Effect of volume concentration and temperature on ... - Springer Link

J Therm Anal Calorim (2016) 123:1399–1409 DOI 10.1007/s10973-015-5034-x

Effect of volume concentration and temperature on viscosity and surface tension of graphene–water nanofluid for heat transfer applications Nizar Ahammed1 • Lazarus Godson Asirvatham1 • Somchai Wongwises2

Received: 11 April 2015 / Accepted: 11 September 2015 / Published online: 29 September 2015 Ó Akade´miai Kiado´, Budapest, Hungary 2015

Abstract In the present study, the effect of volume concentration (0.05, 0.1 and 0.15 %) and temperature (10–90 °C) on viscosity and surface tension of graphene–water nanofluid has been experimentally measured. The sodium dodecyl benzene sulfonate is used as the surfactant for stable suspension of graphene. The results showed that the viscosity of graphene–water nanofluid increases with an increase in the volume concentration of nanoparticles and decreases with an increase in temperature. An average enhancement of 47.12 % in viscosity has been noted for 0.15 % volume concentration of graphene at 50 °C. The enhancement of the viscosity of the nanofluid at higher volume concentration is due to the higher shear rate. In contrast, the surface tension of the graphene– water nanofluid decreases with an increase in both volume concentration and temperature. A decrement of 18.7 % in surface tension has been noted for the same volume concentration and temperature. The surface tension reduction in nanofluid at higher volume concentrations is due to the adsorption of nanoparticles at the liquid–gas interface because of hydrophobic nature of graphene; and at higher temperatures, is due to the weakening of molecular attractions & Lazarus Godson Asirvatham [email protected]; [email protected] Nizar Ahammed [email protected] Somchai Wongwises [email protected] 1

Department of Mechanical Engineering, Karunya University, Coimbatore, Tamil Nadu 641 114, India

2

Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab (FUTURE), Department of Mechanical Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangmod, Bangkok 10140, Thailand

between fluid molecules and nanoparticles. The viscosity and surface tension showed stronger dependency on volume concentration than temperature. Based on the calculated effectiveness of graphene–water nanofluids, it is suggested that the graphene–water nanofluid is preferable as the better coolant for the real-time heat transfer applications. Keywords Graphene Nanofluid Viscosity Surface tension Effectiveness List C Cp k T

of symbols Coefficient of enhancement Specific heat/Jkg-1 K-1 Thermal conductivity/Wm-1 K-1 Temperature/°C

Greek symbols u Volume fraction l Dynamic viscosity/mN s m-2 r Surface tension/mN m-1 q Density/kg m-3 Subscript nf Nanofluid f Base fluid k Thermal conductivity l Dynamic viscosity 1 Ambient P Nanoparticle

Introduction The modern heat transfer systems need enhancement in performance to become further energy efficient. Many industries need ultra-high performance in cooling and

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heating. The miniaturization and ultra-high performance are two important features of high-end electronic devices. Thermal management of electronic components has gained a lot of attention due to the drastic increase in power density, compactness and enhancement in computation speeds leading to high heat fluxes [1–3]. But the current techniques are not adequate to cater the thermal management needs of these compact and high-power density devices. This deteriorates the efficiency and life span of these devices. A fluid with enhanced heat transfer properties can solve this issue to an extent. The thermal and heat transfer properties of the conventional cooling fluids are enhanced by suspending nanometer-sized (1–100 nm) solid particles with higher thermal conductivity and high surface area, resulting in a two-phase mixture called a nanofluid [4–6]. Nowadays, nanofluids are widely used in a variety of applications, such as electronic cooling, internal combustion engine cooling and lubrication, industrial cooling, industrial and comfort air conditioning and extraction of geothermal and solar energy [7, 8] due to its enhanced thermal properties [9–13]. An investigation of the viscosity (one of the thermophysical properties) of nanofluids has inevitable importance in finding the adequate pumping power, Reynolds number, Prandtl number and heat transfer coefficient in thermal systems that employ fluid flow [14, 15]. Pumping power depends on the pressure drop, which, in turn, is associated with fluid viscosity. Hence, studying viscosity becomes very important to understand the utility of nanofluids in various applications [16, 17]. Similarly, the surface tension is also a very important parameter in boiling and two-phase flow heat transfer phenomena, as well as in critical heat flux measurements. Surface tension plays a major role when analyzing the heat transfer performance of heat pipes. Despite many interesting applications, there are only a few recent studies available on viscosity and surface tension of nanofluids in the open literature, a brief review of which is presented below. Silambarasan et al. [18] measured the viscosity of submicron TiO2 particles in water with particle volume concentrations varying from 0.27 to 1.39 % and temperatures ranging from 29 to 55 °C. The results showed that the viscosity increased almost linearly with an increase in the particle concentration. It has also been observed that the viscosity decreased with an increase in temperature at all particle volume concentrations. Fedele et al. [19] studied the effects of particle mass concentration (1–35 mass%) and temperature (10–70 °C) on the viscosity of TiO2–water nanofluids. The deviations of the viscosity value of the nanofluid from that of water were about 20, 60 and 215 % at 10, 20 and 35 mass% of TiO2 nanoparticles concentration, respectively. Tao et al. [20] investigated the effects of nanoparticle size (7, 12, 16, 20 and 40 nm), as well as particle volume concentrations (1, 2 and 4 %) on the viscosity of

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SiO2–water nanofluids at 25 °C. The results showed that the viscosity of SiO2–water nanofluids increased with decreasing particle sizes for the same volume fraction. Duan et al. [21] measured the viscosity of water-based nanofluid with Al2O3 nanoparticle suspension (1–5 vol%) at room temperature. An enhancement of 60 % in viscosity has been observed at 5 % volume concentration. Rudyak et al. [22] studied the effects of nanoparticle size (18.1, 28.3 and 45.6 nm), temperature (20–60 °C) and volume concentration (0.2–8 %) on the viscosity of SiO2– ethylene glycol nanofluids. It has been observed that the smaller the nanoparticles, the higher the viscosity. It has also been found that at a 7 % volume concentration of the nanoparticles, the viscosity of the nanofluids with the largest and smallest particles increased by 40 and almost 80 %, respectively, at 25 °C. Kole et al. [23] investigated the effects of particle loading (0.041–0.395 vol%) and temperature (10 and 70 °C) on the viscosity of graphene–ethylene glycol–water (70:30) nanofluids. The results showed that the viscosity of the nanofluid enhanced nearly by 100 % with that of the base fluid, at a loading of 0.395 vol%. Yang et al. [24] measured the viscosity of viscoelastic fluid-based nanofluids with dispersion of copper nanoparticles concentration (0.1–2.5 vol%) and temperature (25–45 °C). It has been found that the nanofluid showed a non-Newtonian behavior in the viscosity, and the viscosity increased with the increase in Cu nanoparticles concentration and decreased with an increase in temperature. A viscosity decrement of 87.7 % has been observed at 1.6 % volume concentration when the temperature increased from 25 to 45 °C. Utomo et al. [25] investigated the viscosity of waterbased alumina and titania nanofluids. It has been found that the relative viscosity of titania nanofluid is higher than that of the alumina nanofluid. The viscosity enhancement of titania and alumina nanofluids was 185 and 25 % for 6 % volume concentration at 20 °C. Kole et al. [26] also measured the viscosity of CuO–gear oil nanofluids for temperatures ranging between 10 and 80 °C. The volume concentrations of nanoparticles were maintained between 0.5 and 2.5 %. The viscosity of the nanofluids was enhanced by 3 times the base fluid with a CuO volume concentration of 2.5 %. Dehkordi et al. [27] tested the influence of SDBS on the viscosity of alumina–ethylene glycol–water nanofluids for the temperature range of 25–40 °C. The nanoparticles with volume concentrations ranging between 0.01 and 1 % were dispersed. The relative viscosity of the nanofluid showed 1 % enhancement with the addition of the SDBS dispersant at 4 mass% concentrations. Vasheghani et al. [28] measured the viscosities of engine oil-based nanofluids by suspending c-Al2O3 and aAl2O3 nanoparticles with 0.1–3.0 mass percentage and for a temperature range of 25–75 °C. The results showed that

Effect of volume concentration and temperature on viscosity

the viscosity enhancement of c-Al2O3 and a-Al2O3 was found to be 36 and 38 %, respectively, at 25 °C. Zhu et al. [29] measured the viscosity and surface tension of Al2O3– water nanofluids with very low concentrations of nanoparticles (0–1 g/l). No obvious change has been observed in the value of the viscosity due to the addition of nanoparticles, and a maximum enhancement of about 5 % for surface tension was obtained at a concentration of 1 g/l at 21 °C. Wang et al. [30] measured the viscosity of ionic liquid-based nanofluids with graphene and multiwalled carbon nanotubes as suspensions for a temperature range of 25–75 °C at very low mass percentages of 0.03 and 0.06 %. A viscosity decrement of 81.32 and 78.66 % was observed for a volume concentration of 0.03 % of graphene and MWCNT nanoparticles, respectively, when the temperature increased from 25 to 75 °C. Tiwari et al. [31] tested the viscosity of cerium oxide (CeO2)–water nanofluids. The nanoparticles of CeO2 with volume concentrations ranging between 0.5 and 3 % were dispersed and measured at a temperature range of 25–50 °C. A viscosity enhancement of 34 % is observed for a volume concentration of 3 % at 40 °C. Gallego et al. [32] compared the viscosities of water-based nanofluids by dispersing CuO nanoparticles obtained from different sources (sizes of 33 and 11 nm). The nanoparticles of CuO with volume concentrations ranging between 0.16 and 1.7 % were dispersed and measured at a temperature range of 10–50 °C. It has been observed that at 1.7 % volume concentration of nanoparticles, the viscosity of the nanofluids with 33 and 11-nm-sized particles increased by 13.55 % and almost 107 %, respectively, at 50 °C. Rashin et al. [33] investigated the viscosity of CuO– coconut oil nanofluid with nanoparticle concentration of 0–2.5 mass% having a size of 20 nm and tested for a temperature range of 35–55 °C. The results show that at 35 °C, the measured viscosity values have an enhancement from 5 to 28 % with addition of nanoparticles from 0.5 to 2.5 mass% at a constant shear rate of 3.67 s-1. Mehrali et al. [34] measured the viscosity of graphene nanoplatelets (GNP) dispersed in water with no dispersant. The concentrations of nanoparticles were maintained at 0.025, 0.05, 0.075 and 0.1 mass%. The viscosity of nanofluid improved by 44 % when compared to the viscosity of the base fluid for 0.1 mass% of GNPs. Moosavi et al. [35] measured the surface tension of ZnO–ethylene glycol nanofluids with nanoparticle volume concentration ranging from 0 to 3 % and for a temperature range of 20–50 °C. A surface tension increment of 7 % was observed for the volume concentration of 3 % and at a temperature of 25 °C. Khaleduzzaman et al. [36] tested the influence of volume fraction, temperature and additive surfactant over the surface tension of nanofluids from available experimental results. It has been found that with

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the increase in nanoparticle concentrations, the surface tension of some nanofluids increased, and for some other nanofluids, it decreased. Godson et al. [37] measured the surface tension and viscosity of Ag–water nanofluids for temperatures between 50 and 90 °C and volume concentrations from 0.3 to 1.2 %. It has been observed that viscosity enhancement was 2 times higher than that of the surface tension enhancement for the same volume concentration. The maximum increment in viscosity from the base fluid of 48 % was observed for 1.2 % volume concentrations. The increment in surface tension has almost 12 % for the same volume concentration. Based on the survey of the literature mentioned above, it is clear that the viscosity of the nanofluid increases with the increasing volume concentration of nanoparticles and decreases with the increase in temperature. It is also observed that the viscosity of the smaller-diameter particles is found to be higher than that of the higher-diameter particles with the same volume concentration. In contrast, the surface tension of the nanofluid decreases with an increase in both volume concentration and temperature. However, very limited works have been reported on viscosity and surface tension of nanofluids using pure metal nanoparticles with very low volume concentrations (e.g.,\1 %) measured at higher temperatures or a wide range of temperatures. In the case of the surface tension of nanofluids, there are contradictory conclusions regarding the changes of surface tension as a result of addition of nanoparticles. Further, the literatures available on viscosity and surface tension of graphene–water nanofluids at below- and above-ambient temperatures ranging from 10 to 90 °C are not reported. Hence, in the present study, an attempt is made to determine the viscosity and surface tension of graphene–water nanofluid by suspending very low volume concentrations (0.05, 0.1 and 0.15 %) of graphene at temperatures below- and above-ambient conditions ranging from 10 to 90 °C. The results will be useful in the design of heat exchangers and heat pipes that employ fluid flow and two-phase flow under a wide range of temperatures [38–41].

Experimental Preparation and characterization of nanofluid The two-step method was used to prepare the required samples of graphene–water nanofluids. The thickness of the graphene (SkySpring Nanomaterials, Inc. Hoston, USA) used in the present study is 1–5 nm. Only a small amount (5 % of each volume concentration) of SDBS (sodium dodecyl benzene sulfonate) has been used for stabilizing the graphene in the base fluid. The surfactant was firstly dispersed into the base fluid, followed by the

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Total counts

1.5E+5

1.0E+5

5.0E+4

0.0E+0 –200

–100

0

100

200

Zeta potential/mV Fig. 1 SEM image of 0.15 % volume concentration of graphene

Fig. 2 Zeta potential analysis of graphene–water nanofluid

required amount of dry graphene, and then, the mixture was homogenized by an ultrasonic vibrator (UP400S, Hielscher Ultrasound Technology, Germany) for 30 min to break down the agglomerates of graphene. The different samples of graphene–water nanofluid were prepared by maintaining volume concentrations of graphene at 0.05, 0.1 and 0.15 %. The graphene was characterized by scanning electron microscope (SEM, JSM 6390, JEOL, USA) and Zeta potential analyzer (Nano ZS90 ZETASIZER Nano Series, Malvern, USA) to study the shape, size and phase distribution. Figure 1 shows the SEM image of the graphene taken at 50009 magnification. It is clearly observed from Fig. 1 that the graphene is randomly distributed as a flake-like structure. Figure 2 shows zeta potential analysis of graphene–water nanofluid. It is clearly seen from Fig. 2 that the zeta potential value is -63.7 mV for a total count of 175,000. Hence, high electronegative value indicates good size distribution and high stability of graphene–water nanofluid.

viscosity of a fluid. Torque measurement accuracy and repeatability of the equipment are 1 and 0.2 % of the fullscale range, respectively. A constant-temperature, water-circulating bath (WB 2000 V, Duralab) with heating and cooling features for a temperature range between -10 and 100 °C was used to keep the nanofluids at different constant temperatures during the experiment. The temperature deviation for the constant-temperature, water-circulating bath is ±0.05 °C. A chamber tube with an integrated water jacket was specially fabricated in glass for the experiment. The chamber tube held the test fluid during the experiment, and the water jacket circulated the constant-temperature water through it. A thermal insulation was provided outside the water jacket to precisely keep the constant temperature during the experiment. The constant-temperature water from the circulating bath entered at the bottom of the water jacket by a pump and returned through an overflow pipe. The circulating bath and the water jacket were connected with highquality silicone tubes. The chamber assembly was firmly held on a vibration-free ring stand. The viscosity of distilled water was measured first to calibrate the viscometer. The experiment was repeated 5 times for each temperature to calculate the average of the experimental data. The deviations from the mean value were ±1.5 %. Then, the measurement of viscosity of the prepared graphene–water nanofluids with volume concentrations of 0.05, 0.1 and 0.15 % was conducted at different constant temperatures between 10 and 90 °C. The nanofluids were freshly prepared for the repetition of experiments at elevated temperatures, as the evaporation rates are higher at those temperatures. A constant shear rate was maintained during the experiment; it was achieved by maintaining a constant rotational speed of the spindle and

Measurement of viscosity The Brookfield digital viscometer (DV-E, Brookfield, USA) was used for measuring the viscosity at a given shear rate. The viscometer is based on the principle of rotational viscometry. It is the measurement of torque required to turn a spindle in a fluid whose viscosity is to be measured. Torque is applied through a calibrated spring to a disk or cylindrical spindle immersed in test fluid, and the spring deflection measures the viscous drag of the fluid against the spindle. A rotary transducer is used to measure the spring deflection; thus, the torque induced in the spindle. The amount of viscous drag is proportional to the amount of torque required to rotate the spindle and, thus, to the

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The surface tension is the inward pull experienced by molecules at the interface. The liquid molecules are attracted by other molecules from all sides in a bulk liquid. The liquid surface lacks a balanced distribution of molecules, unlike in the bulk liquid. Due to the unbalanced attraction by the liquid molecules, a surface film is formed at the liquid surface. Therefore, the surface tension is the value of the force required to break the surface film of a particular length. The SITA dynotester (SITA Process Solutions, Germany) was used for the measurement of dynamic surface tension. It is based on the maximum bubble pressure principle. The measuring range and resolution of the dynotester are 15–100 and 0.1 mN m-1, respectively. The dynotester was calibrated first by measuring the surface tension of distilled water. The experiment was repeated 5 times for each temperature to calculate the average of the experimental data. The deviations from the mean value are ±1.2 %. Then, the measurement of the surface tension of freshly prepared graphene–water nanofluids of the same volume concentrations of 0.05, 0.1 and 0.15 % was conducted at different constant temperatures ranging from 10 to 90 °C. The nanofluids were freshly prepared for the repetition of experiments at elevated temperatures, as the evaporation rate was higher at those temperatures. The chamber assembly, which includes the constant-temperature, watercirculating bath and water-circulating jacket, was used for measuring the surface tension at different temperatures.

1.35

Viscosity (theoretical)/mPa.s

Measurement of surface tension

1.50 + 4%

1.20 – 4%

1.05 0.90 0.75 0.60 0.45 0.30 0.15 0.00

0

0.15 0.3 0.45 0.6 0.75 0.9 1.05 1.2 1.35 1.5

Viscosity (experimental)/mPa.s

Fig. 3 Viscosity results between experimental and theoretical ones for water

80

Surface tension (theoretical)/mNm–1

by keeping a constant distance between the container wall and the spindle surface. The rotational speed of the spindle was changed to compensate for the change in shear rates at higher temperatures.

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76

–2%

74 72 70 68 66 64 62 60

60

62

64

66

68

Surface tension

70

72

74

76

78

80

(experimental)/mNm–1

Fig. 4 Surface tension results between experimental and theoretical ones for water

Result and discussion Viscosity and surface tension of graphene–water nanofluid Initially, the dynamic viscosity and surface tension of the base fluid (deionized water) were measured for the chosen temperature range (10–90 °C). The results of both viscosity and surface tension with respect to temperature are compared with the theoretical data taken from Incropera [42] and shown in Figs. 3 and 4. It is clearly observed from Figs. 3 and 4 that both viscosity and surface tension agree well with the theoretical data with an average deviation of ±4 and ±2 %, respectively. Figure 5 shows variation in viscosity with temperature for various volume concentrations. It is observed from Fig. 5 that the viscosity increases with an increase in the volume

concentration of graphene and decreases with an increase in the temperature. The values of viscosity of the nanofluid at 10 and 90 °C are 2.16 and 0.49 mN s m-2, respectively, for 0.15 % volume concentration, which are higher by 41.2 and 47.15 % when compared with that of the deionized water. This shows that the loading of nanosheets increases the friction and the flowing resistance of fluids, which ultimately results in an increase in viscosity. Figure 6 shows variation in surface tension with temperature for various volume concentrations. It is clear from Fig. 6 that the surface tension decreases with an increase in both volume concentration and temperature. The values of the surface tension of the nanofluid at 10 and 90 °C are 65.07 and 52.27 mN m-1, respectively, for 0.15 % volume concentration, which are lower by 13.82 and 13.75 % when compared with that of the deionized water. As the

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0.15 vol.% 0.1 vol.% 0.05 vol.% Water

1.75

Viscosity ratio

Viscosity/mPa.s

2

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1

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100

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0.1 %

0.05 %

1.75

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1 0.75

0.75

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0.25

0

0

0.15 %

μ σ

0

20

40

60

80

Surface tension ratio

2.5

0 100

Temperature/°C

Temperature/°C

Fig. 5 Variation in viscosity with temperature for graphene–water nanofluids 80 Water 0.05 vol.% 0.1 vol.% 0.15 vol.%

Surface tension/mNm–1

75

70

65

60

55

50 0

20

40

60

80

100

Temperature/°C

Fig. 6 Variation in surface tension with temperature for graphene– water nanofluids

temperature increases, the inter-attractive forces of molecules weaken, resulting in a lower surface tension. Figure 7 shows the variations in viscosity ratio and surface tension ratio with temperature for graphene–water nanofluids. The enhancement of the viscosity ratio due to the addition of graphene for a particular volume concentration has been observed to be same for the entire range of temperatures studied. The mean enhancements of the viscosity ratios are 20.37, 33.75 and 47.12 % for 0.05, 0.1 and 0.15 % volume concentrations, respectively, at 50 °C. In contrast, the surface tension ratio of the nanofluids decreases with nanopowder loading. The mean decrements of surface tension ratios are 9.95, 13.89 and 18.7 % for 0.05, 0.1 and 0.15 % volume concentrations, respectively, at 50 °C. Figure 8 shows the effect of the wettability of nanoparticles on the surface tension of nanofluids. The

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Fig. 7 Variation in viscosity ratio and surface tension ratio with temperature for graphene–water nanofluids

surface tension of base fluid is shown in Fig. 8a. If the nanoparticles are hydrophobic in nature, they adsorb at the interface and gather on the free surface. Because of this, the repulsion force between the nanoparticles and water molecules increases, leading to an increase in the intermolecular spacing at the interface and reducing the attraction forces between the water molecules inside the bulk liquid and on the free surface region, and thus, reducing the surface tension, as shown in Fig. 8b. The wettability of nanoparticles is responsible for the variations in the surface tension. However, for the nanoparticles that are hydrophilic in nature, the majority of the nanoparticles remain in the bulk fluid, and only a few are transported to the interfacial region due to Brownian motion. Due to the presence of hydrophilic nanoparticles, the water–nanoparticle interaction becomes stronger than the water–water interaction. The attraction between the nanoparticles and water molecules reduces the intermolecular spacing, which increases the surface tension, as shown in Fig. 8c. Figure 9 shows variations in the percentage reduction in viscosity of graphene–water nanofluid for each 10 °C rise in temperature at a constant volume concentration of 0.1 %. It is clear from Fig. 9 that the viscosity decreases with an increase in temperature. The average percentage reduction in the viscosity for each 10 °C rise in temperature to found to be 16.75 %. When the temperature of the nanofluid is raised from 10 to 20 °C, the percentage reduction in viscosity is 28.06, and it is 10.36 when the temperature is raised from 80 to 90 °C. The percentage reduction in the viscosity of the graphene–water nanofluids is higher at lower temperatures than it is at higher temperatures. Figure 10 shows variations in the percentage reduction in the surface tension of the graphene–water nanofluids for each 10 °C rise in temperature. The percentage reduction


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Hydrophobic nanoparticles

Water molecules

(a)

Hydrophilic nanoparticles

(b)

(c)

Fig. 8 Effect of wettability of nanoparticles on surface tension of nanofluids a base fluid, b nanofluid with hydrophobic nanoparticles, c nanofluid with hydrophilic nanoparticles

0

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Reduction of surface tension/%

Reduction of viscosity/%

–5 –10 –10.36 –12.42

–15

–14.02 –16.35 –17.60

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–16.20

–18.98

–25 –30

ϕ = 0.1 %

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–3.32

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–28.06

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–3.02

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–4

Temperature/°C

Fig. 9 Variation in percentage reduction of viscosity of graphene– water nanofluids as a function of temperature

in surface tension for each 10° rise in temperature increases as the temperature increases. When the temperature of the nanofluid is increased from 10 to 20 °C, the percentage reduction in surface tension is 2.93, and it is 3.69 when the temperature is increased from 80 to 90 °C. The percentage reduction in surface tension of graphene–water nanofluids is lower at lower temperatures than it is at higher temperatures. It is relevant to check the benefit of using nanofluids as the heat transfer fluids in spite of the larger increase in viscosity as compared to thermal conductivity. It was already investigated by the present authors [4] that the thermal conductivity and viscosity values of Ag–water nanofluids at higher temperatures did not agree and showed a large deviation against well-known thermal conductivity and viscosity models. Hence, the effectiveness of nanofluids should be evaluated for using it as a heat transfer fluid in the real-time thermal systems. Prasher et al. [43] suggested a method of overall effectiveness to evaluate the cooling efficiency of nanofluids. It was found that if the ratio of viscosity increase to four times the thermal conductivity increase in nanofluids is less than one

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–3.43

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–3.56

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–3.69

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Temperature/°C

Fig. 10 Variation in percentage reduction of surface tension of graphene–water nanofluids as a function of temperature

Cl 4Ck

\1 , then it is advantageous to use nanofluids as the

heat transfer fluids. The thermal conductivity ratio and viscosity ratio of nanofluids can be represented by the Eqs. (1) and (2). knf ¼ 1 þ Ck u kf lnf ¼ 1 þ Cl u lf

ð1Þ ð2Þ

where Cl and Ck are viscosity and thermal conductivity enhancement coefficients, determined from experimental viscosity and thermal conductivity ratios, u is volume concentration. The average value of Cl in this study is 350, and the average value of Ck is 210, which is calculated from the experimental data reported by the same authors. C Therefore, the overall effectiveness 4Clk of graphene–water nanofluid is observed to be 0.42 for an average volume concentration of 0.1 %, suggesting that the graphene–water nanofluids are better heat transfer fluids for cooling applications.

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Figure 11 shows variation in overall effectiveness of graphene–water nanofluids as a function of temperature. From C Fig. 11, it is clear that the 4Clk value decreases with an increase in temperature for all volume concentrations. The effectiveness of graphene–water nanofluids increases as temperature increases. This is attributed to higher enhancement in thermal conductivity at higher temperatures. The overall effectiveness of graphene–water nanofluid is enhanced nearly by 49 % when the temperature is increased from 10 to 50 °C at 0.15 % volume concentration. The overall effectiveness of graphene– water nanofluids at all volume concentrations is almost equal at higher temperatures. The present experimental results of viscosity are validated with those predicted from Brinkman’s correlation [44] as given in Eq. (3) and Wang’s correlation [45] as given in Eq. (4). lnf ¼ lf ð1 uÞ2:5

ð3Þ

lnf ¼ lf ð1 þ 7:3u þ 123u2 Þ

ð4Þ

Figure 12 shows deviation between the predicted viscosity values (a) by Brinkman’s [44] correlation and (b) by Wang’s correlation. From Fig. 12, it is clearly observed that the Brinkman’s correlation and Wang’s correlation under-predict the viscosity results by a mean deviation of 33 and 32 %, respectively. It is clearly observed that the existing well-known correlations have been developed to predict viscosity and surface tension only at room temperatures, and when used under different temperature conditions, it gives inappropriate predictions. Hence, an attempt is made to develop a new correlation for viscosity and surface tension of graphene–water nanofluid based on the present experimental results. Thus, new correlations have been developed to predict viscosity and surface

1.00 0.05 vol.%

0.90

0.1 vol.% 0.15 vol.%

0.80

Cµ /4Ck

0.70 0.60 0.50 0.40 0.30 0.20

tension of graphene–water nanofluid in the following forms as given in Eqs. (5) and (6). 0:00049 lnf T1 ¼ 4:682 u0:1794 ð5Þ lf Tnf 0:163 0:0884 rnf T1 1 ¼ 0:493 ð6Þ u rf Tnf These correlations include effect of both temperatures and volume concentrations. The proposed correlation predicts the viscosity values with a mean deviation of ±2 %. Similarly, Fig. 13 shows the comparisons between the predicted surface tension results obtained from the present correlation (Eq. 6) and with those obtained from the experiment. The proposed correlation predicts the surface tension well with an average deviation of ±2.5 %. It is suggested that these correlations are only formed through use of the data on graphene–water nanofluids. The limitations of these equations are as follows: (1) temperature range between 10 and 90 °C and (2) particle volume concentration range between 0.05 and 0.15 percentage volume concentrations. Density and specific heat of graphene–water nanofluid The density of graphene–water nanofluid is obtained using the Eq. (7) given by Buongiorno [46]. Figure 14 presents variation in density of graphene–water nanofluid as a function of temperature ranging from 10 to 90 °C. The reference value of density for the base fluid (water) is obtained from Incropera [42] for the temperatures ranging from 10 to 90 °C. It is clearly seen from Fig. 14 that the density of water and graphene–water nanofluids decreases with increase in the temperature for a given volume concentration. The density of water decreases from 999.7 to 965.3 kg m-3 when the temperature increases from 10 to 90 °C. The density of 0.15 vol% graphene–water nanofluid decreases from 1001.5 to 967.15 kg m-3 when the temperature increases from 10 to 90 °C. It is also observed that as the volume concentration increases, the density of graphene–water nanofluids increases by 0.06 % for every addition of 0.05 vol% of graphene. The density of graphene–water nanofluid increases from 996.6 to 997.81 kg m-3 when the volume concentration increases from 0.05 to 0.15 % at a temperature of 30 °C. qnf ¼ uqP þ ð1 uÞqf

0.10

Cpnf ¼

0.00 0

10

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30

40

50

60

Temperature/°C Fig. 11 Variation in overall effectiveness of graphene–water nanofluids as a function of temperature

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uCpP qP þ ð1 uÞCpf qf uqP þ ð1 uÞqf

ð7Þ ð8Þ

The specific heat of graphene–water nanofluids is obtained using the Eq. (8) from the Buongiorno [46]. Figure 15 shows variation in specific heat of graphene–


(a)

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σ nf/σ f (predicted)

Viscosity (predicted)/mPa.s

Brinkman [44]

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0.8 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98

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Fig. 13 Mean deviation of surface tension between the predicted and experimental ones

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1.5

2

2.5


0.1 vol.% 0.15 vol.%

990 985 980 975 970

2.5

965 0

Present Viscosity (predicted)/mPa.s

0.05 vol.%

995

Density/kgm–3

Viscosity (predicted)/mPa.s

Wang et al. [45]

(c)

1

σ nf/σ f (experimental)

10

20

30

40

50

60

70

80

90

100

Temperature/°C

2

Fig. 14 Variation in density with temperature for graphene–water nanofluid

+2% 1.5

–2% 1

0.5

0 0

0.5

1

1.5

2

2.5


Fig. 12 a Mean deviation between predicted and experimental viscosity by Brinkman’s correlation. b Mean deviation between predicted and experimental viscosity by Wang’s correlation. c Mean deviation of viscosity between the predicted and experimental ones

water nanofluid as a function of temperature ranging from 10 to 90 °C. It is observed that the specific heat of graphene–water nanofluid decreases with increase in temperature up to 30 °C and inversely, the same increases with

increase in temperature above 30 °C and up to 90 °C. However, the specific heat of graphene–water nanofluid decreases with increase in volume concentration of graphene for entire range of temperature studied. The specific heat of water decreases from 4194 J kg-1 K-1 at 10 °C to 4178 J kg-1 K-1 at 30 °C and then increases to 4206 J kg-1 K-1 at 90 °C. The specific heat of graphene–water nanofluid decreases from 4182.79 J kg-1 K-1 at 10 °C to 4166.8 J kg-1 K-1 at 30 °C and then increases to 4194.34 J kg-1 K-1 at 90 °C at volume concentration of 0.15 %. Figure 16 shows variation in specific heat ratio as a function of temperature. It is observed that specific heat ratio of graphene–water nanofluid decreases with increase in volume concentration. The reduction in specific heat ratio of graphene–water nanofluid is 0.091, 0.181 and 0.271 % for 0.05, 0.1 and 0.15 vol% at an average temperature of 50 °C, respectively.

123

1408

N. Ahammed et al. 4210

0.05 vol.%

4200

Specific heat/Jkg–1 K–1

in the surface tension for each 10 °C increment in temperature has been found as 3.29 %. The average decrement in the surface tension for 0.05 % increment in the volume concentration has been found as 14.18 %. This clearly shows that surface tension has a stronger dependency on the volume concentration than the temperature.

Water

4205

0.1 vol.%

4195

0.15 vol.%

4190 4185 4180 4175 4170 4165 4160

0

10

20

30

40

50

60

70

80

90 100

Temperature/°C Fig. 15 Variation in specific heat with temperature for graphene– water nanofluid

1.005 Water 0.05 vol.% 0.1 vol.%

Cpnf /Cpf

0.15 vol.%

1.000

0.995

0

20

40

60

80

100

Temperature/°C

Fig. 16 Variation in specific heat ratio with temperature for graphene–water nanofluid

Conclusions The effect of temperature and volume concentrations of nanosheets on viscosity and surface tension of graphene water nanofluid has been experimentally studied. The viscosity and surface tension of graphene–water nanofluid show an inverse dependency on temperature. The viscosity shows an average increment of 47.12 %, while the surface tension shows an average decrement of 18.7 % for the measured range of the temperature when the volume concentration is kept at 0.15 %. The average decrement in viscosity for each 10 °C increment in temperature has been found as 16.75 %. The average increment in viscosity for 0.05 % increment in the volume concentration has been found as 33.75 %. This clearly shows that the viscosity has a stronger dependency on the volume concentration of the nanoparticles than the temperature. The average decrement

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Acknowledgements The authors gratefully acknowledge the financial support provided by the funding agency, the Department of Science and Technology (DST), Science and Engineering Research Board (SERB), (SB/FTP/ETA-362/2012), New Delhi, India. The third author would like to thank the National Science and Technology Development Agency for the support, the ‘‘Research Chair Grant’’ National Science and Technology Development Agency (NSTDA), the Thailand Research Fund (IRG5780005) and the National Research University Project (NRU) for the support.

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