Experimental investigations in heat transfer and friction factor of magnetic Ni nanofluid flowing in a tube

International Journal of Heat and Mass Transfer 70 (2014) 224–234

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Experimental investigations in heat transfer and friction factor of magnetic Ni nanofluid flowing in a tube L. Syam Sundar a,⇑, Manoj K. Singh a,b,⇑, Igor Bidkin a, Antonio C.M. Sousa a a b

TEMA, Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, Portugal Aveiro Institute of Nanotechnology, University of Aveiro, 3810-193 Aveiro, Portugal

a r t i c l e

i n f o

Article history: Received 26 June 2013 Received in revised form 26 October 2013 Accepted 1 November 2013

Keywords: Ni nanofluid Heat transfer coefficient Friction factor Enhancement Turbulent flow

a b s t r a c t A magnetic nanofluid was prepared by dispersing magnetic Ni nanoparticles in distilled water. The nanoparticles were synthesized by chemical co-precipitation method and characterised by X-ray diffraction and atomic force microscopy. The average particle size was measured by the dynamic light scattering method. Thermal conductivity and absolute viscosity of the nanofluid were experimentally determined as a function of particle concentration and temperature. In addition, the Nusselt number and friction factor were experimentally estimated as a function of particle concentration and Reynolds number for constant heat flux condition in forced convection apparatus with no phase change of the nanofluid flowing in a tube. The experiments were conducted for a Reynolds number range of 3000–22,000, and for a particle concentration range from 0% to 0.6%. The results indicate that both Nusselt number and friction factor of the nanofluid increase with increasing particle volume concentration and Reynolds number. For 0.6% volume concentration, the enhancement of Nusselt number and friction factor is 39.18% and 19.12%, respectively, as compared to distilled water under the same flow conditions. It was verified the classical Gnielinski and Notter–Rouse correlations under predict the Nusselt number of the nanofluid; therefore, new generalized correlations are proposed for the estimation of the Nusselt number and friction factor based on the experimental data. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Fluids such as water, ethylene glycol, engine oil and transformer oil, just to mention a few, are commonly used in single-phase forced convection heat transfer applications; in particular, heat exchange equipment, which is present in practically every sector of the production cycle ranging from power generation to transportation. Increased thermal effectiveness of this equipment leads to the reduction of its size with the consequent reduction of capital and operating costs; if fouling is taken as a reference for decreased thermal effectiveness, its annual cost can be as high as 0.25% of the GNP of industrialized countries. Therefore, there is a strong economic motivation to increase thermal effectiveness, which can be achieved by increasing the thermal conductivity of the heat exchanging fluids. The simplest of the possible procedures encompasses the dispersion of solid nanoparticles in the fluids. Choi [1] was one of the first researchers to develop nanoparticles and then disperse them in a fluid to which he called nanofluid. Many researchers have investigated the thermal conductivity

⇑ Corresponding authors at: TEMA, Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, Portugal. Tel.: +351 916521110. E-mail addresses: [email protected] (L.S. Sundar), [email protected] (M.K. Singh). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.11.004

enhancement obtained with these nanofluids. Eastman et al. [2] obtained 40% thermal conductivity enhancement by using CuO nanofluid. Lee et al. [3] observed 20% thermal conductivity enhancement with 4% volume concentration of CuO nanofluid. Choi et al. [4] observed thermal conductivity enhancement of 160% with CNTs dispersed in engine oil. Das et al. [5] observed 6.5% to 29% thermal conductivity enhancement for CuO/water nanofluid at 1.0% volume concentration. Sundar and Sharma [6] reported thermal conductivity enhancement of 6.52% for Al2O3 nanofluid and 24.6% for CuO nanofluid at 0.8% volume concentration compared to water, which was the base-fluid used. In general, the research conducted indicates the enhancement of thermal conductivity is far more dependent on the nanoparticles than on the base fluid; therefore, researchers have concentrated their efforts on testing a wide variety of nanoparticles. Pak and Cho [7] conducted pioneering work in what concerns the estimation of the heat transfer coefficient for Al2O3 and TiO2 nanofluid flowing in a tube and also developed new Nusselt number and friction factor correlations. Xuan and Li [8] observed heat transfer enhancement with Cu nanofluid flowing in a tube under turbulent flow condition. Wang et al. [9] observed 70% and 190% heat transfer enhancement with 0.05% and 0.24% volume concentration of CNT-water nanofluid in a horizontal tube for a Reynolds number of 120. Duangthongsuk and Wongwises [10] observed 26% heat transfer

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225

Nomenclature A Cp D f h I k L _ m Nu P Pr Q Re T V

area, m2 specific heat, J/kg K inner diameter of the tube, m friction factor heat transfer coefficient, W/m2 K current, A thermal conductivity, W/m K length of the tube, m mass flow rate, kg/s Nusselt number, hD/k power, W Prandtl number, lCp =k heat flow, W _ p Dl Reynolds number, 4m= temperature, °C voltage, V

enhancement with TiO2 nanofluid at 2.0% volume concentration for turbulent flow in a tube. Asirvatham et al. [11] observed 28.7% and 69.3% heat transfer enhancement with 0.3% and 0.9% of silver nanofluid in a turbulent flow condition. Peyghambarzadeh et al. [12] found 45% heat transfer enhancement with Al2O3 nanofluid in an automobile radiator at 1.0% volume concentration. Fotukian and Esfahany [13] experimentally determined heat transfer and friction factor of Al2O3/water nanofluid in the Reynolds number range from 9000 to 13000 and in the volume concentration range from 0.03% to 0.135%. Fotukian and Esfahany [14] experimentally observed 25% and 20% heat transfer and friction factor enhancements with 0.236% volume concentration of CuO-water nanofluid flowing in a tube under turbulent flow condition. Wen and Ding [15] estimated the convective heat transfer coefficient of Al2O3water nanofluid flowing through a copper tube in the laminar flow region. Experiments with Al2O3/water nanofluid in the laminar flow range of Re = 700 and 2050 has been conducted by Heris et al. [16] and observed heat transfer augmentation with increase in Peclet number and nanoparticle volume fraction. Ding et al. [17] observed 350% heat transfer enhancement with carbon nanotubes (CNTs) flowing in a horizontal tube at 0.5% weight concentration at Reynolds number is 800. Ho et al. [18] have experimentally investigated the convective heat transfer enhancement in Al2O3/water nanofluid in micro-channel for a laminar flow. Anoop et al. [19] observed that Al2O3 nanofluid with 45 nm particles shows higher heat transfer coefficient than that with 150 nm nanoparticles; for instance, at x/D = 147, for 45 nm particle based nanofluid (4 wt.%) with Re equal to 1550, the enhancement in heat transfer coefficient was around 25%, whereas for the 150 nm particle based nanofluids it was found to be around 11%. Sundar and Sharma [20] developed both Nusselt number and friction factor correlations for Al2O3 nanofluid flowing in a tube under turbulent flow condition. Kayhani et al. [21] observed 8% heat transfer enhancement at 2.0% volume concentration of TiO2nanofluid at a Reynolds number of 11,800. Yang et al. [22] measured convective heat transfer of graphite-water nanofluid at different volume concentrations and observed better heat transfer rates. Sajadi and Kazemi [23] investigated the heat transfer behaviour of TiO2-water nanofluid and developed Nusselt number correlation. Yu et al. [24] conducted heat transfer experiments of SiC nanofluid in the volume concentration of 3.7% and in the Reynolds number (Re) range of 3300 < Re < 13000. Chen et al. [25] estimated the thermal conductivity and heat transfer by considering TiO2 (titanium) and TNT (titanate nanotubes) and found better heat transfer rates for TNT

v

velocity, m/s

Greek symbols DP pressure drop u volume concentration of nanoparticles, % l dynamic viscosity, kg/m2 s q density, kg/m3 Subscripts b bulk temperature Exp experimental i inlet o outlet Reg regression w wall temperature

nanofluids compared to TiO2 nanofluid. Rea et al. [26] observed the heat transfer coefficient enhancement of 17% and 27% by considering alumina–water and zirconia-water nanofluid, respectively. Ferrouillat et al. [27] obtained 10% to 60% heat transfer enhancement for SiO2-water in the weight concentration of 5% to 34% and in the Reynolds number range of 200 < Re < 10,000. The earlier research work on heat transfer and friction factor is on non-magnetic type nanofluids. The applications of magnetic nanofluids (fluids contain magnetic particles such as Fe2O3, Fe3O4, Ni and others) are unique in the bio-medical engineering field, including drug delivery, Lajvardi et al. [28] conducted the experiments for Fe3O4 ferrofluids in the laminar flow condition at different magnetic fields. Li and Xuan [29] experimentally investigated the convective heat transfer features of the aqueous magnetic fluid flow over a fine wire under the influence of an external magnetic field. Sundar et al. [30] experimentally observed 35% enhancement in heat transfer coefficient by using Fe3O4 nanofluid in a tube and also developed Nusselt number and friction factor correlations. Sundar and Singh [31] reviewed and analysed the existing Nusselt number correlations for different type of nanofluids flowing in a tube. The literature is relatively scarce in what concerns research work dealing with heat transfer and pressure drop for magnetic nanofluids. The present work is motivated by the need of reliable data for magnetic nanofluids; therefore, an experimental program along with an appropriate data treatment and analysis are conducted to estimate the heat transfer coefficient and friction factor of different concentrations of magnetic Ni nanofluid flowing in a tube under turbulent flow conditions. The experimental data and consequent heat transfer correlations for Ni nanofluid are not available in the literature. Thermal conductivity and viscosity of Ni nanofluid as a function of volume concentration and temperature were estimated experimentally; in addition, Nusselt number and friction factor correlations were developed based on the experimental data.

2. Preparation of Ni nanofluid In the present study, Ni nanoparticles were synthesized by using chemical co-precipitation method. Reagent grade chemicals such as nickel chloride (NiCl2.6H20), sodium borohydrate (NaBH4) and ethylene glycol (EG) were purchased from Sigma–Aldrich Chemicals, USA. Synthesis procedure contains, (1) 0.2 grams of nickel chloride was dispersed in 20 ml of ethylene glycol and stir-

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Fig. 2. (a) Magnetic hysteresis loop of Ni nanoparticles, (b) inset shows coercivity (80 Oe) of Ni nanoparticles samples.

fraction Standards (JCPDS) file. It indicates that the nanopowder contains pure Ni particles and there was no impurities and oxide present. The average crystallite size d was estimated from Sherrer’s equation.

d¼

Fig. 1. (a) XRD pattern of synthesized Ni nanoparticles, (b, c) surface topology studies by atomic force microscopy, (d) average particle size from atomic force microscopy.

red the solution with magnetic stirring under heating (2) the colour of the solution is turns into light green once solution reaches to 140 °C (3) after that added 0.1 grams of sodium borohydrate to the solution and observe immediate formation of black colour – an indication the reaction has occurred; the solution is cooled naturally while maintaining continuous stirring. The solution is diluted by adding small quantities of water and then collecting the precipitate by filtering the solution. The precipitate was washed several times with distilled water and acetone and dried in oven at 80 °C for 24 h. The weight of the residue is measured with sensible weight measuring instrument and it is nearly 0.0696 grams. The synthesized Ni nanoparticles were characterised by X-ray diffraction (Siemens D-500, 45 kV and 40 mA) and the pattern was shown in Fig. 1(a). It is observed from the figure, the patterns were well matched with the standard Joint Committee on Powder Dif-

0:94k ; Bð2hÞ cos h

ð1Þ

where d is the equivalent average core diameter of the particles, k is the wavelength of the incident X-ray, B(2h) denotes the full width in radian subtended by the half maximum intensity width of the powder peak and ‘h’ corresponds to the angle at that maximum peak. For the maximum peak in the XRD pattern (2h) is observed as 44.43 °, and B(2h) is 1.92 °. For a wavelength (k) is 0.15148 nm the value of d is approximately equal to 72 nm, as given by Eq. (1). Atomic force microscopy (AFM, NT-MDT, Ntegra Aura and Nanotec’s AFM with Dulcinea Electronic) was used for surface topography studies on Ni nanoparticles on mica substrate in tapping mode shown in Fig. 1(b) and (c) and particle size distribution is shown in Fig. 1(d) and it is found that the average size is 75 nm. The magnetic property of synthesized Ni nanoparticles was investigated by measuring their magnetization-magnetic field (M-H) hysteresis loops at a temperature of 20 °C with a vibrating sample magnetometer (VSM, Cryogenic). Fig. 2a shows ferromagnetic behavior with saturated magnetic hysteresis loops for Ni nanoparticles with a coercivity of 80 Oe (Fig. 2b). The saturation magnetization (MS) for Ni is 25 emu/g, this indicates that the particles are having good magnetic properties. Magnetic nanofluid was prepared by dispersing synthesized Ni nanoparticles in distilled water. Proper dispersion of nanoparticles in the base fluid is very important. There are several methods for proper dispersion of the particles which includes (i) alerting the pH of base fluid (ii) adding surfactant to the base fluid (iii) formation of carboxyl groups on the surface of the nanoparticles. Pak and Cho [7] used the first method i.e. change of pH of base fluid; in their study they observed uniform dispersion of Al2O3 nanoparticles in water at a pH of 3 and TiO2 nanoparticles in water at a pH of 11. Sundar et al. [30] also used this method and observed uniform dispersion of Fe3O4 nanoparticles in water at a pH of 3; according to these researchers, the uniform dispersion of nanoparticles in water is possible, if the water is either acidic or base. However, if the nanofluid is prepared using either acidic or base water, it will affect the heat transfer test section, which is made out of copper; to avoid

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this particular problem, Pak and Cho [7] used a stainless steel test section. The second method for the preparation of stable nanofluid is adding small quantity of surfactant to the water. Commonly used surfactants are sodium dodecylbenzenesulfonate (SDBS), oleic acid, Sodium dodecyl sulphate (SDS), and polyvinylpyrrolidone (PVP). Xuan and Li [8] used this method and obtained stable Cu nanofluid by dispersing small quantity of oleic acid in water. The disadvantage of this method is the surfactant modifies the thermophysical properties of nanofluid. In the present work third method was used to the preparation of stable nanofluids by formation of carboxyl groups on the surface of nanoparticles. To achieve this, the synthesized Ni nanoparticles were dispersed in 1:3 M ratio of nitric acid (HNO3) and hydrochloric acid (HCl) and stirred up to three days. The solution was washed several times with water and then filtered and dried up to 8 h at 80 °C; as result of this acid treatment, the surface of the nanoparticles were charged with carboxyl groups. These particles are then ready for the preparation of the magnetic nanofluid. The pH of the nanofluid sample was measured and a value of pH equal to 7 was registered on the pH meter; this implies, despite the acid treatment, the nanofluid has a neutral pH and its use will not affect the test section. A Zetasizer Nano ZS (Malvern) instrument, based on dynamic light scattering (DLS) method, was used to check the actual average size of the nanoparticles in solution and found that particle diameter was around 72.5 nm. Fig. 3 presents the particle size distribution measured by the instrument. Based on the XRD, AFM and DLS analysis, the average particle size is less than 75 nm. The above procedure was repeated to synthesize the bulk quantity of Ni nanoparticles. The quantity of nanoparticles required for a given percentage of volume concentration was estimated through Eq. (2). Nanofluid samples were prepared by dispersing 0.17, 0.89, 2.67 and 5.34 grams of nanoparticles in

100 ml distilled water for achieving 0.02%, 0.1%, 0.3% and 0.6% concentrations.



2

W nickel





W water

qnickel

Volume concentration; u  100 ¼ 4

W nickel

qnickel

þ



3 5

ð2Þ

qwater

Where u is the percentage of volume concentration, qNi = 8902 kg/ m3, qwater = 998.5 kg/m3, Wwater = 100 grams, Wnickel is the weight of the nanoparticles. 3. Properties of nanofluid It is important to study the physical properties of nanofluid, because the properties like thermal conductivity, viscosity, density and specific heat are required for the heat transfer calculations. Thermal conductivity and viscosity are determined experimentally, while density and specific heat are determined by using analytical estimates. Thermal conductivity and viscosity of nanofluid are measured with KD-2 Pro Thermal Conductivity Analyzer (Decagon Instruments, USA) and AR-100 Rheometer (TA instruments, UK), respectively. Both the instruments were calibrated with distilled water and found that thermal conductivity as 0.6139 W/m K and absolute viscosity as 0.81 mPa s at a temperature of 20 °C. Under the same temperature of 20 °C, thermal conductivity and viscosity data for water obtained from Incropera and DeWitt [32] is 0.6024 W/m K and absolute viscosity is 0.79 mPa s. A maximum of ±3% deviation was observed between measured and reported values. After that nanofluid concentration of 0.02%, 0.1%, 0.3% and 0.6% were introduced into the apparatus to measure both thermal conductivity and viscosity in the temperature range from 20 °C and 60 °C. The experimental data for thermal conductivity of nanofluid as a func-

Fig. 3. (a) Water and Ni nanoparticles dispersed in water (Ni nanofluid), (b) average particle size distribution from DLS measurement.

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Fig. 4. Experimental thermal conductivity of Ni nanofluid is in comparison with data of Sundar et al. [33] for Fe3O4 nanofluid.

tion of the particle concentration and temperature is shown in Fig. 4. For the sake of comparison, and considering there is no thermal conductivity data for the Ni nanofluid, the thermal conductivity data of Sundar et al. [33] for Fe3O4nanofluid are used. It is observed the thermal conductivity of Ni nanofluid increases with increasing particle concentration and temperature. The enhancement in thermal conductivity for 0.6% particle loading of Ni nanofluid is about 18.37% and 33.92% in the temperature range of 20 °C to 60 °C. Sundar et al. [33] observed a similar trend of the thermal conductivity enhancement for Fe3O4 nanofluid and obtained an enhancement of 14.6% and 29.66% at 0.6% particle loading in the same temperature range. This indicates the thermal conductivity of Ni nanofluid is higher than that of the Fe3O4nanofluid for the same particle concentration and temperature. The thermal conductivity of the Ni nanofluid is 25.82% and 14.36% over that of Fe3O4 nanofluid in the temperature range of 20 °C to 60 °C. The experimental data for absolute viscosity of Ni nanofluid are shown in Fig. 5. In the absence of viscosity data for Ni nanofluid, the viscosity data of Sundar et al. [33] for the Fe3O4 nanofluid is used for comparison. It is observed the absolute viscosity of Ni nanofluid increases with increasing volume concentration and decreases with increasing temperature. The enhancement in viscosity for 0.6% particle loading of Ni nanofluid, as compared to water, is about 39.24% and 70% in the temperature range of 20 °C to 60 °C. Sundar et al. [33] also obtained the similar behaviour of viscosity enhancement with Fe3O4 nanofluid. They obtained viscosity enhancement of 27.24% and 63.77% at 0.6% particle loading in the temperature range of 20 °C to 60 °C. This indicates the viscosity of the Ni nanofluid is about 44% and 9.7% more over Fe3O4 nanofluid for the same particle loading (0.6%) and temperature range. The density and specific heat of Ni nanofluid are estimated based on the Pak and Cho [7] equations with the specific heat of the Ni nanoparticle, C pp , taken equal to 440 J/kg K, namely:

qnf ¼ ð1  uÞqbf þ u  qp C pnf ¼ ð1  uÞC pbf þ u  C pp

ð3Þ ð4Þ

The experimental thermal conductivity, viscosity and density, specific heat estimated from Eqs. (3) and (4) are summarized in Table 1. 4. Experimental setup and procedure

Fig. 5. Experimental viscosity of Ni nanofluid is in comparison with data of Sundar et al. [33] for Fe3O4 nanofluid.

The schematic diagram of the forced convection heat transfer experimental setup is shown in Fig. 6. The setup consists of copper tube, cooler, collecting tank, storage tank, pump, by-pass valve arrangement and data acquisition system. The length and diameter of the copper tube is 1.5 m and 0.014 m, respectively. To achieve the fully developed hydrodynamic flow, the aspect ratio of the test

Table 1 Thermophysical properties of Ni nanofluid. Property

Temperature (°C)

Volume concentration (%) 0.0

0.02

0.1

0.3

0.6

(q), kg/m3

20 40 60

998.5 992.0 983.3

1000.08 993.58 984.88

1006.40 999.81 991.21

1022.21 1015.73 1007.05

1045.92 1039.46 1030.81

(k), W/m K

20 40 60

0.602 0.631 0.653

0.6152 0.6451 0.6742

0.6579 0.7249 0.7645

0.6842 0.7475 0.8145

0.7126 0.8035 0.8745

(l), mPa s

20 40 60

0.79 0.54 0.3

0.81 0.55 0.31

0.84 0.565 0.33

0.97 0.625 0.375

1.1 0.72 0.51

(Cp), J/kg K

20 40 60

4182 4179 4185

4181.25 4178.25 4184.25

4178.25 4175.26 4181.25

4170.77 4167.78 4173.76

4159.54 4156.56 4162.53

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229

Newton’s law of cooling was applied for the estimation of experimental heat transfer coefficient for both water and nanofluid. (i) Experimental heat transfer coefficient

P ¼ V  I ðHeat suppliedÞ _  C p  ðT o  T i Þ ðHeat absorbedÞ Q ¼m Q hExp ¼ AðT wall  T b Þ

ð5Þ ð6Þ ð7Þ

i where A ¼ p D L; T wall ¼ T 1 þT 2 þT53 þT 4 þT 5 and T b ¼ T o þT 2

NuExp ¼

hExp  D k

ð8Þ

(ii) Nusselt number correlation for single-phase forced convection fluid (a) Gnielinski’s [34] equation

 f ðRe  1000ÞPr 2 Nu ¼  0:5 1 þ 12:7 2f ðPr2=3  1Þ Fig. 6. Schematic diagram of an experimental setup.

where f = (1.58 ln (Re)  3.82)2, 2300 < Re < 5  106, 0.5 < Pr < 2000 (b) Notter–Rouse [35] equation

Nu ¼ 5 þ 0:015 Re0:856 Pr0:347 tube is maintained as L/D = 107. Constant heat flux condition for the test tube is maintained by wounding a nicrome heater of 20 mm gauge with a resistance of 53.5 X/m and maximum heating capacity of 1000 W. Heat loss from the test tube to the atmosphere is minimized by wrapping the test section with rock wool and asbestos rope insulation. Fluid inlet, outlet and surfaces temperature of the tube are measured by incorporating seven RTD-thermocouples with an accuracy of ±0.1 °C. Thermocouples are brazed at a distance of 0.1875, 0.375, 0.75, 1.125 and 1.325 m onto the surface of the tube. Before starting the experiment, the storage tank is filled with 14 l of nanofluid and the nanofluid is circulated through the test section with the help of pump. Based on the known Reynolds number, the mass flow rate of the nanofluid is controlled with the help of a by-pass valve arrangement. The flow rate of the nanofluid fluid is measured by a calibrated high precision flow meter with an accuracy of ±0.1 l/s. The outlet temperature of the nanofluid is brought back to atmospheric temperature with the help of a cooler. Once heat is supplied to the test section, the temperatures of thermocouples were noted at regular intervals of time, when the thermocouples indicate the same reading then the steady-state condition is assumed to be reached and the temperature and flow rate readings are recorded. The typical time for the system to reach the steady state conditions is 2 h. After steady state was reached, the data acquisition system records the temperature, for each thermocouple, every 5 s. The bulk mean temperature of the working fluid and the average surface temperature of the tube are used for the heat transfer calculations. The friction factor of the nanofluid flowing in a tube was measured in terms pressure drop. The pressure drop across the test tube was measured with help of a U-tube manometer. Two ends of the test tube, a 4 mm holes were drilled and the U-tube manometer was connected with flexible wire. Carbon tetrachloride (CCl4) was used as manometric fluid and the height of the manometric fluid was recorded for each mass flow rate of the nanofluid. Heat transfer and friction factor experiments are conducted in the Reynolds number range of 3000 to 22,000. Heat supplied to test tube and the amount heat gained by the working fluid was estimated through Eqs. (5) and (6) and a maximum of ±2.5% deviation was found. This indicates the heat loss from the test tube to the atmosphere is practically negligible.

ð9Þ

ð10Þ

(iii) Nusselt number correlation for different nanofluids (c) Pak and Cho [7] equation for Al2O3 and TiO2 nanofluids

Nu ¼ 0:021 Re0:8 Pr0:5 104 < Re < 105 ; 6:54 < Pr < 12:33; 0 < u < 3:0%

ð11Þ

(d) Xuan and Li [8] equation for Cu nanofluid

  Nu ¼ 0:0059 1 þ 7:6286u0:6886 Pe0:001 Re0:9238 Pr0:4 d 10; 000 < Re < 22; 500; 0 < u < 1:5%

ð12Þ

(e) Sundar et al. [30] equation for Fe3O4 nanofluid

Nu ¼ 0:02172 Re0:8 Pr 0:5 ð1 þ uÞ0:5181 3000 < Re < 22; 000; 3:72 < Pr < 6:50; 0 < u < 0:6% ð13Þ (iv) Experimental friction factor

DP f ¼   2  qv L D

ð14Þ

2

(f) Petukhov [36] equation for single-phase fluid

f ¼ ð0:790 ln Re  1:64Þ

2

3000 < Re < 5  106

ð15Þ

(g) Sundar et al. [30] equation for Fe3O4 nanofluid

f ¼ 0:3491 Re0:25 ð1:0 þ uÞ0:1517 3000 < Re < 22; 000; 3:72 < Pr < 6:50; 0 < u < 0:6% ð16Þ In order to assess the reliability of the experimental facility, the uncertainties of the experimental data were determined. The calculations of the data uncertainties were based on the work by Kline and McClintock [37]. All the quantities measured to estimate the Nusselt number and friction factor are subjected to certain uncertainties due to errors in the measurements. The uncertainty analyses of the Reynolds number, heat flux, heat transfer coefficient, Nusselt number and friction factor are presented and obtained from the equations shown below. The

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Table 2 Measured ranges of various parameters. S.No.

Instrument

Minimum–maximum range (least division)

Measured range

1 2 3 4 5 6

Thermocouple, (°C) (Wall temperature) Thermocouple, (°C) (Fluid temperature) Voltage, (V) Current, (I) U-tube manometer, (m) Flow meter, (Liters)

0°–120° (±0.1) 0°–120° (±0.1) 0–220 (±1) 0–20 (±0.1) 0–0.5 (±0.1) 0–20 (±0.1)

45.66°–72.96° 31.25°–42.90° 220.0 5.0 2.0–38.3 1–15

instruments used in the experimental analysis and their maximum range and measured range is given in table Table 2. Heat flux:

Friction factor: DP f ¼   2  qv L D

P V I q¼ ) A "p D L  2  2  2  2 #0:5 Dq 1 @ @ @ @ ¼ ðqÞDV þ ðqÞDI þ ðqÞDD þ ðqÞDL q q @V @I @D @L (    )0:5 Dq DV 2 DI 2 DD 2 DL 2 ¼ þ þ þ q V I D L ( )0:5 2  2 Dq 1 0:1 2 2 ¼ þ þ ð0:1Þ þ ð0:1Þ ¼ 0:67% q 220 20 ð17Þ

2

" 2  2  2 Df 1 @ @ @ ¼ ðf ÞDL þ ðf ÞDD ðf ÞðDðDPÞÞ þ f f @ðDPÞ @L @D  2  2 #0:5 @ @ þ ðf ÞDq þ 2 ðf ÞDv @q @v ( 2  2  2  2  2 )0:5 Df DðDPÞ DL DD Dq 2Dv ¼ þ þ þ þ v f L D q DP ( 2  2 )0:5 Df 1 2x0:1 2 2 2 ¼ þ ð0:001Þ þ ð0:001Þ þ ð0:001Þ þ ¼ 3:05% f 36:3 15

ð21Þ

5. Results and discussion

Heat transfer coefficient: 5.1. Nusselt number

q ðT w  T b Þ " 2  2  2 #0:5 Dh 1 @ @ @ ¼ ðhÞDq þ ðhÞDT w þ ðhÞDT b h h @q @T w @T b ( )   0:5 Dh Dq 2 DT w 2 DT b 2 ¼ þ þ h q Tw Tb (  2  2 )0:5 Dh 0:1 0:1 2 ¼ ð0:0067Þ þ þ ¼ 1:09% h 72:96 11:65

h¼

ð18Þ Nusselt number:

Nu ¼

hD k

" 2  2  2 #0:5 DNu 1 @ @ @ ¼ ðNuÞDh þ ðNuÞDD þ ðNuÞDk Nu Nu @h @D @k (  2  2 )0:5 2 DNu Dh DD Dk ¼ þ þ Nu h D k

Validation of the experimental setup is done by circulating the distilled water into the test section. The experimental Nusselt number estimated from Eq. (8) is represented in Fig. 7 along with the data obtained from Eq. (9) of Gnielinski [34] and Eq. (10) of Notter–Rouse [35]. The deviation between experimental and theoretical Nusselt number is obtained as ±3.0%. This reflects the experimental setup is well designed and, consequently, it can be used to estimate the heat transfer coefficient for different volume concentrations of the Ni nanofluid. The experimental heat transfer coefficient and Nusselt number for different volume concentrations of Ni nanofluid estimated from Eqs. (7) and (8) is shown in Fig. 8(a) and (b) along with the data of distilled water. The experimental thermal conductivity of Ni nanofluid was used for the estimation of Nusselt number as per Eq. (8). It is observed from both the figures,

0:5 DNu ¼ fð0:0109Þ2 þ ð0:001Þ2 þ ð0:001Þ2 g ¼ 1:09% Nu

ð19Þ Reynolds number:

Re ¼

_ 4m

pDl

" 2  2  2 #0:5 DRe 1 @ @ @ _ ¼ ðReÞDm þ ðReÞDD þ ðReÞDl _ Re Re @ m @D @l (  2  2 )0:5 _ 2 DRe DD Dl m ¼ þ þ _ Re D l m ( )0:5 2 DRe 1 ¼ þ ð0:001Þ2 þ ð0:001Þ2 ¼ 6:66% Re 15 ð20Þ

Fig. 7. Experimental Nusselt number of water from Eq. (8) along with the correlated data of Gnielinski [34] and Notter–Rouse [35].

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Fig. 9. Experimental Nusselt number of Ni nanofluid is in comparison with Eq. (11) of Pak and Cho [7] for Al2O3 and TiO2 nanofluids.

Fig. 8. (a) Experimental heat transfer coefficient of Ni nanofluid from Eq. (7) as a function of particle concentration and Reynolds number. (b) Experimental Nusselt number of Ni nanofluid from Eq. (8) as a function of particle concentration and Reynolds number.

heat transfer coefficient and Nusselt number increases with increasing particle concentration in the base fluid and it also increases with increasing Reynolds number. The use of nanoparticles in the base fluid causes the enhancement in Nusselt number, which is due to the thermophysical properties of the nanoparticles, increased surface area and Brownian motion. The enhancement in Nusselt number for 0.02% of Ni nanofluid is approximately 10% and 9.5% for Reynolds numbers of 3000 and 22,000, respectively; while, for the 0.6% of Ni nanofluid is approximately 29.12% and 39.18% for the Reynolds numbers of 3000 and 22,000 respectively. For the volume concentrations of 0.02%, the percentage of enhancement in Nusselt number is more or less constant throughout the Reynolds number range tested but for 0.6% volume concentration, the percentage of Nusselt number at a Reynolds number of 22,000 is much higher than that for the Reynolds number of 3000, in part due to the enhanced mixing facilitated by the nanoparticles in the high turbulent flow regime. The similar trend of enhanced Nusselt number is observed by Pak and Cho [7] by conducting the heat transfer experiments with Al2O3 and TiO2 nanofluid in the Reynolds number range from 104 to 105 in the particle volume concentration of 3.0%. They obtained 75% Nusselt number enhancement with 2.78% volume concentration of

Al2O3 nanofluid. Their study also indicates that Nusselt number enhancement with the use of nanoparticles in the base fluid. The same Nusselt number enhancements with Cu and Fe3O4 nanofluids have been obtained by Xuan and Li [8] and Sundar et al. [30], respectively. Assuming the applicability of the Nusselt number correlations for single phase fluid, Eq. (9) of Gnielinski [34] and Eq. (10) of Notter–Rouse [35], they are used to calculate the Nusselt number for 0.6% of Ni nanofluid for different Reynolds number and Prandtl number. The Eq. (9) of Gnielinski [34] and Eq. (10) of Notter–Rouse [35] underpredict by 26% and 29% the Nusselt number for 0.6% of Ni nanofluid in the Reynolds number of 22,000. This indicates these Nusselt number correlations are not adequate to predict the Nusselt number for nanofluids. Hence, based on the literature, the available Nusselt number correlations developed by various researchers were considered to evaluate the present data of Ni nanofluid. Pak and Cho [7] developed a Nusselt number correlation for Al2O3 and TiO2 nanofluid in turbulent flow conditions. The present experimental Nusselt number for Ni nanofluid is shown in Fig. 9 along with the values obtained from Eq. (11) of Pak and Cho [7]. The Eq. (11) gives a value lower than that for 0.6% of Ni nanofluid by 7.3% at a Reynolds number of 22,000. The difference between the values predicted by the Nusselt number correlation of Pak and Cho [7] and the present data can be attributed to the different thermal properties of the nanoparticles. The equation developed by Xuan and Li [8] for Cu nanofluid in the turbulent flow regime is also used for comparison. The present experimental Nusselt number for Ni nanofluid is shown in Fig. 10 along with the predictions obtained using Eq. (12) of Xuan and Li [8]. The Nusselt number for 0.6% of Ni nanofluid is 13.79% higher than the predictions obtained with Eq. (12) for the Reynolds number of 22,000. Sundar et al. [30] obtained for the magnetic Fe3O4 nanofluid experimental data for the turbulent flow regime and they developed a Nusselt number correlation (Eq. (13)). Fig. 11 reports the present experimental data along with the predictions obtained with Eq. (13). The comparison indicates the present data is higher than the predictions of Eq. (13), with differences of 6.8% and 4.2% for 0.6% of Ni nanofluid at Reynolds numbers of 3000 and 22,000, respectively. The various comparisons indicate the Ni nanofluid, in general, presents an improved thermal performance in relation to the Al2O3, Cu and Fe3O4 nanofluids. New correlation for the estimation of Nusselt number is proposed in similar lines of Eq. (13)

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Fig. 10. Experimental Nusselt number of Ni nanofluid is in comparison with Eq. (12) of Xuan and Li [8] for Cu nanofluid.

Fig. 11. Experimental Nusselt number of Ni nanofluid is in comparison with Eq. (13) of Sundar et al. [30] for Fe3O4 nanofluid.

based on the experimental data, Reynolds number, Prandtl number and volume concentration with an average deviation of 3.65% and standard deviation of 4.56%.

NuReg ¼ 0:0221 Re0:8 Pr0:5 ð1 þ uÞ0:54 3000 < Re < 22; 000; 0 < u < 0:6%; 3:72 < Pr < 6:37

ð22Þ

The proposed Eq. (22) is also capable of estimating the Nusselt number of water under different Reynolds number by substituting u = 0. The validation of proposed equation is shown in Fig. 12 along with experimental data. 5.2. Friction factor Experimental friction factor of water estimated from Eq. (14) is shown in Fig. 13 along with the data from the Eq. (15) of Petukhov [36]. The deviation between measured and theoretical values is found to be ±3.0%. Experimental friction factor for different volume concentrations of Ni nanofluid estimated from Eq. (14) is shown in Fig. 14 along with base fluid data. The enhancement in friction

Fig. 12. Comparison of the correlated values (Eq. (22)) with the experimental data for the Nusselt number.

Fig. 13. Experimental friction factor of water from Eq. (14) is in comparison with Eq. (15) of Petukhov [36].

factor for 0.02% of Ni nanofluid is about 4.5% and 5.56% in the Reynolds number of 3000 and 22,000 respectively. The enhancement in friction factor for 0.6% of Ni nanofluid is about 15.9% and 19.12% in the Reynolds number of 3000 and 20000 respectively. Because of dispersion of Ni nanoparticles in the base fluid, little bit enhancement in friction factor takes place. This is not a much more high, compared to heat transfer augmentation, friction factor augmentation is negligible. Comparison of the present experimental friction factor with the predictions using Eq. (16) of Sundar et al. [30] is shown in Fig. 15. The results indicate the Fe3O4 nanofluid (Eq. (16)) has lower friction factor than that for the 0.6% Ni nanofluid; the difference is 34.7% and 14.21% for the Reynolds numbers of 3000 and 22,000, respectively. Friction factor correlation developed based on the experimental data, Reynolds number and particle volume concentration is given by:

fReg ¼ 0:35662 Re0:25 ð1 þ uÞ0:2375

ð23Þ

3000 < Re < 22; 000; 0% < u < 0:6%; 3:72 < Pr < 6:37

ð24Þ

The proposed Eq. (23) has an average deviation of 3.12% and standard deviation of 4.1%.; it can be used to estimate the friction factor

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of water by taking u = 0. Validation of proposed equation is made by comparing the experimental friction factor and both the data is shown in Fig. 16. 6. Conclusion Nickel nanoparticles with an average particle size of less than 75 nm were prepared by using chemical co-precipitation method. Water based magnetic Ni nanofluid was prepared for the estimation of thermal conductivity, absolute viscosity and convective heat transfer coefficient. Major findings can be summarized as follows:

Fig. 14. Experimental friction factor as a function of the Reynolds number for different Ni concentrations in the Ni nanofluid.

Fig. 15. Experimental friction factor of Ni nanofluid is in comparison with Eq. (16) of Sundar et al. [30] for Fe3O4 nanofluid.

1. Thermal conductivity of Ni nanofluid increases in increase of particle concentration and temperature compared to base fluid. A maximum enhancement of 33.92% was observed for 0.6% particle loading at a temperature of 60 °C. 2. Absolute viscosity of Ni nanofluid increases with increase of particle concentration and decreases with temperature compared to base fluid. A maximum enhancement of 70% was found for 0.6% particle loading at a temperature of 60 °C. 3. The heat transfer coefficient of Ni nanofluid increases with increase of volume concentration and Reynolds number. This is caused due to influence of particle Brownian motion and micro-convection of the particles in the base fluid. Maximum heat transfer enhancement of 39.18% was obtained for 0.6% particle loading in the Reynolds number of 22,000 compared to water under same flow conditions. 4. The Nusselt number correlations available for nanofluids such as Al2O3, Cu and Fe3O4 indicate the Ni nanofluid has superior thermal performance. 5. The friction factor of Ni nanofluid also increases with increasing particle concentration and Reynolds number. Maximum of 19.12% was obtained for 0.6% particle loading at a Reynolds number of 22,000 compared to water. 6. For a particular Reynolds number and temperature, the pressure drop due to the increase of friction factor is relatively negligible, when compared to the benefits arising from heat transfer enhancement. 7. The developed Nusselt number and friction factor correlations are

NuReg ¼ 0:0221 Re0:8 Pr0:5 ð1 þ uÞ0:54 fReg ¼ 0:35662 Re0:25 ð1 þ uÞ0:2375

Acknowledgment The authors would like to thank the Portuguese Foundation of Cinecia e Technologia, through a grant funded by Ministry of Science and Technology (PTDC/EME-MFE/105031/2008). One of the authors (L.S.S.) would like to thank FCT for his Post-Doctoral research grant (SFRH/BPD/79104/2011). References

Fig. 16. Experimental friction factor from Eq. (14) along with the data from Eq. (23).

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