.

and Mujumdar

A. S.

, “Heat transfer characteristics of nanofluids: a review,” International Journal of Thermal Sciences, vol. 46, no. 1, pp. 1–19, 2007.

12.

Kline

S. J.

and McClintock

F. A.

, “Describing uncertainties in single-sample experiments,” Mechanical Engineering, vol. 75, no. 1, pp. 3–8, 1953.

13.

Hamilton

R. L.

and Crosser

O. K.

, “Thermal conductivity of heterogeneous two-component systems,” Industrial and Engineering Chemistry Fundamentals, vol. 1, no. 3, pp. 187–191, 1962.

14.

Batchelor

G. K.

, “The effect of Brownian motion on the bulk stress in a suspension of spherical particles,” Journal of Fluid Mechanics, vol. 83, no. 1, pp. 97–117, 1977.

15.

Gnielinski

, “New equations for heat and mass transfer in turbulent pipe and channel flow,” International Chemical Engineering, vol. 16, pp. 359–368, 1976.