Experimental investigation of thermal conductivity of nanofluids

(1)

Experimental investigation of thermal conductivity of nanofluids

containing of hybrid nanoparticles suspended in binary base fluids and propose a new correlation

Amir Kakavandi, Mohammad Akbari

^⇑

Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

a r t i c l e i n f o

Article history:

Received 28 December 2017

Received in revised form 18 March 2018 Accepted 28 March 2018

Keywords:

Hybrid nanofluid Stability

Thermal conductivity New correlation

a b s t r a c t

In this experimental study, preparation, stability and thermal conductivity of the MWCNTs-SiC/Water-EG hybrid nanofluid were investigated. Scanning electron microscopy (SEM) and X-ray diffraction (XRD) methods were used to characterize the nanoparticles. Nanofluid stability was monitored by DLS test.

According to the DLS results, the nanofluid contained nanoparticles. The thermal conductivity of the hybrid nanofluid was measured using the KD2-Pro thermal analyzer and the KS-1 sensor at a temperature range of 25–50°C and a solid volume fraction range of 0–0.75%. According to the results, the thermal conductivity of the nanofluid increased further at higher concentrations of the nanoparticles. Therefore, the effect of temperature on the thermal conductivity was higher at higher temperatures. The maximum thermal conductivity of the nanofluid increased up to 33% relative to the base fluid at a temperature of 50°C and a concentration of 0.75%. A correlation with high accuracy was obtained by fitting the experimental data. The correlation was used to calculate the thermal conductivity of the nanofluid. Given the desirable thermal properties of this nanofluid, it can be used as an alternative fluid in practical systems with high heat transfer potential in the field of heat transfer.

1. Introduction

Today, heat transfer science is one of the most important and most applied engineering sciences. Given the need for energy management, saving energy and achieving a higher efficiency are of great importance[1–3]. The fluid heat transfer is extensively used in various industries including cooling of power plant equipment, automobile industry, electronic equipment and heat exchangers.

Increased heat transfer rate by fluids increases thermal efficiency while improving the design and performance of thermal systems.

Conventional fluids in the industry have insignificant heat transfer capability. From an industrial perspective, there is a need for developing fluids with a higher thermal conductivity and higher heat transfer coefficients[4,5].

Nanofluids, as a new achievement, have a higher heat transfer potential than conventional heat transfer fluids. Nanofluids are prepared from the suspension of metallic and non-metallic nanoparticles of dimensions less than 100 nm in a base fluid such

as water, oil, ethylene glycol, etc.[6]. Due to the very small size of the particles, corrosion, impurities and pressure drop are reduced significantly. Furthermore, the stability of nanofluids is consider- ably improved against sedimentation[7,8]. By adding nanoparticles to the base fluid in a nanofluid, thermophysical properties will change relative to the base fluid. Since thermophysical properties are dependent on temperature and the concentration of nanoparticles in the base fluid, maximum desirable thermophysical properties can be achieved by changing these two factors. Gen- erally, nanofluids have a high thermal conductivity leading to a high heat transfer rate[9–11].

Thermal conductivity of nanofluids plays a very important role in heat transfer applications. The thermal conductivity of nanoparticles is much higher than that of liquids. Consequently, the addition of nanoparticles to liquids will increase their thermal conductivity.Table 1 shows a summary of previous studies on methods for improving the thermal conductivity of nanofluids.

It can be seen from the results inTable 1that the thermal conductivity increases significantly compared to the base fluid by adding a limited mass of nanoparticles. This nanofluid feature can greatly help its application in various industries.

⇑Corresponding author at: Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran.

E-mail address:[email protected](M. Akbari).

Contents lists available atScienceDirect

International Journal of Heat and Mass Transfer

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j h m t

(2)

Below, literature in this field is reviewed. Maxwell was one of the first researchers who analytically studied the thermal conductivity using a suspension of particles. He considered a very dilute suspension of spherical particles by ignoring interactions between the particles and the base fluid. The results of this study were presented in the form of following analytical relationship[19].

knf

kbf ¼knpþ2kbfþ2ðknpkbfÞ

u

knpþ2kbf ðknpkbfÞ

u

^ð1Þ

Other researchers such as Hamilton-Crosser [20]and Yu and Choi[21]studied the impact of various parameters such as particle shape, interfacial effects and thermal resistance on the effective thermal conductivity of mixtures.

Advances in the manufacture of nanoparticles in the last decade have led to new compounds of nanofluid called hybrid nanoparticles. Here, some studies in this area are reviewed.

Hemmat et al.[22]studied the effect of temperature rise (in the range of 30–50°C) as well as solid volume fraction (up to 1 vol%) of zinc oxide and multi-wall carbon nanotube hybrid nanoparticles in the water-ethylene glycol as base fluid. According to their results, the thermal conductivity increased by 28.1% at 1% concentration and 50°C of this hybrid nanofluid.

In an experimental study, the thermal conductivity of ZnO-Ag (50–50) hybrid nanofluid in the water base fluid was investigated at a temperature range of 25–50°C and a solid volume fraction of 0.125–2%. According to the results, the maximum thermal conductivity of the nanofluid was measured at a concentration of 2% at 50

°C[23]. Hemmat et al. experimentally studied the effects of temperature and solid volume fraction of hybrid nanofluids composed of SWCNT-MgO nanoparticles in the ethylene glycol base fluid at a temperature range of 30–50°C and solid volume fraction of 0.05–

2%. The results showed that the maximum thermal conductivity increased by 32% relative to the base fluid at 50°C and a solid volume fraction of 2%[24].

Hemmat et al. experimentally investigated the effects of temperature and solid volume fraction of hybrid nanofluids composed of SWCNT-ZnO nanoparticles dispersed in the water-ethylene glycol base fluid at a temperature range of 26–50°C and solid volume fraction of 0.05–1.25%. According to their results, the maximum thermal conductivity increased by 45% at 50°C and solid volume fraction of 1.25%. They also provided a correlation to calculate the thermal conductivity [25]. Harandi et al. [26] introduced F- MWCNTs-Fe3O4nanoparticles as a suitable compound for improving the thermal properties of ethylene glycol base fluid. According to their results, the thermal conductivity of the nanofluid increased by 30% relative to the base fluid at a volume fraction of 2.3%.

Munkhbayar et al.[27] used silver nanoparticles to improve the surface properties of carbon nanotubes. They studied effective

parameters such as concentration and temperature in the range of 0–3 vol% and 15–40°C, respectively. According to their results, the thermal conductivity increased by 14.5% relative to the base fluid. In an experimental study, Siam et al. investigated the effects of temperature rise and solid volume fraction in a hybrid nanofluid composed of iron oxide nanoparticles and multi-wall carbon nanotubes in water base fluid. They performed experiments at temperatures between 20 and 60°C and solid volume fraction up to 3%.

According to their results, the thermal conductivity increased by 31% at 60°C at a volume fraction of 3% [28]. They also studied the effect of hybrid nanofluid on convective heat transfer and friction coefficient. In another experimental study, Hemmat et al.

investigated the effects of temperature rise and concentration of copper and titanium oxide nanoparticles in a hybrid base fluid and a mixture of water and ethylene glycol at temperatures between 30 and 60°C and a solid volume fraction of 2%. The results showed that the thermal conductivity increases by 44% at a temperature of 60°C and a volume fraction of 2%[29]. Due to desirable properties of nanofluids, in addition to overcoming the problems with energy conversion and transmission, nanofluids can be an alternative fluid for development of thermal systems to reduce the size of heat exchangers, increase productivity, reduce fuel con- sumption, and save costs[30–33,35–41].

In this study, hybrid carbon nanotubes and silicon carbide nanoparticles are used to improve the heat transfer properties of the base fluid. Silicon carbide nanoparticles are easily dispersed in the water-ethylene glycol base fluid and have long-time stability. On the other hand, functionalized carbon nanotubes have unique thermal properties. The mixture of water-ethylene glycol (50–50) was used as the base fluid in this study. This study aims at improving the thermal properties of the water-ethylene glycol base fluid because of its widespread use in the industry. Experi- ments were carried out at a temperature range of 25–50°C and a solid volume fraction of 0.05–0.75%. Finally, the results of experiments were analyzed and compared in the form of graphs. A correlation was presented for the ratio of the thermal conductivity variation of the hybrid nanofluid to calculate the thermal conductivity of the nanofluid.

2. Experiments

2.1. Preparation methods of nanofluids

One of the challenges in the use of nanofluids is their successful preparation and stability because uniform and improved properties in nanofluids are dependent on nanofluid stability. A two- stage method was used in this study to prepare a stable nanofluid.

The base fluid was water-ethylene glycol with a volume ratio of Nomenclature

DLS dynamic light scattering EG ethylene glycol

kðW=mKÞ thermal conductivity MWCNT multi-wall carbon nanotubes SEM scanning electron microscope SiC silicon carbide

TðCÞ temperature

XRD X-ray crystallography Greek symbol

u

ð%Þ nanoparticle volume concentration

q

ðkg=m³Þ density Subscripts

bf base fluid Exp experimental nf nanofluid np nanoparticle pred predicted

(3)

50–50. Carbon nanotubes-silicon carbide hybrid nanoparticles were used with a volume ratio of 50–50. The characteristics of the base fluid and hybrid nanoparticles are presented inTables 2 and 3, respectively.

Nanoparticles used in this study were obtained from US Research Nanomaterials, Inc. SEM and XRD analyses were performed to ensure their surface and atomic structure. The results are shown inFigs. 1 and 2.

The tubular surface structure for carbon nanotubes and almost spherical SiC nanoparticles are observed inFig. 1. The diameter of the carbon nanotubes and the silicon carbide particles are also visible.

Fig. 2shows the XRD spectra of the nanoparticles. The X-ray diffraction test is a non-destructive method with several applications which provides comprehensive information on the chemical composition and crystalline structure of materials. The XRD results are in acceptable agreement with those provided by other researchers.

In this study, the water-ethylene glycol base fluid was used due to its widespread use in the industry. The mass of the nanoparticles, as well as the base fluid, is calculated by Eq. (2)using the properties of the materials in the above tables. The mass of nanoparticles was measured using the A & D digital scale (GF- 300) with an accuracy of 0.001 g (Fig. 3a). The mass of nanoparticles and base fluid at different concentrations is presented in Table 4.

u

¼

mq _MWCNTþ ^m_q

SiC mq _MWCNTþ ^m_q

SiCþ ^m_q

H₂Oþ ^m_q

EG

100 ð2Þ

where

u

is the percentage of solid volume fraction,

q

is the density andm is the mass. The MWCNT, SiC, H2O and EGsubscripts are related to multi-walled carbon nanotube, silicon carbide, water and ethylene glycol.

After measuring the mass of the base fluid and nanoparticles, the nanoparticles were added to the base fluid using the IKA magnetic stirrer (C-MAG HS7 Digital) (Fig. 3b) in 60 min. After prepar- ing this suspension, an ultrasonic probe device (Fig. 3c) (UP400St (400 W, 24 kHz), Germany, Hesher) was used for 45 min for break- ing agglomerates of nanoparticles to achieve long time stability.

2.2. Measurement of thermal conductivity of nanofluids

There are various methods for measuring the thermal conductivity of nanofluids[42]. One of the most used methods is transient hot wire method. In this research, the thermal conductivity of the nanofluid was measured by the KD2-Pro (made by Decagon Devices, Inc., USA) using the same method. The KS-1 sensor with a length of 60 mm and a diameter of 0.9 mm was used in measurements.

The WNB 7 water bath (made by MEMMERT, Germany) was used for temperature control to achieve uniform temperature dur- ing the test.

3. Results and discussion 3.1. Stability of nanofluids

Dynamic light scattering (DLS) is a physical method to determine the distribution of particles in nanofluids. This is a non- destructive and fast method to determine the size of particles in the range of several nanometers to microns. This method depends on the interaction of light with particles. The light scattered by the nanoparticles in the suspension is varied with time which can be related to the diameter of particles. In this study, the DLS- VASCOTM

c

series was used in DLS tests. Analyzing data from an incident laser beam with a wavelength of 657 nm to a solution containing nanoparticles, information about their size range will be obtained according to Mie theory[43].

The particle size distribution of nanoparticles is shown inFig. 4.

This chart indicates the size of particles in the water-ethylene glycol base fluid in terms of the intensity of the laser beam from the particle surface. In fact, based on the physical principles governing the laser beam, the larger particles scatter the laser beam of a higher intensity while smaller particles scatter the laser beam of a less intensity. As a result, the smaller particles in the suspension are sometimes not monitored by the sensors and their intensity may not be reported.

According to the results, the highest intensity was obtained for a particle size of 61 nm. The particle size range is also visible.

Table 1

Literature review on the improvement of thermal conductivity of nanoparticles compared to base fluid.

Ref. Nanoparticle Base fluid Temperature (°C) Concentration (%) Enhancement (%)

Esfahani et al.[10] GO Water 25–60 0.01–0.5 19.9

Wei et al.[11] TiO2 Oil 20–50 0.1–1 7.08

Esfe et al.[12] Al2O3 Ethylene glycol 24–50 0.2–5 40.5

Pang et al.[13] SiO2 Methanol 20 0.01–1 10.3

Esfe et al.[14] MgO Water/Ethylene glycol 20–50 0.1–2 34.5

Glory et al.[15] MWCNT Water 15–75 0.01–3 48

Esfe et al.[16] MWCNT Water 25–55 0.05–1 45

Shima et al.[17] CuO Ethylene glycol Ambient 0.18–1.14 14

Sundar at al.[18] Fe3O2 Water 20–60 0–2 48

Table 2

Thermophysical properties of the base fluid at T = 20°C.

Properties Water EG

Chemical formula H2O C2H6O2

Thermal conductivity (W/mK) 0.606 0.251

Melting point (°C) 0 13

Molar mass (g/mol) 18.01528 62.07

Density (g/m³) 0.998 1.11

pH 6–7 6–7.5

Boiling point (°C) 100 197.6

Vapor pressure (kPa) 3.1690 0.053

Table 3

Thermophysical properties of nanoparticles.

Properties MWCNTs SiC

Color Black Grayish white

Purity 97 99

Thermal conductivity (W/mK) 3000 120

Specific Heat (J/kgK) – 750

Density (g/m³) 2.1 3.216

Structure Tube Almost spherical

Dimensions (nm) 20–30 45–65

Specific surface area (m²/g) 110 40–80

(4)

3.2. Validation

To validate the thermal conductivity of the nanofluid, the results for pure water and water-ethylene glycol mixtures with a ratio of 50–50 were validated in a temperature range of 20–60°C

and presented inFig. 5. The results were validated by measuring the thermal conductivity of the base fluid and comparing the results with those in ASHRAE Handbook[34]. The experimentally measured thermal conductivity of the base fluid is in agreement with the original reference with a very slight difference.

Fig. 1.SEM images of the nanoparticles used in this study, A: MWCNT, B: SiC.

Fig. 2.The XRD spectra of the nanoparticles, A: MWCNT particles, B: SiC particles.

Fig. 3.Laboratory equipments used to prepare the nanofluid.

(5)

3.3. Thermal conductivity measurement

In this section, the thermal conductivity of the water-ethylene glycol/carbon nanotube-silicon carbide hybrid nanofluid is

presented in the range of 0.05–075 vol% at a temperature range of 25–50°C. The ratio of the thermal conductivity of the nanofluid to the base fluid is defined by Eq.(3).

Table 4

Mass of nanoparticles at different concentrations in 60 ml of hybrid nanofluids.

Concentration Mass [±0.001] (g)

Water EG MWCNT SiC

0 29.4 33.3 0 0

0.05 29.384 33.281 0.035 0.054

0.1 29.367 33.263 0.070 0.107

0.15 29.351 33.244 0.105 0.161

0.25 29.318 33.207 0.175 0.269

0.4 29.269 33.152 0.281 0.430

0.6 29.204 33.078 0.421 0.644

0.75 29.155 33.022 0.526 0.806

Fig. 4.The diameter of the distributed nanoparticles with respect to intensity.

Fig. 5.Validation of experimental results on thermal conductivity of pure water and a mixture of water-ethylene glycol (50–50) at different temperatures.

Fig. 6.The thermal conductivity of the hybrid nanofluid in terms of the solid volume fraction at different temperatures.

(6)

Thermal conducti

v

^{ity ratio}^{ð%Þ ¼}^k_k^nf

bf ð3Þ

Fig. 6shows the thermal conductivity of the nanofluid in terms of solid volume fraction of nanoparticles at 25–50°C. According to the results, the thermal conductivity is increased as the solid volume fraction of nanoparticles increases. The slope of thermal conductivity increases with increasing concentration. Since the thermal conductivity of the nanoparticles is much higher than base fluids, these positive changes in higher concentrations can be attributed to the thermal conductivity of nanoparticles. Another reason for improved thermal conductivity is mixing in the nanofluid due to an increase in the number of particles in the base fluid.

The changes in the thermal conductivity are also improved with temperature rise.

Fig. 7shows the changes in the ratio of the thermal conductivity of the nanofluid to the base fluid. Eq. (3) is used to cal-

culate the ratio of thermal conductivity variations. According to the results, the thermal conductivity ratio of the hybrid nanofluid is increased with increasing solid volume fraction of nanoparticles and reaches a maximum of 28.86%. These changes show an improvement in the thermal conductivity of the nanofluid in comparison with the base fluid by adding nanoparticles to the base fluid. On the other hand, by increasing the solid volume fraction, the number of suspended nanoparticles increases. In addition to improving heat transfer rate, this increases the nanofluid viscosity. Furthermore, the nanofluid stability is reduced at high concentrations leading to agglomer- ation of particles.

Fig. 8 shows the changes in the thermal conductivity of the nanofluid in terms of temperature at different solid volume fractions. According to the results, the thermal conductivity increases by increasing temperature. Improvement of the thermal conductivity of the nanofluid can be partly due to the intrinsic Fig. 7.The ratio of the thermal conductivity of the nanofluid to the base fluid in

terms of solid volume fraction at different temperatures.

Fig. 8.Thermal conductivity of the hybrid nanofluid in terms of temperature at different volume fractions.

Fig. 9.The ratio of thermal conductivity of the nanofluid to the base fluid at different temperatures.

Fig. 10.The margin of deviation of calculated results relative to the experimental results.

(7)

thermal conductivity of the material with increasing temperature.

As temperature rises, the molecular movements of the fluid between the base fluid atomic structure as well as the Brownian

motion of nanoparticles in the base fluid increased. These changes are always associated with energy transfer between the nanofluid layers.

Fig. 11.Comparison of experimental results with those predicted by the proposed correlation at different temperatures.

(8)

Fig. 9shows the ratio of the thermal conductivity of the nanofluid to the base fluid at different temperatures. As seen, the thermal conductivity ratio increases with temperature. Due to these changes, this nanofluid can be considered as a smart fluid because its heat transfer characteristics are improved with temperature.

Due to the low number of nanoparticles in the base fluid at low concentrations, the change in the number of collisions and energy transfer between the fluid layers is not significant with temperature rise. With increasing the solid volume fraction, the slope of heat transfer coefficient variation significantly increases with temperature. This can be attributed to the increase in the number of particles in the base fluid. As temperature increases, the molecular movements are rapidly activated and causing a significant increase (a maximum of 28.86%) in the heat transfer rate.

3.4. Thermal conductivity correlation

Since different parameters such as temperature, solid volume fraction, particle size, surface structure, atomic and chemical properties of nanoparticles and nanofluid production method lead to a complex structure in nanofluids, the experimental results are significantly different with those obtained from theoretical relations [44–48]. On the other hand, due to the lack of an accurate and proper relationship to predict the thermal conductivity of the carbon nanotubes-silicon carbide/water-ethylene glycol hybrid nanofluid, a correlation is presented by curve fitting method. This correlation is a function of the solid volume fraction and the nanofluid temperature.

The correlation is presented as Eq.(4):

knf

kbf

¼0:0017

u

^0:698^T¹^:³⁸⁶^þ^0:981 ^ð4Þ

where k is the thermal conductivity, T the nanofluid temperature in

°C anduis the solid volume fraction. Moreover, the subscripts nf and bf represent the nanofluid and base fluid, respectively.

To examine the accuracy of the proposed correlation, the maximum margin of deviation of the calculated results relative to experimental results is calculated by Eq.(5).

margin of deviationð%Þ ¼kExpk_Pred

kExp 100 ð5Þ

In the above equation, the subscripts Exp and Pred respectively represent the experimental and predicted values in the proposed correlation.

Fig. 10shows the maximum deviation between the calculated and experimental thermal conductivity ratios. As seen, most points are on the bisector or just with a short distance from the bisector.

This indicates the proper accuracy of the proposed correlation. The maximum margin of deviation for the thermal conductivity ratio is 1.58%, which is acceptable for an empirical correlation.

For a more accurate comparison of the experimental results with the results of the proposed model, comparative diagrams of the thermal conductivity coefficient are shown inFig. 11in terms of nanofluid concentration at different temperatures. According to the results, the correlation obtained by the curve fitting method appropriately predicts the behavior of the nanofluid. This correlation can be used to calculate the thermal conductivity of the nanofluid in this study.

3.5. Comparison of experimental results with experimental results of similar studies

As already mentioned, carbon nanotubes have better thermal properties than other materials and therefore the production cost of these nanoscale materials is high. In this study, a hybrid nanofluid was produced using carbon nanotubes and silicon carbide.

This nanofluid is much cheaper compared to nanofluid containing carbon nanotubes alone. Therefore, with regard to the research goals and the improvement of the thermal conductivity of nanofluids to the base fluid, the results of this study were compared with the results of other studies that used carbon nanotubes. The results of this comparison were performed at two temperatures of 25 and 50°C and was shown inFig. 12.

InFig. 12, the comparison of the results of the ratio of thermal conductivity variations with other investigations in different solid volume fractions was presented. The results showed that the upward trend of thermal conductivity improvement in this study is established and hence the improvement of the thermal conductivity ratio at 50°C is much higher than the temperature of 25°C. It can be concluded that the changes made by the combination of nanoparticles will be better for higher temperatures. By comparing the presented graphs, it is observed that the slope of changes in Fig. 12.Comparison of experimental data with experimental results of previous studies, a: 25°C, b: 50°C.

(9)

higher temperatures is increasing. Finally, it can be understood that the use of combined nanoparticles, in addition to reducing the cost of production than nanofluid containing carbon nanotubes, leads to improve the thermal conductivity of the nanofluid.

4. Conclusion

In this study, preparation, stability and thermal conductivity of the water-ethylene glycol/SiC-MWCNTs hybrid nanofluid was experimentally investigated at a temperature range of 25–50°C and a solid volume fraction of 0.05–0.75%. The results obtained from the research variables are presented below:

1. Given the preparation procedure and the use of mechanical mixing and ultrasonic processes, this nanofluid showed reason- able stability.

2. The results of dynamic light scattering (DLS) test indicate acceptable stability of nanofluids containing different solid volume fractions of nanoparticles at different temperatures.

3. The thermal conductivity of the nanofluid significantly increased with increasing the solid volume fraction of nanoparticles. It increased up to 28.86% atu= 0.75%.

4. The thermal conductivity increased with increasing temperature. The slope of these positive changes was higher at higher temperatures. As a result, the thermal efficiency of this nanofluid increased at higher temperatures.

5. An empirical correlation was obtained for the thermal conductivity coefficient by the curve fitting method. Given its acceptable accuracy, this correlation is suggested to be used to calculate the thermal conductivity of the water-ethylene glycol/carbon nanotube-silicon carbide hybrid nanofluid.

Conflict of interest

The authors declare that there is no conflict of interest.

References

[1]S.K. Das, S.U. Choi, W. Yu, T. Pradeep, Nanofluids: Science and Technology, John Wiley & Sons, 2007.

[2]K.Y. Leong, K.K. Ahmad, H.C. Ong, M.J. Ghazali, A. Baharum, Synthesis and thermal conductivity characteristic of hybrid nanofluids – a review, Renew.

Sustain. Energy Rev. 31 (75) (2017) 868–878.

[3]R. Ranjbarzadeh, A.M. Isfahani, M. Afrand, A. Karimipour, M. Hojaji, An experimental study on heat transfer and pressure drop of water/graphene oxide nanofluid in a copper tube under air cross-flow: applicable as a heat exchanger, Appl. Therm. Eng. 1 (125) (2017) 69–79.

[4]M.R. Shamsi, O.A. Akbari, A. Marzban, D. Toghraie, R. Mashayekhi, Increasing heat transfer of non-Newtonian nanofluid in rectangular microchannel with triangular ribs, Physica E. 93 (2017) 167–178.

[5]O.A. Akbari, H.H. Afrouzi, A. Marzban, D. Toghraie, H. Malekzade, A. Arabpour, Investigation of volume fraction of nanoparticles effect and aspect ratio of the twisted tape in the tube, J.Therm. Anal. Calorim. 129 (3) (2017) 1911–1922.

[6]S.U. Choi, J.A. Eastman, Enhancing Thermal Conductivity of Fluids with Nanoparticles, Argonne National Lab., IL, United States, 1995.

[7]S.K. Das, S.U. Choi, H.E. Patel, Heat transfer in nanofluids – a review, Heat Transf. Eng. 27 (10) (2006) 3–19.

[8]Q. Xue, W.M. Xu, A model of thermal conductivity of nanofluids with interfacial shells, Mater. Chem. Phys. 90 (2) (2005) 298–301.

[9]F. Pourfattah, M. Motamedian, G. Sheikhzadeh, D. Toghraie, O.A. Akbari, The numerical investigation of angle of attack of inclined rectangular rib on the turbulent heat transfer of Water-Al2O3nanofluid in a tube, Int. J. Mech. Sci. 131 (2017) 1106–1116.

[10]M.R. Esfahani, E.M. Languri, M.R. Nunna, Effect of particle size and viscosity on thermal conductivity enhancement of graphene oxide nanofluid, Int. Commun.

Heat Mass Transf. 31 (76) (2016) 308–315.

[11]B. Wei, C. Zou, X. Li, Experimental investigation on stability and thermal conductivity of diathermic oil based TiO2nanofluids, Int. J. Heat Mass Transf.

31 (104) (2017) 537–543.

[12]M.H. Esfe, A. Karimipour, W.M. Yan, M. Akbari, M.R. Safaei, M. Dahari, Experimental study on thermal conductivity of ethylene glycol based nanofluids containing Al2O3nanoparticles, Int. J. Heat Mass Transf. 30 (88) (2015) 728–734.

[13]C. Pang, J.Y. Jung, J.W. Lee, Y.T. Kang, Thermal conductivity measurement of methanol-based nanofluids with Al2O3and SiO2nanoparticles, Int. J. Heat Mass Transf. 55 (21) (2012) 5597–5602.

[14]M.H. Esfe, M. Afrand, A. Karimipour, W.M. Yan, N. Sina, An experimental study on thermal conductivity of MgO nanoparticles suspended in a binary mixture of water and ethylene glycol, Int. Commun. Heat Mass Transf. 31 (67) (2015) 173–175.

[15]J. Glory, M. Bonetti, M. Helezen, M. Mayne-L’Hermite, C. Reynaud, Thermal and electrical conductivities of water-based nanofluids prepared with long multiwalled carbon nanotubes, J. Appl. Phys. 103 (9) (2008) 094309.

[16]M.H. Esfe, A. Naderi, M. Akbari, M. Afrand, A. Karimipour, Evaluation of thermal conductivity of COOH-functionalized MWCNTs/water via temperature and solid volume fraction by using experimental data and ANN methods, J. Therm. Anal. Calorim. 121 (3) (2015) 1273–1278.

[17]P.D. Shima, J. Philip, B. Raj, Influence of aggregation on thermal conductivity in stable and unstable nanofluids, Appl. Phys. Lett. 97 (15) (2010) 153113.

[18]L.S. Sundar, M.K. Singh, A.C. Sousa, Investigation of thermal conductivity and viscosity of Fe3O4nanofluid for heat transfer applications, Int. Commun. Heat Mass Transf. 31 (44) (2013) 7–14.

[19] J.C. Maxwell, A treatise on electricity and magnetism. Clarendon Press, 1881.

[20]R.L. Hamilton, O.K. Crosser, Thermal conductivity of heterogeneous two- component systems, Indust. Eng. Chem. Fundam. 1 (3) (1962) 187–191.

[21]W. Yu, S.U. Choi, The role of interfacial layers in the enhanced thermal conductivity of nanofluids: a renovated Maxwell model, J. Nanopart. Res. 5 (1–

2) (2003 Apr 1) 167–171.

[22]M.H. Esfe, S. Esfandeh, S. Saedodin, H. Rostamian, Experimental evaluation, sensitivity analyzation and ANN modeling of thermal conductivity of ZnO- MWCNT/EG-water hybrid nanofluid for engineering applications, Appl. Therm.

Eng. (2017).

[23]N.N. Esfahani, D. Toghraie, M. Afrand, A new correlation for predicting the thermal conductivity of ZnO–Ag (50%–50%)/water hybrid nanofluid: An experimental study, Powder Technol. 1 (323) (2018) 367–373.

[24]M.H. Esfe, A. Alirezaie, M. Rejvani, An applicable study on the thermal conductivity of SWCNT-MgO hybrid nanofluid and price-performance analysis for energy management, Appl. Therm. Eng. 25 (111) (2017 Jan) 1202–1210.

[25]M.H. Esfe, A.A. Arani, M. Firouzi, Empirical study and model development of thermal conductivity improvement and assessment of cost and sensitivity of EG-water based SWCNT-ZnO (30%: 70%) hybrid nanofluid, J. Mol. Liq. 1 (244) (2017 Oct) 252–261.

[26]S.S. Harandi et al., An experimental study on thermal conductivity of F- MWCNTs–Fe3O4/EG hybrid nanofluid: effects of temperature and concentration, Int. Commun. Heat Mass Transf. 76 (2016) 171–177.

[27]B. Munkhbayar, M.R. Tanshen, J. Jeoun, H. Chung, H. Jeong, Surfactant-free dispersion of silver nanoparticles into MWCNT-aqueous nanofluids prepared by one-step technique and their thermal characteristics, Ceram. Int. 39 (6) (2013 Aug 31) 6415–6425.

[28]L.S. Sundar, M.K. Singh, A.C. Sousa, Enhanced heat transfer and friction factor of MWCNT–Fe3O4/water hybrid nanofluids, Int. Commun. Heat Mass Transf. 31 (52) (2014 Mar) 73–83.

[29]M.H. Esfe, S. Wongwises, A. Naderi, A. Asadi, M.R. Safaei, H. Rostamian, M.

Dahari, A. Karimipour, Thermal conductivity of Cu/TiO2–water/EG hybrid nanofluid: experimental data and modeling using artificial neural network and correlation, Int. Commun. Heat Mass Transf. 31 (66) (2015 Aug) 100–104.

[30]R. Ranjbarzadeh, A. Karimipour, M. Afrand, A.H. Isfahani, A. Shirneshan, Empirical analysis of heat transfer and friction factor of water/graphene oxide nanofluid flow in turbulent regime through an isothermal pipe, Appl. Therm.

Eng. 5 (126) (2017 Nov) 538–547.

[31]J. Philip, P.D. Shima, Thermal properties of nanofluids, Adv. Colloid Interface Sci. 15 (183) (2012 Nov) 30–45.

[32]M. Afrand, A. Karimiopour, A. Ahmadi Nadooshan, M. Akbari, The variations of heat transfer and slip velocity of FMWNT-water nano-fluid along the microchannel in the lack and presence of a magnetic field, Physica E: Low-dimens.

Syst. Nanostruct. 84 (2016) 474–481.

[33]Q. Gravndyan, O.A. Akbari, D. Toghraie, A. Marzban, R. Mashayekhi, R. Karimi, F. Pourfattah, The effect of aspect ratios of rib on the heat transfer and laminar water/TiO2nanofluid flow in a two-dimensional rectangular microchannel, J.

Mol. Liq. 236 (2017) 254–265.

[34] Handbook AF. American society of heating, refrigerating and air-conditioning engineers. Inc.: Atlanta, GA, USA, 2009.

[35]A. Ahmadi Nadooshan, M. Hemmat Esfe, M. Afrand, Evaluation of rheological behavior of 10W40 lubricant containing hybrid nano-material by measuring dynamic viscosity, Physica E: Low-dimens. Syst. Nanostruct. 92 (2017) 47–54.

[36]M. Hemmat Esfe, A. Ahmadi Nadooshan, A. Arshi, A. Alirezaie, Convective heat transfer and pressure drop of aqua based TiO2 nanofluids at different diameters of nanoparticles: data analysis and modeling with artificial neural network, Physica E: Low-dimens. Syst. Nanostruct. 97 (2018) 155–161.

[37]R. Yadollahi Farsania, A. Raisi, A. Ahmadi Nadooshan, S. Vanapalli, Does nanoparticles dispersed in a phase change material improve melting characteristics?, Int Commun. Heat Mass Transf. 89 (2017) 219–229.

[38] A. Ahmadi Nadooshan, M. Hemmat Esfe, M. Afrand, Prediction of rheological behavior of SiO2-MWCNTs/10W40 hybrid nanolubricant by designing neural network, J. Therm. Anal. Calorimetry, http://doi.org/10.1007/s10973-017- 6688-3.

[39]M. Afrand, Experimental study on thermal conductivity of ethylene glycol containing hybrid nano-additives and development of a new correlation, Appl.

Therm. Eng. 110 (2017) 1111–1119.

(10)

[40]M.A. Esfahani, D. Toghraie, Experimental investigation for developing a new model for the thermal conductivity of Silica/Water-Ethylene glycol (40%–60%) nanofluid at different temperatures and solid volume fractions, J. Mol. Liq. 232 (2017) 105–112.

[41]M. Hemmat Esfe, M. Afrand, S.H. Rostamian, D. Toghraie, Examination of rheological behavior of MWCNTs/ZnO-SAE40 hybrid nano-lubricants under various temperatures and solid volume fractions, Exp. Therm Fluid Sci. 80 (2017) 384–390.

[42]S.S. Murshed, C.N. de Castro (Eds.), Nanofluids: Synthesis, Properties, and Applications, Nova Science Publishers, 2014, Incorporated.

[43] R.G. Newton, Scattering theory of waves and particles, Springer Science &

Business Media, 2013.

[44]M. Zadkhast, D. Toghraie, A. Karimipour, Developing a new correlation to estimate the thermal conductivity of MWCNT-CuO/water hybrid nanofluid via an experimental investigation, J.Therm. Anal. Calorim. 129 (2) (2017) 859–867.

[45]R.A. Dehkordi, M.H. Esfe, M. Afrand, Effects of functionalized single walled carbon nanotubes on thermal performance of antifreeze: an experimental study on thermal conductivity, Appl. Therm. Eng. 25 (120) (2017 Jun) 358–

366.

[46]D. Wen, Y. Ding, Effective thermal conductivity of aqueous suspensions of carbon nanotubes (carbon nanotube nanofluids), J. Thermophys. Heat Transf.

18 (2004) 481–485.

[47]M. Soltanimehr, M. Afrand, Thermal conductivity enhancement of COOH- functionalized MWCNTs/ethylene glycol–water nanofluid for application in heating and cooling systems, Appl. Therm. Eng. 105 (2016) 716–723.

[48]A.D. Zadeh, D. Toghraie, Experimental investigation for developing a new model for the dynamic viscosity of silver/ethylene glycol nanofluid at different temperatures and solid volume fractions, J.Therm. Anal. Calorim. 131 (2) (2018) 1449–1461.