Effects of multi walled carbon nanotubes shape and size on thermal conductivity and viscosity of nanofluids

Accepted Manuscript Effects of multi walled carbon nanotubes shape and size on thermal conductivity and viscosity of nanofluids

A.N. Omrani, E. Esmaeilzadeh, M. Jafari, A. Behzadmehr PII: DOI: Reference:

S0925-9635(18)30621-6 https://doi.org/10.1016/j.diamond.2019.02.002 DIAMAT 7330

To appear in:

Diamond & Related Materials

Received date: Revised date: Accepted date:

5 September 2018 30 January 2019 1 February 2019

Please cite this article as: A.N. Omrani, E. Esmaeilzadeh, M. Jafari, et al., Effects of multi walled carbon nanotubes shape and size on thermal conductivity and viscosity of nanofluids, Diamond & Related Materials, https://doi.org/10.1016/j.diamond.2019.02.002

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ACCEPTED MANUSCRIPT Effects of multi walled carbon nanotubes shape and size on thermal conductivity and viscosity of nanofluids A.N. Omrani a, E. Esmaeilzadeh a,, M. Jafari a, A. Behzadmehr b a

Heat and Fluid Flow Research Laboratory, Department of Mechanical Engineering,

University of Tabriz, Tabriz, Iran b

Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran

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ABSTRACT In this study, effective thermal conductivity and viscosity of multi walled carbon nanotubes

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water based nanofluids containing multi walled carbon nanotubes with various geometrical characteristics were investigated, with volume fraction 0.05%vol. The experimental results

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demonstrated that thermophysical properties of the nanofluids depend on the geometrical characteristics of carbon nanotubes. The results were compared with some well-known models

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for thermal conductivity enhancement and relative viscosity and good conformities were observed. In this research, maximum enhancements of 36% and 5.5% were achieved for

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nanofluids effective thermal conductivity and dynamic viscosity respectively; these improvements were established in comparison to the base fluid at 45 ºC. In addition, the results indicate that applying processes based on the surface modification on the nanotubes and

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improvement in nanoparticles dispersion can lead to enhancement in thermophysical properties

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in the nanofluids. During the experiments, the effective procedure of nanofluids stabilization was obtained. These findings combined with obtaining a pH value near the neutral state result

Keywords

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an improvement in heat transfer and flow characteristics of the nanofluids.

Stability.

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Carbon nanotubes; Nanofluids; Effective thermal conductivity; Viscosity; Aspect Ratio;

1. Introduction

With developments in new technologies, using conventional methods of heat transfer has been replaced by novel approaches. Among the most important breakthroughs, advent and development of nanofluids can be considered, which was first introduced by Choi [1]. Actually, nanofluids are suspensions of fluids and nanoparticles, the main objective of which is obtaining the highest thermal properties at the lowest solid nanoparticles concentration in the



Corresponding author. Tel: +98- 914- 116-0374. E-mail: [email protected] (Esmaeil Esmaeilzadeh) Mechanical Engineering Faculty, University of Tabriz, 29 th Bahman Blvd., 5166616471 Tabriz, IRAN

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ACCEPTED MANUSCRIPT base fluid. Nanofluids can be categorized depending on the material of the dispersed nanoparticle in the base fluid; the categories would be metal-based and non-metal-based. Therefore, the nanoparticle material is one of the most substantial factors in improving thermal performance of the nanofluids. Among non-metal-based nanoparticles, carbon nanotubes possess significant importance. This is due to high thermal conductivity ability of carbon and special geometry of the carbon nanotubes. These tubes are cylindrical with either a single walled or multi walled, the diameter of which is usually a few nanometers and their length is not more than a few micrometers; thus, carbon nanotubes are among the materials with high

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aspect ratios [2]. Synthesis of these materials is possible through some methods and procedures, which are not covered in this study; the reader is referred to check [2], [3], and [4]

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for further information. Nanofluids effective thermal conductivity has absorbed researchers’ attention for the past two decades. Considering the fact, that carbon has a high thermal

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conductivity, nanofluids based on carbon nanotubes have been deemed considerably important from heat and fluids engineering standpoint. In addition to this importance, there have been

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crucial challenges, among which one can refer to preparation and stabilization of nanofluids containing carbon nanotubes, and providing the ability of conveying high capabilities of

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thermophysical properties of the carbon nanotubes to the obtained nanofluids. Despite the attraction of using nanofluids with carbon nanotubes, some issues such as carbon being hydrophobic to polarized base fluids like water has led to less research being done on these

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nanofluids in comparison to other nanoparticles. Hence, this study has focused on multi walled

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nanotube nanoparticles with water as the base fluid. The studies include thermophysical and rheological properties of water/carbon nanotube nanofluids.

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1.1 Thermal Conductivity

The state of art literature shows that various factors as nanoparticles concentration or

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volume fraction, size and shape of the dispersed nanoparticles, the temperature of the nanofluids, and the distribution of the dispersed nanoparticles can affect the thermal properties of the nanofluids. Each of these factors has been the source of extensive research in learning heat transfer phenomena in nanofluids, resulting in development of knowledge in this field. Choi’s studies [5] about multi walled carbon nanotubes (MWCNTs) at Argon National Laboratory has been considered a significant step in utilizing these materials, an improvement of 150% in thermal conductivity has been reported in this study. Xie [6] investigated the effects of volume fraction and pH on nanofluids stability, enhancements of 7-20% were observed in thermal conductivity as well. Assael et al [7] studied the effect of Cetyl trimethylammonium bromide (CTAB) surfactant, they reported that thermal conductivity had seen an 8% growth. Ding’s study [8] illustrates the effect of ambient temperature on the enhancement of thermal 2

ACCEPTED MANUSCRIPT conductivity, improvements about 80% are reported in high concentrations. Hwang et al [9] studied MWCNTs in the base fluid of mineral oil with a mass concentration of 0.5%wt. the result was a 9% increase in thermal conductivity. Garg et al [10] studied a MWCNT with water as the base fluid, they used Arabic gum as the surfactant, the temperature of the experiments was 35 ºC, mass fraction was 1%wt. and a 40 minute ultrasonication time was applied. They reported a 20% enhancement for thermal conductivity in their results. Chen and Xie [11] investigated MWCNTs, water was employed as the base liquid as was Cationic Gemini for surfactant, and the temperature was varied from 5 to 65 ºC. At a mass fraction of 0.6%wt., they

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observed growths from 5.6 to 34%. Phuoc at al [12] conducted experiments on MWCNT with Chitosan surfactant; water was used as the base fluid and mass fractions varied between 3 and

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5% wt. The results showed thermal conductivity enhancements from 2.3 to 13%. Singh et al [13] investigated a functionalized MWCNT in water and Ethylene Glycol mixtures, mass

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fraction was 0.4%wt., and this led to 72% improvement in thermal conductivity. Indhuja et al [14] studied MWCNT nanofluids; they used Arabic gum as surfactant to investigate the effects

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of mass fraction and temperature. Enhancements between 3.2 and 33% were reported. Meyer et al [15] obtained a 8% improvement on thermal conductivity of MWCNT nanofluids with a

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water base fluid at 2.6%wt. Wusiman et al [16] used Sodium dodecylbenzenesulfonate (SDBS) and Sodium dodecyl sulfate (SDS) as surfactant for MWCNT nanofluids with water base fluid, the obtained better results, in terms of thermal conductivity enhancement, for SDBS rather than

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for SDS. They achieved a 2.8% growth at 0.5% mass fraction, with SDBS surfactant, in

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comparison with distilled water (DW). Mare et al [17] conducted research on deionized water (DIW) and MWCNT, SDBS surfactant was employed at volume fractions from 0.008 to 0.9%vol., two temperatures were used in the experiments, namely 20 and 46 ºC. The range of

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improvements in thermal conductivity was obtained to be from 5 to 45%.

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1.2 Rheological Behavior As mentioned earlier, considering the elite and excellent conditions of carbon nanotubes, nanofluids that are based on them have constituted an important range of nanofluids with high capabilities for heat absorbing and transfer. Thus, studies on rheological properties of these nanofluids possess a significant portion in state of art literature, this is due to their undeniable rheological properties in ability to circulate and convey heat in transfer phenomena applications. Through reviewing the sources, it is observed that rheological properties depends on various factors including base fluid properties, shape and geometrical characteristics of the nanoparticle, pH quantity of nanofluids, temperature, nanofluids mass fraction, synthesis of nanoparticles and stable dispersion methods, the stability time in the base fluid, and the employed surfactants. Therefore, in the present study, Newtonian or non-Newtonian behaviors 3

ACCEPTED MANUSCRIPT of nanofluids based on carbon nanotubes are investigated as well as their viscosity. Potschke et al [18] used polycarbonate as the base fluid for MWCNT, they tested different mass fractions including 0.5, 1, 2, and 5%wt. It was observed that the nanofluids with 2%wt. mass fractions shower non-Newtonian behavior. Yang et al [19] used PA06 as the base fluid for MWCNT; the mass fraction was selected to be 1%vol., they observed that the nanofluids, at 15 ºC and without using surfactant, showed a behavior similar to slight shear thinning. However, at 75 ºC a very strong shear thinning behavior was detected. Chen et al [20] studied the rheological behavior of MWCNTs in different base fluids such as water, Ethylene Glycol, Glycerol and

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Silicon oil. The results indicated that, in all the mentioned cases, the viscosity of nanofluids increases with growth in volume fraction, although 0.2%vol. was an exception. In this case, the

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viscosity was observed less than that of the base fluid. Furthermore, they reported rheological behavior of the nanofluids as Newtonian. Hung et al [21] carried out a study on the impacts of

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Chitosan surfactant and the concentration on the viscosity and thermal conductivity of the nanofluids. They concluded that adding chitosan and increasing the concentration would lead

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to viscosity growth. Using deionized water, they observed a 233% rise in the viscosity with 1.5 and 0.4%wt. mass fractions of MWCNT and Chitosan respectively. Estelle et al [22]

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investigated MWCNT nanofluids in water with SDBS surfactant; they found that, with low shearing rates, it showed a behavior similar to that of a viscoelastic medium. However, with high shearing rates, there was a shear thinning behavior. Wang et al [23] conducted in research

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on the rheological properties of MWCNT dispersed in water. A combination of SDBS and

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Triton X- 100 was utilized as surfactant and three volume fractions including 0.05, 0.24, and 0.27%vol. were experimented. They observed that despite a Newtonian behavior in the nanofluids viscosity increased in comparison with water and an increase in temperature would

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cause a decline in the viscosity. Ruan et al [24] studied the ultrasonication effects on MWCNT nanofluids dispersed in Ethylene Glycol with 0.5%wt. mass fraction. The results reported that

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in spite of a shear thinning behavior in the range of 10-100s-1 for shearing rate with a constant shear rate viscosity would decline comparing to ultrasonication after experiencing a rise. The reason of which was a decrease in nanotubes size and agglomerates under ultrasonication. Maillaud et al [25] investigated rheological properties of CNT nanotube in water, a combination of SDS and Triton X- 100 was used as surfactant with nanoparticles mass fractions between 1 and 8%wt. They reported that despite a Newtonian behavior for SDS/TX100, the resultant nanofluids showed shear thinning behavior in all mass fractions in addition with increasing TX100, a rise in the viscosity was detected.

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ACCEPTED MANUSCRIPT 1.3 Present Study As observed in the literature, there is no previous study focusing on the effect of the aspect ratio on dispersion energy, thermal conductivity and rheological behavior for Carboxyl functionalized MWCNT/water based nanofluids in presence of a binary surfactant mixture. In the present study, MWCNT-COOH with six types of different aspect ratios were dispersed in deionized water with 0.05%vol. A binary surfactant mixture including SDBS and Triton X-100 was used to achieve better stability of the nanofluids. The effect of MWCNT

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aspect ratio on the dispersion energy, thermal conductivity and rheological behavior of the nanofluids was studied experimentally. The results of experimental thermal conductivity and

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viscosity of the samples are discussed and compared with some known models at temperatures

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in between 10 and 45ºC. 2. Material and Methods

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2.1 Materials

In the present study, MWCNTs were purchased from Neutrino Company. Considering the

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hydrophobic nature of carbon nanotubes and the impact of this fact on nanofluids stability, Carboxyl functionalized (-COOH) MWCNT were employed. Using these nanotubes not only led to better and more effective dispersion in the base fluid (i.e. deionized water), but also

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provided better interfacial bonding strength. These tubes also show a better surface activity

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compared to pristine MWCNT that causes higher flexibility and results in maintaining its initial dimensions and reveals their prominent properties more consummately. In this study, six different geometry characteristics of carbon nanotubes have been used which are presented in

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Table 1. Moreover, Transmission Electron Microscopy (TEM) pictures are depicted in Figure 1. Considering the benefits of a dual combination, SDBS and Triton X- 100 were employed as

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ionic and nonionic surfactants respectively [23, 26, 27]. This combination has been employed to disperse all of the nanotubes in order to obtain a stable nanofluids. The mass fraction was fixed at 1:20 for SDBS/ Triton X-100. In addition, the surfactants mixture mass fraction to MWCNT-COOH was set to 3:20 [23]. In addition, both elements for the surfactant were provided by Sigma-Aldrich Company.

Table 1. Properties for the selected Nanotubes Figure 1. Transmission Electron Microscopy images of MWNCT-COOH samples

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ACCEPTED MANUSCRIPT 2.2 Preparation of nanofluids A two-step method was used to process the nanofluids. In order to obtain MWCNTCOOH/DIW nanofluids at a volume fraction of 0.05%vol. at the volume required for the experiments, pertinent amounts of SDBS and Triton X- 100 were weighted according to the mention fraction. The resultant mixture was stirred in an electromagnetic stirrer for 2 hours. According to the mentioned fractions, masses of MWCNT-COOH were added to the mixture of DIW-Triton X- 100/SDBS. In order to improve the dispersion and to obtain a homogenous nanofluids the mixture was exposed to ultrasonic water bath before adding the MWCNT-

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COOH. The apparatus of the mentioned bath was as follows: CD- 4820 Cleaner/ 170W/ 42 kHz. Under this condition, MWCNT-COOH was added to the combination at a mass rate of 1

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gr/hr in 0.1 per each step. After this adding process, each suspension was exposed to a unique

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amount of ultrasonic energy according to the details provided in Table 2, which led to harnessing stable homogeneous nanofluids. During ultrasonication, bath temperature was

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maintained around 25±5 ºC.

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Table 2 The amount of energy to which nanofluids samples were exposed Following the ultrasonication, each of the suspensions underwent centrifugal rotation for half an hour, the rotation rate was 3000 rpm and it separated the probable no dispersed particles

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from the suspension. The details of obtaining the mentioned nanofluids were not observed in

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the reviewed literature. By the end of dispersion stage, the suspensions were exposed to infrared ray under a 60X microscope, which yielded an ink-like black homogenous suspension

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as shown in Figure 2.

Figure 2. The prepared samples of MWCNT-COOH/DIW

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3. Nanofluids characterization 3.1 Nanofluids stability Considering the impact of electrokinetic properties in nanofluids stability, investigations on electrophoretic behavior through Zeta potential and pH are essential to understand the stability. In order to study the stability for the nanofluids samples, which had been kept in stationary condition for four months, a Dynamic Light Scattering (DLS) instrument namely Zeta Sizer-Nano ZS ZEN 360 (Malvern Instruments Ltd) was utilized. The results of this investigation are reported in form of diagrams of size distribution, zeta potential distribution, particles average hydrodynamic diameter and the amount of zeta potential for Nanofluids

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ACCEPTED MANUSCRIPT samples. To ensure data accuracy each experiment was performed twelve times and average results were calculated. Considering the fact that pH is one of the most influential factors in zeta potential measurements especially in water based mixtures, nanofluids samples pH values were measured by 744 pH meter (Metrohm AG/ Switzerland). 3.2 Measuring nanofluids effective thermal conductivity Nanofluids thermal conductivity were evaluated using Transient Hot Wire (THW) method. The KD2 Pro Thermal Properties Analyzer (Decagon Device Inc.) was utilized. This device

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has tolerance accuracy equal to 5% and operates according to ASTM D5334 and IEEE 4221981. Before the start of measuring, the system was calibrated using distilled water in the

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temperatures 10, 15, 20, 25, 30, 35, 40, and 45 ºC provided.

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considered temperature range. Values of nanofluids effective thermal conductivity at

3-3 Rheological evaluation of nanofluids

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Rheological properties of the samples were measured by Brookfield digital cone/plate viscometer (model LVDV-II with cone spindle) instrument with reported accuracy at 1%.,

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which is equipped with a thermostatic bath to control and maintain uniform temperature with an accuracy of ±0.1 ºC. Calibration for this instrument was achieved through standard viscous

4. Results and Discussion

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fluids provided by Brookfield Company.

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The six mentioned MWCNT-COOH/DIW Nanofluids with different aspect ratios were investigated in terms of nanofluids stability, thermal conductivity and rheological properties, the volume fraction was equal to 0.05%. The following includes complete details on these

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investigations.

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4.1 Nanofluids stability

As mentioned in the previous section, in order to evaluate nanofluids stability, samples had been maintained in static conditions in standard atmospheric temperature for four months. DLS measurement results are presented in Table 3. The measurements were performed at 25 ºC with a tolerance of 0.1 ºC. Table 3 The results of DLS and zeta potential measurements The results of DLS and Zeta potential measurements of the samples are presented in Figure 3. Figure 3. The amounts of zeta potentials and Z-Average particle sizes for nanofluids samples after static retention for four months

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ACCEPTED MANUSCRIPT Considering the fact that obtained Zeta potential values are between -20 and -30mV, and their static retention for four months, the stability indexes of the results are completely appropriate [28]. Paying attention to the results reveals that sample A has a higher tendency to agglomeration since it has the highest aspect ratio and the topmost spent energy to disperse the particles. Therefore, from a stability standpoint, it has the lowest score. Since the Derjiaguin, Landau, Verwey and Overbeet (DLVO) theory [29] states that colloid stability depends on the net Van der Waals and repulsive electrostatic forces. It seems that in the case for sample A, the repulsive has grown weaker in comparison to the sample A from four months before. When the

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pH value the samples has been varied from 6.43 to 6.73, which belong to all of the samples. Wherein the maximum and minimum pH values are quite close to the neutral point of 7, which

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is deemed an advantage when corrosion property is considered for each of the six samples. Moreover investigating the PDI index of the samples indicates that employing DLS method

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and Zeta potential are quite pertinent for these studies. Finally, the operated dispersion energy is an important factor on the nanofluids stability. In the available literature, the impact of

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dispersion energy on fracture and change in length of nanotubes and their effects on the nanofluids thermophysical properties and stability have been investigated [10, 24].What makes

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this research different from the previous studies is using carbon nanotubes with different initial properties in the experiments and determining the dispersion energy. In addition, specific amount of dispersion energy pertinent to carbon nanotube aspect ratio is used for each

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suspension, which is presented in Figure 4. It is seen with increase in carbon nanotubes aspect

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ratio, the dispersion energy rises as well. Fortunately, in the studied samples, a simple linear relation is obtained, which interprets to proper stability results according to the provided

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explanations.

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Figure 4. The amounts of dispersion energy to carbon nanotubes aspect ratio In view of the explanations and the observations, it is concluded that the selected methods for dispersing nanotubes in the base fluid including Carboxyl functionalizing of carbon nanotubes, using a dual ionic and nonionic surfactant, deionized water, and using proper dispersion energy values for the samples have been effective in nanofluids stability. Furthermore, the fact that the pH values of the samples are obtained near neutral state is considered acceptable from a practical point of view and it is deemed as a benefit. Evidently, in transfer phenomena applications, where the mission is to use these properties, the time of experiments is significantly less than the stability time.

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ACCEPTED MANUSCRIPT 4.2 Thermal conductivity Effective thermal conductivity variation with temperature for all of the samples is presented in Figure 5. A range of 10 to 45ºC is considered for temperature. The main reason of defining the selected temperatures range for the experiments is probable destruction of bonds between surfactant and carbon nanotubes in high temperatures that may cause instabilities [7, 30]. As it is illustrated in Figure 5, all of the samples possess higher effective thermal

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conductivity in comparison with the base fluid of water.

Figure 5. Variation of thermal conductivity for nanofluids samples and base fluid of water with

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temperature

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In Figure 6, enhanced relative thermal conductivity of nanofluids to base fluid is provided. From this diagram, one can realized that the highest enhancement is equal to 36% for sample

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A, which has the highest aspect ratio in the samples at 45 ºC. The least improvement between all of the samples is obtained for sample F with the smallest aspect ratio at 10 ºC, which is about 3%. The results of experiments indicate that with increase in nanofluids temperature,

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thermal conductivity increases in all of the samples. This growth has an approximately linear behavior in comparison to nanofluids temperature, a similar trend has been reported in Wen

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and Ding [30].

Figure 6. Enhancement in nanofluids samples thermal conductivity to the base fluid Another point that is observed in this diagram is that with increase in carbon nanotubes

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aspect ratio one can expect a rise in effective thermal conductivity, which is in agreement with the reports of [7, 31-34]. In addition for carbon nanotubes having equal diameters, the

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nanofluids with more lengthy nanotubes represent higher effective thermal conductivity [35]. With increasing the nanofluids temperature, effective thermal conductivity would enhance more, as indicated in Figures 5 and 6. The reason can be Brownian motions intensification owing to phonon propagation in higher temperatures, which is in agreement with the results reported by Hone et al [36] and Yan et al [37]. Moreover, with increase in temperature, nanoparticles and base fluid fluctuation frequencies increases. This increase leads to growth of energy transfer intensity in the nanofluids, which is reflecting in a rise in thermal conductivity. Comparing the obtained enhancements in the diagrams of Figures 5 and 6 with the results of other studies in the literature, one can observe that using MWCNT-COOH has led to more improvement in thermal conductivity than in case of mere MWCNT. The reason can be traced

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ACCEPTED MANUSCRIPT in the faster movement in Brownian motions of functionalized MWCNT with modified surfaces because of the better stability promoted by the carboxyl groups on the surface raising a greater enhancement in thermal conductivity. Since the effects of MWCNT shape on thermal conductivity of the nanofluids are investigated in this paper, certain known models are selected to be compared with experimental results. These models are based on the nanoparticle shape, which are listed as follows:

keff kb.f.

=

kp +(n−1)kb.f. +(n−1)(kp −kb.f. )φ kp +(n−1)kb.f. −(kp −kb.f. )φ

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(a) Hamilton- Crosser (H-C) model [38]: ,

(1)

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where n and φ are the empirical shape factor and volume fraction, respectively.

kb.f.

k k 1+ b.f. rφ0.2 +(1− b.f. )rφ1.2

=

kp

kp kb.f. k 1+ rφ0.2 −(1− b.f.)φ kp kp

,

(2)

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keff

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(b) Yamada- Ota (Y-O) model [39]:

βx = βz = Lx =

(3)

,

(4)

,

(5)

3+2φ[βx (1−Lx )+βz (1−Lz )] 3−φ(2βx Lx +βz Lz ) kx −kb.f.

,

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kb.f.

=

kb.f. +Lx (kp −kb.f. ) kz −kb.f.

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keff

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(c) Nan et al model [40]:

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where r is aspect ratio of the nanoparticle.

kb.f. +Lz (kp −kb.f. ) r2

2(r2 −1)

−

r

2(r2 −1)3⁄2

cosh−1 r ,

(6)

Lz = 1 − 2Lx ,

(7)

where k x , k z , are the transverse and longitudinal equivalent thermal conductivity of the carbon nanotubes, respectively. Also, Lx and Lz are geometrical factors dependent on the nanotube aspect ratio.

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ACCEPTED MANUSCRIPT Figure 7. Variation of relative thermal conductivity with MWCNT aspect ratio- Comparison between experimental relative thermal conductivity and some theoretical models at 25C Figure 7 presents the comparison of the experimental results with the data predicted by three mentioned models. In Figure 7, error bars show up to ±10% deviation from the experimental results for all of the samples. As it is seen, Yamada- Ota model predictions have good agreement with experimental results, which are located in error bars. Also, HamiltonCrosser model predictions are located in ±14%, which shows lower accuracy in thermal

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conductivity prediction for Hamilton- Crosser model than Yamada- Ota model. In addition, as observed in Figure 7, Nan et al model predictions exceed the error bars and are greater than the

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other models for all of the aspect ratios except for the smallest aspect ratio. It shows that Nan et al model have not good accuracy for COOH-MWCNT/DIW based nanofluids with increasing

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aspect ratio. Undoubtedly, it is clear that several factors are important in analysis of the deviations of the models, such as the methods for nanofluids preparation, effective factors in

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surface charging and interfacial forces, aggregation effect, and volumetric fraction. Also, Hamilton -Crosser and Yamada- Ota predictions are placed in the range of the bars having

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good agreement with the experimental results, especially in the small aspect ratios. Therefore, these trends show that Hamilton-Crosser and Yamada- Ota models can be utilized accurately for predicting the effective thermal conductivity of COOH-MWCNT/DIW nanofluids with

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varied aspect ratios.

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4.3 Rheology

Figure 8 defines the rheological behavior of MWCNT-COOH/DIW nanofluids samples AF at 25ºC with a volume fraction of 0.05%vol. As can be observed a linear relation exists

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between shear stress and shear rate, which refers Newtonian behavior of nanofluids.

Figure 8. Newtonian behavior evaluation diagram

Figure 9 shows the dynamic viscosity for the samples in a temperature range from 10 to 45ºC. As it is detectable for all of the samples at a specified constant temperature, the dynamic viscosity has a higher value than the base fluid, although differences are quite insignificant. The obtained results show a close agreement with Wang et al results [23].

Figure 9. Nanofluids samples and base fluid of water dynamic viscosity variation with temperature

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ACCEPTED MANUSCRIPT Figure 10 illustrates the variation of average dynamic viscosity of nanofluids with change in carbon nanotubes aspect ratio at the temperature range of 10 to 45 ºC. In fact, this diagram has similar trend to Figure 9. It is obvious these results satisfy our estimates about nanofluids and base fluid viscosity behavior with temperature. Nevertheless, Figure 11 presents some comparative differences between nanofluids and base fluid in reason of the nature of carbon nanotubes affecting on suspension behavior.

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Figure 10. Nanofluids dynamic viscosity variation with carbon nanotubes aspect ratio Figure 11 illustrates the ratio between samples dynamic viscosity and water as base fluid in

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the defined temperature range. In this diagram, one can see that the minimum relative dynamic

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viscosity belongs to sample A, which is from 0.34% increase at 10 ºC. The maximum value belongs to sample F, which is approximately 5.5% at 45 ºC. As seen in Figure 11, relative

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temperature and decreasing the aspect ratio.

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dynamic viscosity of nanofluids samples presents more enhancements with increasing

Figure 11. The ratio of nanofluids samples dynamic viscosity growth to the base fluid of water

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Several models have been developed to correlate the relative viscosity of the nanofluids with effective parameters. Considering the aims of this research, two models based on the

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shape of the nanoparticle were selected. Brenner and Condiff (B-C) [41] , modified Maron and Pierce (mM-P) by Mueller et al [42] models were utilized to be compared with experimental results. These models have been correlated for nanoparticles with rod-like shapes or fibers in

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dilute suspensions, which are presented as below:

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(d) Brenner and Condiff model [41]: µeff

= 1 + ηφ

µb.f.

η=

0.312 r Ln 2r−1.5

+2−

(8) 0.5 Ln 2r−1.5

−

1.872

(9)

r

where r is aspect ratio of the nanoparticle. According to Thomas [44] and Rutgers [45] studies, dilute suspension is defined as 𝜑 ≤ 0.01 [44] or 𝜑 ≤ 0.02 [45]. (e) Maron-Pierce et al model [46] modified by Mueller et al [42]: µeff µb.f.

= (1 −

φ φm

−2

)

(10) 12

ACCEPTED MANUSCRIPT φm =

2

(11)

0.321 r+3.02

where φm is the maximum particle packing fraction. Also, equation (11) was developed by Mueller et al [42] for non-spherical nanoparticles. The described models in (d) and (e) were used for CNT water based nanofluids first time by Halelfadl et al [47]. Figure 12. Variation of relative dynamic viscosity with MWCNT aspect ratio- Comparison between experimental relative dynamic viscosity and some models at 25C

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Figure 12 shows the comparison of the experimental results with the data predicted by the two mentioned models. The error bars in Figure 12, indicate up to ±3% deviation from

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experimental results for all of the samples. As seen in Figure 12, Brenner- Condiff models

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predictions lie in the range of the error bars having good compatibility with experimental results for the samples A- E in Brenner- Condiff model. However, modified Maron-Pierce model predictions are overestimated values, exceeding error bars limit from aspect ratio 600 to

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2500. This trend points out that agglomeration of the nanoparticles has the main role in viscosity prediction.

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The reason of the differences is special characteristics of dispersed carbon nanotubes in base fluid, which cause increase in relative dynamic viscosity of nanofluids to base fluid. Some

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important influential factors are Brownian forces, the possibility of rotational and transitional

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movements of carbon nanotubes and electro-viscose effects in functionalized nanoparticle surface encountering with base fluid and the surfactant. These factors would intensify in nanofluids containing low aspect ratio carbon nanotubes considering the fact that pH values are close to the neutral index for all samples.

However, in general, it can be claimed that

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nanofluids rheological behavior depends on several factors such as geometrical characteristics of carbon nanotubes, surface parameters between nanotubes and the base fluid, the base fluid

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material, nanoparticle volume fraction, nanofluids pH, nanofluids temperature, the type and amount of surfactant and the methods for particle dispersion. 5. Uncertainty analysis The uncertainty of thermal conductivity and viscosity measurements were calculated through Beckwith et al. method [48]. Table 4 presents the uncertainties of instruments. In addition, the uncertainty calculations are presented in Appendix A. Table 4. Uncertainties of instruments The accuracy for temperature measurement in the bath is 0.1ºC between 10 ºC to 45 ºC. The 𝑈 maximum ( 𝑇𝑇 ) will be equal 0.01 or 1%. Also, the accuracy for thermal conductivity is 13

ACCEPTED MANUSCRIPT reported equal to 5% by Decagon Inc. according the instrument operator’s manual for 𝑈

Decagon- KD2 Pro. Therefore( 𝑘𝑘 ) = 5%. Hence, the uncertainty in the effective thermal conductivity is calculated as below equation: 𝑈

𝑈

𝑢𝑘 = √( 𝑇𝑇 )2 + ( 𝑘𝑘 )2 = √(0.3636)2 + (5)2 = 5.0132% The accuracy for temperature measurement in the bath is 0.1ºC between 10 ºC to 45 ºC. The 𝑈 maximum ( 𝑇𝑇 ) will be equal 0.01 or 1%. Also, the accuracy for viscosity is reported 1% by 𝑈µ

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Brookfield Inc. according the instrument operator’s manual. Therefore, ( µ )= 1%. Therefore, the uncertainty in the effective viscosity is calculated as below equation:

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Conclusion

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𝑈µ

𝑈

𝑢µ = √( 𝑇𝑇 ) 2 + ( µ )2 = √(0.3636)2 + (1)2 = 1.0641%

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In this study, the geometrical characteristics impact of multi walled carbon nanotubes on the major thermophysical properties of MWCNT/DIW nanofluids was investigated. These properties consist of effective thermal conductivity and dynamic viscosity. Moreover, stability

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and rheological behavior of the nanofluids were studied, which led to the following concluding remarks.

Obtaining an effective method for dispersing carbon nanotubes, this includes a

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chemical approach for surface modification of carbon nanotubes to achieve higher adaptability with the base fluid of deionized water medium. This was obtained through carboxyl functionalizing of MWCNT and utilizing a dual surfactant consisting of SDBS

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and Triton X- 100. In addition, a mechanical approach was utilized to ensure safe and stable nanofluids.

Obtaining stable nanofluids with pH values close to neutral state,



Enhancement of nanofluids effective thermal conductivity through increasing the aspect

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

ratio of MWCNT relative to the base fluid of water, 

Observing a linear growth in the enhancement of the effective thermal conductivity of nanofluids with increase in temperature for all the studied nanotubes with various aspect ratios,



Adaption of the experimental thermal conductivities with Yamada- Ota model,



All of the studied Nanofluids have Newtonian behavior,



Adaption of the experimental viscosities with Brenner and Condiff model,



Decreasing viscosity of nanofluids with increasing carbon nanotubes aspect ratio,



Conformity of the experimental viscosities with Brenner and Condiff model, 14

ACCEPTED MANUSCRIPT Acknowledgment This project is supported partially by the University of Tabriz.

Appendix A Uncertainties for thermal conductivity and viscosity varying with temperature are calculated as follow and summarized in Table 5.

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Table 5. Uncertainties of variables

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ACCEPTED MANUSCRIPT References

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[1] S.U.S. Choi, Developments and Applications of Non-Newtonian Flows, 1995. [2] S. Iijima, Helical microtubules of graphitic carbon, Nature 354 (1991) 56. [3] T.W. Ebbesen, P.M. Ajayan, Nature (London) 358 (1992) 220. [4] H. Dai, Carbon nanotubes: synthesis, integration, and properties, Accounts of chemical research 35(12) (2002) 1035-44. [5] S.U.S. Choi, Z.G. Zhang, W. Yu, F.E. Lockwood, E.A. Grulke, Anomalous thermal conductivity enhancement in nanotube suspensions, Appl. Phys. Lett. 79 (2001) 2252. [6] H. Xie, H. Lee, W. Youn, M. Choi, Nanofluids containing multiwalled carbon nanotubes and their enhanced thermal conductivities, Journal of Applied Physics 94(8) (2003) 4967-4971. [7] M.J. Assael, Metaxa, I.N., Arvanitidis, Christofilos, D. and Lioutas, C., Thermal Conductivity Enhancement in Aqueous Suspensions of Carbon Multi-Walled and Double-Walled Nanotubes in the Presence of Two Different Dispersants, Int J Thermophys 26 (2005) 647-664. [8] Y. Ding, H. Alias, D. Wen, R.A. Williams, Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids), International Journal of Heat and Mass Transfer 49(1) (2006) 240-250. [9] Y. Hwang, H.S. Park, J.K. Lee, W.H. Jung, Thermal conductivity and lubrication characteristics of nanofluids, Current Applied Physics 6 (2006) e67-e71. [10] P. Garg, J.L. Alvarado, C. Marsh, T.A. Carlson, D.A. Kessler, K. Annamalai, An experimental study on the effect of ultrasonication on viscosity and heat transfer performance of multi-wall carbon nanotube-based aqueous nanofluids, International Journal of Heat and Mass Transfer 52(21) (2009) 5090-5101. [11] L. Chen, H. Xie, Properties of carbon nanotube nanofluids stabilized by cationic gemini surfactant, Thermochimica Acta 506(1) (2010) 62-66. [12] T.X. Phuoc, M. Massoudi, R.-H. Chen, Viscosity and thermal conductivity of nanofluids containing multi-walled carbon nanotubes stabilized by chitosan, International Journal of Thermal Sciences 50(1) (2011) 12-18. [13] N. Singh, G. Chand, S. Kanagaraj, Investigation of Thermal Conductivity and Viscosity of Carbon Nanotubes–Ethylene Glycol Nanofluids, Heat Transfer Engineering 33(9) (2012) 821-827. [14] A. Indhuja, K.S. Suganthi, S. Manikandan, K.S. Rajan, Viscosity and thermal conductivity of dispersions of gum arabic capped MWCNT in water: Influence of MWCNT concentration and temperature, Journal of the Taiwan Institute of Chemical Engineers 44(3) (2013) 474-479. [15] J.P. Meyer, T.J. McKrell, K. Grote, The influence of multi-walled carbon nanotubes on single-phase heat transfer and pressure drop characteristics in the transitional flow regime of smooth tubes, International Journal of Heat and Mass Transfer 58(1) (2013) 597-609. [16] K. Wusiman, H. Jeong, K. Tulugan, H. Afrianto, H. Chung, Thermal performance of multi-walled carbon nanotubes (MWCNTs) in aqueous suspensions with surfactants SDBS and SDS, International Communications in Heat and Mass Transfer 41 (2013) 28-33. [17] T. Maré, S. Halelfadl, S. Van Vaerenbergh, P. Estellé, Unexpected sharp peak in thermal conductivity of carbon nanotubes water-based nanofluids, International Communications in Heat and Mass Transfer 66 (2015) 80-83. [18] P. Pötschke, T.D. Fornes, D.R. Paul, Rheological behavior of multiwalled carbon nanotube/polycarbonate composites, Polymer 43(11) (2002) 3247-3255. [19] Y. Yang, E.A. Grulke, Z.G. Zhang, G. Wu, Temperature effects on the rheological properties of carbon nanotube-in-oil dispersions, Colloids and Surfaces A: Physicochemical and Engineering Aspects 298(3) (2007) 216-224. [20] L. Chen, H. Xie, W. Yu, Y. Li, Rheological Behaviors of Nanofluids Containing Multi-Walled Carbon Nanotube, Journal of Dispersion Science and Technology 32(4) (2011) 550-554. [21] Y.-H. Hung, W.-C. Chou, Chitosan for Suspension Performance and Viscosity of MWCNTs, International Journal of Chemical Engineering and Applications 3(5) (2012) 343-346. [22] P. Estelle, S. Halelfadl, N. Doner, T. Mare, Shear History Effect on the Viscosity of Carbon Nanotubes Water-based Nanofluid, Current Nanoscience 9(2) (2013) 225-230. [23] J. Wang, J. Zhu, X. Zhang, Y. Chen, Heat transfer and pressure drop of nanofluids containing carbon nanotubes in laminar flows, Experimental Thermal and Fluid Science 44 (2013) 716-721. 16

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[24] B. Ruan, A.M. Jacobi, Ultrasonication effects on thermal and rheological properties of carbon nanotube suspensions, Nanoscale Res Lett 7 (2012) 127. [25] L. Maillaud, P. Poulin, M. Pasquali, C. Zakri, Effect of the rheological properties of carbon nanotube dispersions on the processing and properties of transparent conductive electrodes, Langmuir 31(21) (2015) 5928-34. [26] A.H. Saiyad, S.G.T. Bhat, A.K. Rakshit, Physicochemical properties of mixed surfacant systems: sodium dodecyl benzene sulfonate with triton X 100, Colloid and Polymer Science 276(10) (1998) 913919. [27] O.V. Kharissova, B.I. Kharisov, E.G. de Casas Ortiz, Dispersion of carbon nanotubes in water and non-aqueous solvents, RSC Advances 3(47) (2013) 24812-24852. [28] A. Ghadimi, R. Saidur, H.S.C. Metselaar, A review of nanofluid stability properties and characterization in stationary conditions, International Journal of Heat and Mass Transfer 54(17) (2011) 4051-4068. [29] J.H. Adair, E. Suvaci, J. Sindel, Surface and Colloid Chemistry, in: K.H.J. Buschow, R.W. Cahn, M.C. Flemings, B. Ilschner, E.J. Kramer, S. Mahajan, P. Veyssière (Eds.), Encyclopedia of Materials: Science and Technology, Elsevier, Oxford, 2001, pp. 1-10. [30] D. Wen, Y. Ding, Effective Thermal Conductivity of Aqueous Suspensions of Carbon Nanotubes (Carbon Nanotube Nanofluids), Journal of Thermophysics and Heat Transfer 18(4) (2004) 481-485. [31] Y. Yang, E.A. Grulke, Z.G. Zhang, G. Wu, Thermal and rheological properties of carbon nanotubein-oil dispersions, Journal of Applied Physics 99(11) (2006) 114307. [32] H. Attari, F. Derakhshanfard, M.H.K. Darvanjooghi, Effect of temperature and mass fraction on viscosity of crude oil-based nanofluids containing oxide nanoparticles, International Communications in Heat and Mass Transfer 82 (2017) 103-113. [33] A.S. Cherkasova, J.W. Shan, Particle Aspect-Ratio and Agglomeration-State Effects on the Effective Thermal Conductivity of Aqueous Suspensions of Multiwalled Carbon Nanotubes, Journal of Heat Transfer 132(8) (2010) 082402-082402-11. [34] S. Harish, K. Ishikawa, E. Einarsson, S. Aikawa, S. Chiashi, J. Shiomi, S. Maruyama, Enhanced thermal conductivity of ethylene glycol with single-walled carbon nanotube inclusions, International Journal of Heat and Mass Transfer 55(13) (2012) 3885-3890. [35] 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, Journal of Applied Physics 103(9) (2008) 094309. [36] J. Hone, M.C. Llaguno, M.J. Biercuk, A.T. Johnson, B. Batlogg, Z. Benes, J.E. Fischer, Thermal properties of carbon nanotubes and nanotube-based materials, Applied Physics A 74(3) (2002) 339343. [37] X.H. Yan, Y. Xiao, Z.M. Li, Effects of intertube coupling and tube chirality on thermal transport of carbon nanotubes, Journal of Applied Physics 99(12) (2006) 124305. [38] R.L. Hamilton, O.K. Crosser, Thermal Conductivity of Heterogeneous Two-Component Systems, Industrial & Engineering Chemistry Fundamentals 1(3) (1962) 187-191. [39] E. Yamada, T. Ota, Effective thermal conductivity of dispersed materials, Wärme - und Stoffübertragung 13(1) (1980) 27-37. [40] C.W. Nan, Z. Shi, Y. Lin, A simple model for thermal conductivity of carbon nanotube-based composites, Chemical Physics Letters 375(5) (2003) 666-669. [41] H. Brenner, D.W. Condiff, Transport mechanics in systems of orientable particles. IV. convective transport, Journal of Colloid and Interface Science 47(1) (1974) 199-264. [42] S. Mueller, E.W. Llewellin, H.M. Mader, The rheology of suspensions of solid particles, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 466(2116) (2010) 1201. [43] T. Kitano, Kataoka, T. & Shirota, T., An empirical equation of the relative viscosity of polymer melts filled with various inorganic fillers, Rheol Acta 20(2) (1981) 207-209. [44] D.G. Thomas, Transport characteristics of suspension: VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles, Journal of Colloid Science 20(3) (1965) 267-277. [45] I.R. Rutgers, Relative viscosity and concentration, Rheol Acta 2(4) (1962) 305-348. [46] S.H. Maron, P.E. Pierce, Application of ree-eyring generalized flow theory to suspensions of spherical particles, Journal of Colloid Science 11(1) (1956) 80-95. 17

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[47] S. Halelfadl, P. Estellé, B. Aladag, N. Doner, T. Maré, Viscosity of carbon nanotubes water-based nanofluids: Influence of concentration and temperature, International Journal of Thermal Sciences 71 (2013) 111-117. [48] T.G. Beckwith, R.D. Marangoni, J.H. Lienhard, Mechanical Measurements, Pearson Prentice Hall2007. [49] P. Kim, L. Shi, A. Majumdar, P.L. McEuen, Thermal Transport Measurements of Individual Multiwalled Nanotubes, Physical Review Letters 87(21) (2001) 215502.

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ACCEPTED MANUSCRIPT Table 1. Properties for the selected Nanotubes B

C

D

E

F

Outer Diameter (nm)

<8

10-20

50<

<8

10-20

50<

Inner Diameter (nm)

2-5

5-10

5-15

2-5

5-10

5-15

Length (µm)

10-30

10-30

10-30

0.5-2

0.5-2

0.5-2

1250-

500-

200-

3750

3000

400

70- 250

20- 200

10- 40

500<

200<

40<

500<

200<

40<

3000

3000

3000

3000

3000

3000

True Density (gr/cm3)

~ 2.1

~ 2.1

~ 2.1

~ 2.1

~ 2.1

~ 2.1

Tap Density (gr/cm3)

0.27

0.22

0.18

0.27

0.22

0.18

Purity

95%<

95%<

95%<

95%<

95%<

95%<

Special Surface Area (m2/gr) Thermal conduction coefficient (W/m.K) [49]

3.86

-COOH Content

2.00

0.49

3.86

2.00

0.49

%wt.

%wt.

%wt.

%wt.

%wt.

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%wt.

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Aspect Ratio

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Properties

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Samples

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ACCEPTED MANUSCRIPT Table 2. The amount of energy to which nanofluids samples were exposed Sample

B

C

D

E

F

3111 1857 1400 900 854 714

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kJ/L

A

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ACCEPTED MANUSCRIPT Table 3. The results of DLS and zeta potential measurements Z-Average

Potential

Particle Size

(mV)

(d.nm)

A

-26.9

B

pH

400.7

0.434

6.70

-21.3

234.4

0.359

6.73

C

-26.8

244.9

0.236

6.44

D

-28.2

310.0

0.428

E

-29.6

231.9

F

-27.2

220.7

21

6.43

0.257

6.63

0.316

6.73

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Sample

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PdI

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Zeta

ACCEPTED MANUSCRIPT Table 4. Uncertainties of instruments

Variable measured

Last division in measuring instrument

Min. and Max. values measured in experiment

Uncertainty

Thermocouple

Bath temperature in thermal conductivity measurement

0.1 ºC

10- 45 ºC

0.3636%

2

DecagonKD2 Pro

Thermal conductivity

3

Thermocouple

Bath temperature in viscosity measurement

4

Brookfield Digital Viscometer

Viscosity

5% 0.1 ºC

10- 45 ºC

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No.

Name of instrument

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0.3636% 1%

ACCEPTED MANUSCRIPT Table 5. Uncertainties of variables No. Variable name

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1 2

Uncertainty error (%) Thermal conductivity, k 1.0641 Viscosity, µ 5.0132

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ACCEPTED MANUSCRIPT (a)

(b)

MWCNT-COOH

Item A (OD<8 nm, Length 10- 30 µm)

Item B (10
Aspect Ratio ~ 1250- 3750

Aspect Ratio ~ 500- 3000 (d)

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(c)

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MWCNT-COOH

MWCNT-COOH

Short MWCNT-COOH

Item C (50 nm
D

Item D (OD<8 nm, Length 0.5- 2 µm)

Aspect Ratio ~ 200- 400

PT E

Aspect Ratio ~ 70- 250 (f)

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(e)

Short MWCNT-COOH

Short MWCNT-COOH

Item E (10
Item F (50
Aspect Ratio ~ 20- 200

Aspect Ratio ~ 10- 40

Figure 1. Transmission Electron Microscopy images of MWNCT-COOH samples

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Figure 2. The prepared samples of MWCNT-COOH/DIW

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ACCEPTED MANUSCRIPT MWCNT-COOH/DIW Samples Code

450 A_05

B_05

C_05

D_05

E_05

F_05

-5

400

350 300

-15

250

-20

200 150

-25

100

PT

Zeta Potential (mV)

-10

Z- Average Particle Size (d.nm)

0

-30

50 0

Zeta Potential

SC

Particle Size

RI

-35

Figure 3. The amounts of zeta potentials and Z-Average particle sizes for nanofluids samples

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after static retention for four months

26

ACCEPTED MANUSCRIPT 3500

y = 0.929x + 745.45 R² = 0.9924

2500 2000 1500 1000

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Dispersing Energy (kJ/L)

3000

500

0

500

1000

1500

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Aspect Ratio

2000

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0

2500

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Figure 4. The amounts of dispersion energy to carbon nanotubes aspect ratio

27

ACCEPTED MANUSCRIPT 0.9

Nano_A

Nano_B

Nano_C

Nano_D

Nano_E

Nano_F

Water

0.85 0.8 0.75

Keff

0.7

0.65

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0.6 0.55 15

20

25

30

35

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T (C)

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10

40

45

Figure 5. Variation of thermal conductivity for nanofluids samples and base fluid of water with

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temperature

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ACCEPTED MANUSCRIPT Nano_A

Nano_B

Nano_C

Nano_D

Nano_E

Nano_F

1.4 1.35

Keff/Kb.f.

1.3 1.25 1.2 1.15

PT

1.1 1.05

10

15

20

25

30

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T (C)

35

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1

40

45

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Figure 6. Enhancement in nanofluids samples thermal conductivity to the base fluid

29

ACCEPTED MANUSCRIPT Nan

Yamada-Ota

Hamilton- Crosser

Exp.

2.8

keff/ k b.f.

2.3

1.8

0.8 500

1000 1500 Aspect Ratio

SC

0

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PT

1.3

2000

2500

Figure 7. Variation of relative thermal conductivity with MWCNT aspect ratio- Comparison

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between experimental relative thermal conductivity and some theoretical models at 25C

30

ACCEPTED MANUSCRIPT Nano_A

Nano_B

Nano_C

Nano_D

Nano_E

Nano_F

1

0.6

0.4

0.2

0 300

500

700

RI

100

PT

Shear Stress, τ [pa]

0.8

SC

Rate of Shear Strain, du/dy [1/s]

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Figure 8. Newtonian behavior evaluation diagram

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900

ACCEPTED MANUSCRIPT Nano_A

Nano_B

Nano_C

15

20

Nano_D

Nano_E

Nano_F

Water

1.30E-03 1.20E-03 1.10E-03

µ (pa.s)

1.00E-03 9.00E-04

PT

8.00E-04

6.00E-04

10

25

30

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T (C)

RI

7.00E-04

35

40

45

Figure 9. Nanofluids samples and base fluid of water dynamic viscosity variation with

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temperature

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ACCEPTED MANUSCRIPT 8.10E-04

F_05

8.05E-04

8.00E-04

E_05

7.90E-04

C_05

D_05

y = 0.0008x-0.006 R² = 0.9063

B_05

7.85E-04

7.80E-04

7.75E-04 500

1000

1500

SC

Aspect Ratio

2000

RI

0

PT

µ (pa.s)

7.95E-04

A_05

2500

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Figure 10. Nanofluids dynamic viscosity variation with carbon nanotubes aspect ratio

33

ACCEPTED MANUSCRIPT 1.08

Nano_A

Nano_B

Nano_C

Nano_D

Nano_E

Nano_F

1.07

µeff./µb.f.

1.06 1.05 1.04 1.03

1.01 1 15

20

25

30

SC

T (C)

35

40

RI

10

PT

1.02

45

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Figure 11. The ratio of nanofluids samples dynamic viscosity growth to the base fluid of water

34

ACCEPTED MANUSCRIPT Present Work

Brenner & Condiff

Modifed Maron- Pierce

1.7 1.6

µeff/ µ b.f.

1.5 1.4 1.3 1.2

PT

1.1

0.9 0

500

1000

1500

2000

2500

SC

Aspect Ratio

RI

1

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Figure 12. Variation of relative dynamic viscosity with MWCNT aspect ratio- Comparison

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between experimental relative dynamic viscosity and some theoretical models at 25C

35

PT

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Graphical abstract

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ACCEPTED MANUSCRIPT Highlights

Research on Carboxyl-multi walled carbon nanotubes aqueous nanofluids.



Utilization of a binary surfactants mixture to the dispersion in the base fluid.



Obtaining stable multi walled carbon nanofluids with pH values close to neutral.



Observing Newtonian behavior in Carboxyl-multi walled carbon nanofluids.

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

37