Experimental Investigation and Molecular Dynamics Simulations of

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Experimental Investigation and Molecular Dynamics Simulations of Viscosity of CNT-Water Nanofluid at Different Temperatures and Volume Fractions of Nanoparticles Fatemeh Jabbari,† Seyfolah Saedodin,*,† and Ali Rajabpour*,‡,§ †

Faculty of Mechanical Engineering, Semnan University, Semnan, Iran Mechanical Engineering Department, Imam Khomeini International University, Qazvin, Iran § School of Nano-Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran Downloaded via TULANE UNIV on December 15, 2018 at 04:52:38 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

ABSTRACT: The viscosity of nanofluids, and consequently their energy dissipation, is a challenging factor in real applications because it affects the pressure drop and pumping power of equipment in industries. The aim of this experimental and simulation study is to measure and calculate the viscosity of a carbon nanotube (CNT)− water nanofluid by employing a rotational viscometer and by molecular dynamics (MD) simulation. The effects of temperature, solid concentration, and CNT diameter on the dynamic viscosity were examined within the temperature and volume concentration ranges of 25−65 °C and 0.125%−1%, respectively. Interestingly, the maximum observed increase in the relative viscosity of CNT−water nanofluid occurred at 65 °C, whereas the absolute viscosity of the nanofluid was minimum at this temperature. It was further found that the dynamic viscosity increases with increasing volume fraction of nanoparticles and with decreasing nanofluid temperature, whereas changing the diameter of the CNT does not have a significant effect on nanofluid viscosity. Furthermore, a correlation function was proposed in terms of solid concentration and nanofluid temperatures based on the MD simulation results, and its accuracy was investigated by analyzing the margin of deviation. The findings of this study are useful for industrial applications of CNT/water nanofluids. gated.27−31 Ponmozhi et al.32 studied the thermophysical properties of CNT−water nanofluids. They showed that the shear viscosity of nanofluids increases with decreasing temperature and increasing CNT concentration, even at very small nanoparticle contents, particularly at 328.15 K. Halelfadl et al.33 also confirmed the results of a previous review for a multiwalled CNT (MWCNT)−water nanofluid system. They performed examinations in the temperature range of 0 °C− 40 °C and volume fraction range of 0.0055% to 0.55% and suggested that by increasing the shear rate, the shear viscosity decreases and the nanofluid behavior resembles that of a shear-thinning fluid. Xing et al.34 experimentally calculated the thermophysical properties of a water-based single-walled CNT (SWCNT) at different temperatures ranging from 10 to 60 °C and mass fractions in the range of 0.1−1 wt %. Their results showed that the highest viscosity increment was 35.9%. They further showed that for a given concentration, the viscosity ratio is not temperaturedependent, but nearly fixed at different temperatures. Said35 also measured the thermophysical properties (density, thermal conductivity, viscosity, and specific heat) of an SWCNT−

1. INTRODUCTION In the mid 1990s, Choi1 was the first one who introduced the idea of producing a new category of fluids called nanofluids to improve the heat-transfer properties of conventional fluids such as water, ethylene glycol, and engine oil by adding a small volume fraction (within the range of 1%−10%) of solid particles that are usually less than 100 nm in size.2 In general, the nanoparticles used in nanofluids are made of metals, oxides, carbides, or carbon nanotubes (CNTs).3−5 Compared with conventional fluids, nanofluids have better potential for heat transfer applications owing to their higher thermal conductivity, better convective heat transfer, and lower pressure drop.6−11 Accordingly, the emergence of nanofluids has created new challenges in refrigeration techniques and thermal handling of high heat flux equipment.12−16 Previous research works have shown that nanofluids have higher thermal conductivities and shear viscosities than the corresponding base fluids.17−21 Hence, researchers have been trying to predict the thermophysical properties (e.g., thermal conductivity and shear viscosity) of nanofluids through different theoretical and empirical methods.22−26 In previous studies, the effects of different parameters such as volume fraction, size and shape of nanoparticles, and nanofluid temperature on the thermophysical properties of nanofluids have been investi© XXXX American Chemical Society

Received: September 1, 2018 Accepted: December 4, 2018

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DOI: 10.1021/acs.jced.8b00783 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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findings about the effect of temperature on viscosity,50,51 the viscosity decreases at higher nanofluid temperatures, where the constraint between nanoparticles and base fluid can be weakened more conveniently.43 Despite numerous studies on nanofluids, few studies have been performed to compare experimental measurements and simulation results in calculating the thermophysical properties of nanofluids. The present research is an attempt to calculate the dynamic viscosity of SWCNT/water nanofluids using MD simulation and experimental methods, and to compare the corresponding results. Effects of nanofluid temperature, volume fraction, and diameter on the dynamic viscosity of a nanofluid will be examined using both experimental and MD simulation methods. Ultimately, a correlation function will be proposed for the viscosity of SWCNT/water in terms of volume fraction of nanoparticles and nanofluid temperatures, that is, from 0.125% to 1% (0.125%, 0.25%, 0.5%, 0.734%, and 1%) and from 25 to 65 °C (25, 35, 45, 55, and 65 °C), respectively.

water nanofluid. While the results of his review confirmed the results of previous researchers on the effect of nanofluid temperature and volume fraction of nanoparticles on the dynamic viscosity, he found that the dynamic viscosity decreases significantly with increasing shear rate, resulting in a shearthinning behavior at different volume fractions of nanoparticles. Sabiha et al.36 experimentally studied the viscosity of waterbased SWCNT nanofluids with sodium dodecyl sulfate as a surfactant. Their results showed that the measured values of shear viscosity were in the range of 0.67−1.28 mPa·s when the system temperature ranged from 20 to 60 °C and the volume concentration varied from 0.05% to 0.25%. They stated that an increase in the volume fraction of nanoparticles increases the internal viscous shear stress, thereby further increasing the nanofluid viscosity. For instance, at 20 °C, the measured values of SWCNT−water nanofluid viscosity were 1.18, 1.21, 1.23, 1.26, and 1.28 mPa·s at volume fractions of 0.05%, 0.1%, 0.15%, 0.2%, and 0.25%, respectively. Moreover, intermolecular forces among the particles and the fluid itself decrease with increasing temperature, ultimately leading to a reduction in the nanofluid viscosity. In another study, Dalkilic et al.37 investigated the dynamic viscosity of water−CNT and antifreeze−CNT nanofluid systems experimentally, and considered the effect of nanoparticle volume concentration and temperature on the systems. They conducted experiments at temperature and nanoparticle volume concentration ranges of 15 °C−50 °C and 0−2%, respectively, in both pure water and antifreeze. They showed that the dynamic viscosity decreases with increasing temperature and decreasing nanoparticle volume concentration. Although determining the thermophysical properties of nanofluids experimentally offers noteworthy results, using other methods such as computer simulations along with experimental methods have been very efficient in increasing our understanding of nanofluids.38−42 Molecular dynamics (MD) is a computer simulation method in which Newton’s equations of motion are solved for a system of interacting particles to determine trajectories of atoms and molecules, and interparticle forces and their potential energies are computed by applying interatomic potentials or molecular mechanics force fields. Hence, many researchers utilized MD simulation to study the rheological properties of nanofluids.43−45 Lu and Fan46 investigated the effects of volume fraction and size of Al2O3 nanoparticles on the dynamic viscosity of water- and ethyleneglycol-based nanofluids. Their results showed that the dynamic viscosity of nanofluids was higher than that of the corresponding base fluid. Their results were later confirmed by other researchers who examined different nanofluids such as gold− water,47 liquid argon with aluminum and lithium nanoparticles,48,49 and Al2O3−water.50 The latter system was studied by Lou and Yang24 who stated that the effect of nanoparticle volume fraction is more significant at lower temperatures. Results of the study by Lu and Fan46 also showed that by increasing the nanoparticle size, the nanofluid shear viscosity decreases in the same manner as the thermal conductivity. The same results were also obtained in subsequent studies on the effect of nanoparticle size on the dynamic viscosity of nanofluids.28,46,48,49 This trend was found to be the result of an increased particle−fluid interaction energy (Eint) as more molecules of the base fluids surrounded the nanoparticles owing to the smaller size of nanoparticles at a given volume fraction of nanoparticles. Therefore, for nanofluids with higher Eint values, the friction between the base fluid and nanoparticles is higher, leading to an increase in shear viscosity.43 Based on previous

2. EXPERIMENTAL METHOD Generally, there are two techniques for preparing a nanofluid:52 Single-step method, where chemical methods53,54 are used to synthesize the nanoparticles in the base fluid. Two-step method, where nanoparticle powders are first produced using chemical or physical methods and then suspended in the base fluid.55,56 The single-step and two-step methods have been used well for metallic and oxide nanoparticles, respectively.57 In this work, to prepare SWCNT−water nanofluid systems at five different nanoparticle volume fractions (0.125%, 0.25%, 0.5%, 0.734%, and 1%), the two-step method was used with deionized water as base fluid and SWCNT nanoparticles with the chemical and physical properties as presented in Table 1. The particles were procured from the Research Institute of Petroleum Industry (Tehran, Iran). Table 1. Chemical and Physical Properties of SWCNT parameters

value

surface area (m2/g) pore diameter (Å) length (Å) purity (%)

700 10−30 50−100 95−99

Finally, in order to provide stable SWCNT−water nanofluids and break the agglomeration by physical processes, magnetic stirring was applied for 30 min followed by ultrasonication (Hielscher Company, Germany) at a power of 400 W and frequency of 24 kHz for 50 min. The suspension was then resubjected to magnetic stirring, and the above steps were repeated 8 times. Furthermore, chemical processes and a gum Arabic surfactant were applied to provide nanofluids with better stability.58 After approximately 72 h, no sedimentation was observed with the naked eye in the samples. In the present study, the dynamic viscosity of SWCNT−water nanofluid was measured using a Brookfield viscometer (DV-I Prime Viscometer) with an accuracy of ±1.0% of range and repeatability of ±0.2%, coupled with a temperature-controlled bath. Figure 1 shows a view of the Brookfield viscometer and its spindles. The reported results are average values of more than three measurements at the same volume fraction of nanoparticles or temperature, to ensure repeatability. B



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Figure 1. A view of the Brookfield viscometer and its spindles.

3. MD SIMULATION DETAILS 3-1. Viscosity Calculation Method. In general, there are two methods for computing the dynamic viscosity through MD simulation: equilibrium molecular dynamics (EMD) and nonequilibrium molecular dynamics.59 Owing to the features and advantages of EMD,50 it was used in the present study to predict the dynamic viscosity of SWCNT−water nanofluid system. In this method, the dynamic viscosity is calculated using the Green−Kubo formula as follows:60−62 μ=

V kBT

∫0

Table 2. Length of SWCNTs and Number of Their Atoms at Different Volume Fractions of Nanoparticles volume fractions of nanoparticles (%)

length of SWCNT (Å)

number of SWCNT atoms

0.125 0.25 0.5 0.734 1

2.2 4.4 8.8 13 17.8

48 96 144 192 240

∞

⟨τxy(t )τxy(0)dt ⟩

istics of each modeled nanofluid system to study the effect of SWCNT diameter.

(1)

where μ, V, kB, T, and τxy are the shear viscosity, system volume, Boltzmann constant, temperature, and element of shear stress tensor, respectively. The shear stress tensor is computed from the following equation:63 ÄÅ ÉÑ Å ÑÑ Ñ 1 ÅÅÅÅ 1 τxy = ÅÅ∑ mjvj , xvj , y + ∑ rij , xfij , y ÑÑÑÑ ÑÑ V ÅÅÅ j 2 i≠j ÑÑÖ (2) ÅÇ

Table 3. Characteristics of Each Modeled Nanofluid System with Constant Volume Fraction (0.734%) and Length (25 Å) of SWCNT Nanoparticle

where mj is the mass of atom j, rij is the distance between atom i and atom j (ri,j = rj − ri,), and f ij is the force acting on a particle (molecule or atom) by a neighboring particle, which is governed by the interaction potential function. 3-2. Simulation Systems. In the present work, water was used as the base fluid in the simulation box with a simple cubic cell 50 Å in length, which contains 12 240 atoms, with an SWCNT at its center. The SWCNT used in this study was of zigzag geometry with a chiral vector (12, 0) and diameter of 9.5 Å. In order to investigate the effect of nanoparticle concentration, the length of the SWCNT was changed while keeping its diameter and the water simulation box dimensions constant. The length of the SWCNTs and the number of their atoms at different volume fractions of nanoparticles are listed in Table 2. Furthermore, in order to examine the effect of SWCNT diameter on the dynamic viscosity of the nanofluid, the systems examined were further modeled with different diameters while keeping the volume fraction (0.734%) and length (25 Å) of SWCNT nanoparticles constant. Table 3 provides the character-

type of SWCNT

diameter of SWCNT (Å)

dimensions of water simulation box (Å)

number of carbon atoms

number of water molecules

(14,0) (16,0) (18,0) (20,0)

11.1 12.7 14.3 16

68.9 75.3 81.5 87.4

336 384 432 480

31200 40845 51795 64008

The initial configuration of the system in two different views at a volume fraction of 1% is illustrated in Figure 2. All MD simulations in this study were carried out using the large-scale atomic/molecular massively parallel simulator. The initial configuration of the nanofluid system with periodic boundary conditions in a 3D-computing domain was relaxed in a constant energy ensemble (NVE) by applying the Langevin thermostat over 100 ps; then, the system was operated in isothermal−isobaric ensemble (NPT) for 100 ps using the Nose−Hoover thermostat and barostat.64,65 Finally, a canonical ensemble (NVT) was used with the Nose−Hoover thermostat for 100 ps. After system equilibrium at a fixed temperature and atmospheric pressure, the MD simulation was run with a time increment of 1 fs for 4 000 000 time steps (4 ns). In general, four independent simulations have been performed to obtain each MD result and error estimation. C



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Figure 2. Nanofluid molecular dynamic model with periodic boundary conditions in a 3D-computing domain: SWCNT nanoparticle with diameter and length of 9.51 and 17.8 Å, respectively, and surrounding water in the simulation box with dimensions of 50 Å (volume fraction of 1%) in two different views.

Liquid water is composed of water molecules that are supposed to interact according to the TIP4P/2005 model. Furthermore, interactions among carbon atoms in SWCNT are supposed to follow the Tersoff potential with the SWCNT− water interactions being supposedly modeled by the Lennard− Jones potential. While the cutoff distance for the Lennard-Jones potential is 9 Å and the used LJ parameters in this simulation are listed in Table 4: Table 4. Used LJ Parameters in This Simulation O−O H−H C−C

ε (kcal/mol)

σ (Å)

0.1852 0 0.07

3.1589 0 3.550053

Furthermore, the Lorentz−Berthelot law is employed to modeling other reactions include carbon−water reaction as follows: εxy = σxy =

εxxεyy

Figure 3. Comparison between MD simulation results, experimental data,35,66 and ref 67.

(3)

σxx + σyy

function (SACF) curve, because the nanofluid viscosity is computed by integrating the relevant SACF. Figures 4a and 3b show the convergence of the shear SACF over time for the simulation systems of base fluid and nanofluid, respectively. For generating the convergent data, SACF must decay to zero within the integral time length. It could be observed from Figure 4a that SACF decayed monotonically to zero without any oscillation in 3 ps for the base fluid, and it decayed to zero while oscillating in 6 ps for the nanofluids at T = 298.15 K, where the oscillatory behavior of the SACF increases with the volume fraction of nanoparticles (Figure 4b). Comparing the base fluid and nanofluid systems, it can be deduced that fluctuations of shear stresses in the nanofluid system were slowly damped, leading to an excellent integral of SACF and a high dynamic viscosity. The freedom of movement of water molecules causes the uniform behavior of SACF in Figure 4a, because the molecules of water have strong cohesion between different degrees of freedom including rotational and transitional.68

(4) 2 Before calculating the dynamic viscosity of the nanofluid, it was necessary to check the accuracy of the computational strategy including the simulation model, computer code, and the interatomic potential used. Therefore, in the present work, first, the results of the simulations performed were compared with experimental data35,66 for the water base fluid at different temperatures in the range of 25 °C−65 °C and atmospheric pressure. Figure 3 shows a comparison between the MD simulation results and experimental data on the dynamic viscosity of the water base fluid, demonstrating a good agreement between them. Therefore, the employed algorithm in this study validates our MD simulation and can be applied to other nanofluids. According to Equation 1, in order to calculate the dynamic viscosity of nanofluid using the Green−Kubo formula, first, one should check the area under the shear stress autocorrelation D



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Figure 4. Convergence of shear stress autocorrelation function (SACF) over time for the simulation systems of (a) base fluid and (b) nanofluid

Figure 5. Experimental results of (a) dynamic viscosity and (b) its increase for SWCNT−water nanofluid versus volume fraction of nanoparticles at different temperatures.

Figure 6. Experimental results of (a) dynamic viscosity and (b) its increase for SWCNT−water nanofluids versus temperature for different volume fractions of nanoparticles

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4. EXPERIMENTAL RESULTS

5. MD SIMULATION RESULTS

4-1. Effects of Nanoparticle Volume Fraction. Figure 5a,b show the dynamic viscosity of SWCNT−water nanofluid and its increase versus volume fraction of nanoparticles at different temperatures in the range of 25−65 °C, respectively. It can be observed that the dynamic viscosity of the nanofluid increases with increasing volume fraction of nanoparticles at different temperatures. This is because of the greater percentage of water molecules affected by the nanoparticles in this case, which increases the contribution of forces between nanoparticles and water. Finally, the increased forces between the nanoparticles and water prevent momentum transfer between the nanofluid layers, leading to an increased dynamic viscosity of the nanofluid. For instance, at 45 °C, the viscosities of SWCNT−water nanofluids were 1.06, 1.15, 1.62, 1.9, and 2.49 mPa·s at volume fractions of 0.125, 0.25, 0.5, 0.734, and 1%, respectively. It can also be understood that higher increase in dynamic viscosity are expected at higher volume fractions of nanoparticles (0.5%, 0.734%, and 1%), but those are insignificant at lower volume fractions (0.125% and 0.25%). Furthermore, the maximum increase observed in the viscosity of SWCNT−water nanofluid was approximately 436% of the viscosity of pure water at a solid volume concentration of 1% and temperature of 65 °C. 4-2. Effects of Nanofluid Temperature. Figure 6a,b illustrate the dynamic viscosity and its increase for SWCNT− water nanofluids versus temperature at different volume fractions of nanoparticles ranging from 0.125% to 1% (0.125%, 0.25%, 0.5%, 0.734%, and 1%), respectively. The results show that the dynamic viscosity decreases with increasing nanofluid temperature. Indeed, an increase in temperature attenuates intermolecular forces of the nanoparticles and base fluid while increasing intermolecular distances, thereby resulting in a lower effect of molecules on each other. In other words, at higher temperatures, the limitations between SWCNTs and water atoms are easily removed, leading to a lower viscosity. For example, at the volume fraction of 0.734%, the viscosities of SWCNT−water nanofluids were 3.3, 2.88, 1.9, 1.85, and 1.58 mPa·s at 25, 35, 45, 55, and 65 °C, respectively.

In the present study, in addition to the experimental method, an MD-based simulation method was further used to investigate the rheological behavior of SWCNT−water nanofluid for comparison to the experimental results. 5-1. Density. Figure 7 shows the values of density of SWCNT−water nanofluid (as calculated from simulations) versus volume fraction of nanoparticles at different temperatures ranging from 25 to 65 °C. It can be observed that the density of the nanofluid increases with increasing volume fraction of nanoparticles at different temperatures. For instance, at 45 °C, the densities of SWCNT−water nanofluids were calculated as 1014.71, 1017.65, 1019.95, 1022.74, and 1025.43 kg/m3 with nanoparticle concentrations of 0.125, 0.25, 0.5, 0.734, and 1%, respectively. Furthermore, it is indicated that the density of nanofluids increases with decreasing temperature at the same volume fraction of nanoparticles.

Figure 8. Density profile of water near SWCNT in the radial direction.

Previously, in the analysis of experimental results, it was stated that the higher total shear viscosities of nanofluids with respect to bulk water are due to the higher affinity of water toward the CNT outer surface with respect to bulk water, leading to more frictional effects. In order to confirm this claim, the distribution of the density of water around the SWCNT is investigated and shown in Figure 8. As observed, the density of the base fluid near the SWCNT nanoparticle is higher, and by getting away from the nanoparticle, the density decreases to the base fluid density. 5-2. Effects of Nanoparticle Volume Fraction. Figure 9a,b show the values of dynamic viscosity of SWCNT−water nanofluid and its increase (as calculated from simulations) versus volume fraction of nanoparticles at different temperatures ranging from 25 to 65 °C, respectively. It can be observed that the dynamic viscosity of the nanofluid increases with increasing volume fraction of nanoparticles at different temperatures. It also worth noting that the CNTs used in the experiments were of different diameter and length than those of the modeled CNTs in the MD simulation; this could lead to differences between the experimental data and simulation results. 5-3. Effects of Temperature. The obtained results on the effects of nanofluid temperature on the dynamic viscosity and its increase by MD simulation are illustrated in panels a and b, respectively, of Figure 10. It can be observed that the MD results exhibit similar trends of changes in viscosity with increasing

Figure 7. MD results for density of SWCNT−water nanofluid versus volume fraction of nanoparticles at different temperatures. F



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Figure 9. MD results of (a) dynamic viscosity and (b) its increase for SWCNT−water nanofluid versus volume fraction of nanoparticles at different temperatures.

Figure 10. MD results of (a) dynamic viscosity and (b) its increase for SWCNT−water nanofluids versus temperature for different volume fractions of nanoparticles.

Figure 11. MD results of (a) dynamic viscosity and (b) its increase by nanofluids as a function of particle size for different temperatures.

of studying many influencing parameters (e.g., CNT diameter) in a quick and cost-efficient manner. The dynamic viscosity of nanofluids and its increase with particle size at different temperatures are shown in Figure 11a,b, respectively. MD

temperature and solid concentration as those in the experiment and other studies.33,69−76 5-4. Effects of SWCNT Diameter. One of the advantages of the simulation methods over experimental ones is the possibility G



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Table 5. Percent Differences between MD Results and Measured Experimental Values ϕ (%) = 0

ϕ = 0.125%

viscosity (mPa·s)

ϕ (%) = 1%

viscosity (mPa·s)

viscosity (mPa·s)

T (°C)

exp.

MD

diff. (%)

T (°C)

exp.

MD

diff. (%)

T (°C)

exp.

MD

diff. (%)

25 35 45 55 65

0.89 0.71 0.59 0.49 0.41

0.87 0.73 0.60 0.48 0.41

2.24 2.81 3.05 2.04 1.46

25 35 45 55 65

1.18 1.12 1.06 0.96 0.82

0.98 0.81 0.61 0.50 0.42

16.94 27.68 42.45 47.08 48.78

25 35 45 55 65

3.57 3.2 2.49 2.42 2.2

2.19 1.85 1.78 1.56 1.47

38.40 42.18 28.51 35.53 33.18

Furthermore, the deviations between the simulation results and predicted values versus the volume fraction of nanoparticles at different temperatures are shown in Figure 13; these are calculated using the following equation: ÄÅ ÉÑ ij μnf yz ÅÅÅ ij μnf yz ÑÑÑ ÅÅ jj μ zz ÑÑ − jj μ zz ÅÅ k bf { k bf {correlation ÑÑÑÑ Å MDSimulation Å Dev (%) = ÅÅ ÑÑ × 100 ÅÅ ÑÑ jij μnf zyz ÅÅ ÑÑ jμ z ÅÅ ÑÑ ÅÅÇ ÑÑÖ k bf {MDSimulation (7)

simulations were performed at a solid concentration of 0.734% and different particle diameters ranging from 11.1 to 15.8 Å (11.1, 12.7, 14.3, and 15.9 Å). As can be observed, the values of dynamic viscosity and its increase almost constant in all CNT diameter at a given volume concentration at all nanofluid temperatures. In other words, changing the diameter of the CNT does not have a significant effect on nanofluid viscosity. For instance, at the volume fraction of 0.734% and temperature of 35 °C, the viscosities of SWCNT−water nanofluids were calculated as 1.178, 1.110, 1.119, and 1.089 mPa·s with nanoparticle diameters of 11.1, 12.7, 14.3, and 15.9 Å, respectively. Moreover, it can be observed that the maximum viscosity increase is 148.3%, which was obtained at a temperature of 65 °C and diameter of 11.1 Å.

As observed, the simulation results and those of the proposed model are in good agreement with one another. Furthermore, Figure 13 shows that the maximum value of deviation is less than 10%, which indicates adequate precision of the suggested correlation.

6. COMPARISON OF EXPERIMENT AND MD Although one could find a good agreement between the simulation results and experimental data by comparing the graphs presented in sections 4 and 5, Table 5 provides percent differences between the MD results and measured experimental values, according to Equation 5, for a better comparison: |MD results − experiment results| difference (%) = × 100 experiment results

8. CONCLUSIONS In the present study, the effects of nanofluid temperature, solid volume concentration, and nanoparticle diameter on the dynamic viscosity of SWCNT−water nanofluid were examined using both experimental and MD simulation methods. The temperatures and volume concentration used ranged from 25 °C−65 °C and 0.125%−1%, respectively. The following conclusions could be drawn from the experimental results: The values of dynamic viscosity and its growth increase with increasing volume fraction of nanoparticles at all temperatures. The values of dynamic viscosity decrease with increasing nanofluid temperature at all solid concentrations, and the amount of reduction increases at larger volume fractions of nanoparticles. Variations of nanofluid viscosity increase with temperature did not show any particular behavior; thus, it could be stipulated that the changes were not significant. Similar to the results obtained from the experimental method, the MD values of dynamic viscosity and its increase increase with increasing volume concentration at all temperatures. Moreover, based on the results obtained from the MD simulation, a correlation was proposed for estimating the viscosity in terms of the volume fraction of nanoparticles and nanofluid temperatures. Comparing the simulation results with those of the proposed correlation model and considering the resulting margin of error, the suggested correlation was found to be of acceptable accuracy. The values of dynamic viscosity decrease with increasing nanofluid temperature for all volume concentrations, while its increase decrease with increasing nanofluid temperature for volume concentration of 0.125% and 0.25% and increase for all volume concentrations more than 0.5%. The values of dynamic viscosity and its increase are almost constant for all CNT diameters at a given volume concentration at all nanofluid temperatures. In other words, changing the

(5)

7. PROPOSED CORRELATION Because this study investigated the influences of such parameters as solid concentration and temperature for a limited number of cases only, it was desired to develop a correlation to represent the behavior of nanofluid viscosity at different temperatures and volume fractions of nanoparticles. Therefore, a correlation was Table 6. Constant Values of Proposed Correlation (eq 6) a

b

c

d

e

f

1.186

−0.2624

181.5

−3.869 × 104

3.463 × 106

0.7447

proposed for the viscosity of SWCNT−water nanofluid in terms of volume fraction of nanoparticles and nanofluid temperature based on the simulation data, as follows: μnf μbf

iT y = a + (b + cφ + dφ 2 + eφ3)jjj zzz k 25 {

f

(6)

where a, b, c, d, e, and f are constant values, as presented in Table 6. In order to verify the accuracy of the proposed correlation for the nanofluid viscosity, the presented correlation predictions were compared to the MD simulation results in terms of increase of viscosity of SWCNT−water nanofluid, as shown in Figure 12. H



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Figure 12. Comparison between the presented correlation predictions (eq 4) and MD simulation results at (a) T = 25 °C, (b) T = 45 °C.

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(1) Choi, S. U. S., Eastman, J. A. Enhancing Thermal Conductivity of Fluids with NanoparticlesPhys. Fluids; Report No. ANL/MSD/CP84938; Argonne National Laboratory: Argonne, IL, 1995.73000 (2) Sergis, A.; Hardalupas, Y. Molecular Dynamic Simulations of a Simplified Nanofluid. Comput. Methods Sci. Technol. 2014, 20, 113− 127. (3) Seshadri, I.; Gardner, A.; Mehta, R. J.; Swartwout, R.; Keblinski, P.; Borca-Tasciuc, T.; Ramanath, G. Gating Heat Transport by Manipulating Convection in a Magnetic Nanofluid. Appl. Phys. Lett. 2013, 102, 203111. (4) Buongiorno, J.; Venerus, D. C.; Prabhat, N.; McKrell, T.; Townsend, J.; Christianson, R.; Tolmachev, Y. V.; Keblinski, P.; Hu, L. w.; Alvarado, J. L.; Bang, C.; Bishnoi, S. W.; Bonetti, M.; Botz, F.; Cecere, A.; Chang, Y.; Chen, G.; Chen, H. A Benchmark Study on the Thermal Conductivity of Nanofluids. J. Appl. Phys. 2009, 106, 094312. (5) Sadri, R.; Ahmadi, G.; Togun, H.; Dahari, M.; Kazi, S. N.; Sadeghinezhad, E.; Zubir, N. An Experimental Study on Thermal Conductivity and Viscosity of Nanofluids Containing Carbon Nanotubes. Nanoscale Res. Lett. 2014, 9, 151. (6) Hemmati-Sarapardeh, A.; Varamesh, A.; Husein, M. M.; Karan, K. On the Evaluation of the Viscosity of Nanofluid Systems: Modeling and Data Assessment. Renewable Sustainable Energy Rev. 2018, 81, 313− 329. (7) Bigdeli, M. B.; Fasano, M.; Cardellini, A.; Chiavazzo, E.; Asinari, P. A Review on the Heat and Mass Transfer Phenomena in Nanofluid Coolants with Special Focus on Automotive Applications. Renewable Sustainable Energy Rev. 2016, 60, 1615−1633. (8) Asadi, A. A Guideline Towards Easing the Decision-Making Process in Selecting an Effective Nanofluid as a Heat Transfer Fluid. Energy Convers. Manage. 2018, 175, 1−10. (9) Ding, Y.; Alias, H.; Wen, D.; Williams, R. A. Heat Transfer of Aqueous Suspensions of Carbon Nanotubes (Cnt Nanofluids). Int. J. Heat Mass Transfer 2006, 49, 240−250. (10) Phuoc, T. X.; Massoudi, M.; Chen, R. H. Viscosity and Thermal Conductivity of Nanofluids Containing Multi-Walled Carbon Nanotubes Stabilized By Chitosan. Int. J. Therm. Sci. 2011, 50, 12−18. (11) Zeng, Y.; Fan, L.; Xiao, Y. Q.; Yu, Z. T.; Cen, K. F. An Experimental Investigation of Melting of Nanoparticle-Enhanced Phase Change Materials (NePCMs) in a Bottom-Heated Vertical Cylindrical Cavity. Int. J. Heat Mass Transfer 2013, 66, 111−117. (12) Bahiraei, M.; Rahmani, R.; Yaghoobi, A.; Khodabandeh, E.; Mashayekhi, R.; Amani, M. Recent Research Contributions Concerning Use of Nanofluids in Heat Exchangers: A Critical Review. Appl. Therm. Eng. 2018, 133, 137−159. (13) Gao, Y.; Wang, H.; Sasmito, A. P.; Mujumdar, A. S. Measurement and Modeling of Thermal Conductivity of Graphene Nanoplatelet

Figure 13. Margin of deviation between simulation results and predicted values versus volume fraction of nanoparticles at different temperatures.

diameter of the CNT does not have a significant effect on nanofluid viscosity. Furthermore, the maximum observed increase in viscosity of SWCNT−water nanofluid occurred at a solid volume concentration of 1% and temperature of 65 °C.

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Fatemeh Jabbari: 0000-0002-6185-5622 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank Nanofluid Laboratory of Science and Technology Park of Semnan University for providing the necessary equipment for the experimental work and Imam Khomeini International University for providing the computational facilities. I



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Experimental Investigation and Molecular Dynamics Simulations of

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