SAE40 hybrid nano-lubricant

Applied Thermal Engineering 123 (2017) 1419–1433

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Experimental investigation, sensitivity analysis and modeling of rheological behavior of MWCNT-CuO (30–70)/SAE40 hybrid nano-lubricant Mohammad Abdollahi Moghaddam ⇑, Kazem Motahari Department of Chemical Engineering, Faculty of Engineering, Arak University, Arak 38156-8-8349, Iran

h i g h l i g h t s
Surveying rheological behavior of MWCNT-CuO/SAE40 hybrid nano-lubricant in details.
Obtaining 29.74% viscosity enhancement at 1% solid volume fraction.
A new correlation is suggested in terms of concentration for each temperature.
Sensitivity of hybrid nano-lubricant viscosity is analyzed.
ANN’s R-squared and MSE are calculated 0.9966 and 0.00002081, respectively.

a r t i c l e

i n f o

Article history: Received 31 December 2016 Revised 9 May 2017 Accepted 31 May 2017 Available online 2 June 2017 Keywords: Hybrid nano-lubricant Non-Newtonian Shear thinning New correlation Sensitivity ANN

a b s t r a c t In this project, rheological variations of hybrid nano-lubricant with temperature and solid volume fraction have been tested. Nano-lubricant was prepared by dispersing copper oxide (CuO) nanoparticles and multi walled carbon nanotubes (MWCNTs) to SAE40 engine oil. The viscosity of volume fractions 0.0625– 1% was measured in temperatures 25–50 °C and different shear rates. The results showed that in concentration 1 vol.%, the viscosity of hybrid nano-lubricant was 29.47% more than the viscosity of the base oil. The study conducted on rheological behavior proved that nano-lubricant and pure oil were nonNewtonian so they followed Ostwald de Waele relationship. The estimation of indices revealed that the behavior is shear thinning. Due to disability of the current models to predict nano-lubricant viscosity, a new correlation in each temperature in terms of solid volume fraction was proposed. The accuracy of correlations in different temperatures varied from 99.64 to 98.06%. Sensitivity of nano-lubricant to 10% increase in concentration was estimated. Also, an Artificial Neural Network was designed by multilayer perceptron method including two hidden layers, one of which had five neurons and the other one had four neurons. R-squared, MSE, and AARD were calculated 0.9966, 0.00002081, and 0.0055, respectively. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Increasing the efficiency and improving energy consumption in industry have always attracted researchers’ attention. The improvement of heat transfer in heating and cooling systems is not an exception. As a result, a great number of researches have been conducted on using substitute fluids instead of common fluids such as water and ethylene glycol (EG) so that they can show more appropriate heating properties. In the recent years, nanofluids have been considered important in many engineering fields like solar systems, cooling electronic equipment and car engines, ⇑ Corresponding author. E-mail address: [email protected] (M.A. Moghaddam). http://dx.doi.org/10.1016/j.applthermaleng.2017.05.200 1359-4311/Ó 2017 Elsevier Ltd. All rights reserved.

medical devices, fuel batteries, nuclear reactors, and heating systems [1–5]. Extensive researches have been conducted experimentally and numerically on properties of these fluids in different conditions. Many of these researches showed noticeable increase in nanofluid heat transfer compared to usual fluids [6–12]. Increase in heat transfer in thermal transformers can lead to reduction in transformer size, the fluid, and fixed and operation costs [13]. The proportion of nanoparticles surface to their volume is a great number so while hitting each other inside the fluid, they can transfer a great deal of energy. So it is expected that nanofluid has a great thermal conductivity. The studies have shown that as the amount of nanoparticle increases inside base fluid and as nanofluid temperature goes up, nanofluid thermal conductivity increases [12,14–16]. On the other hand, some studies have reported that

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Table 1 Studies on rheological behavior of Nanofluids and nano-lubricants. Author(s)

Nanofluid

Temp.

Conc. (vol.%)

Size (nm)

Shear rate range

Rheological behavior

Eshgarf et al. [30]

COOH functionalized MWCNTs-SiO2/EG-water MWCNT/[Bmim][PF6]

Ambient temperature Ambient temperature

0.0625–2

0.612–122.3

Shear thinning

0.01 – 1000

10–50 25 15.6

0.1–1.5 5–12 1&2

3–74 10–1000 100–1000

Low concentration: shear thinning High concentration: Newtonian Bingham plastic Shear thinning Shear thinning

25–50 30

0.0375–1.2 5–25 wt.%

12.23–122.3 0.1–1000

Shear thinning Shear thinning

Chen et al. [37] Abareshi et al. [38] Duan et al. [39] Soltani and Akbari [40]

Al2O3/EG-water TiO2/ water CuO/Oil Al2O3/Oil TiO2/Oil Fe3O4-Ag/ EG Anatase-TiO2/EG Rutile-TiO2/EG TNT/EG Fe2O3/ glycerol Graphite/ water MgO-MWCNTs/EG

20–30 nm Inner diameter 5–15 nm Diameter: 20–40 nm Length: 5–15 lm 50 7–20 40 15 20

20–60 25 25 30–60

0–8 0.25–0.8 1–4 0–1

0.03–3000 0.01–264 1–100 1.342–134

Shear thinning Shear thinning Shear thinning Newtonian behavior

Bahrami et al. [14]

Fe-CuO/EG-water

25–50

0.05–1.5

3.669–122.3

Asadi and Asadi [20]

MWCNT-ZnO/engine oil

5–55

0.125 – 1

Low concentration: Newtonian High concentration: Shear thinning Newtonian behavior

Wei et al. [41]

SiC-TiO2/diathermic oil

20–60

0–1

0–1000

Newtonian behavior

Kumar et al. [42]

Cu-Zn/SAE oil Cu-Zn/paraffin Cu-Zn/vegetable oil

Ambient temperature

0–0.5

0–100

Shear thinning Shear thinning Newtonian behavior

Wang et al. [31]

Kole and Dey [32] Tseng et al. [33] Jamal-Abad et al. [34]

Afrand et al. [35] Cabaleiro et al. [36]

0–0.1 wt.%

37 ± 17 47 ± 18 10 26 3–4 OD: 3–5 Inner diameter 5–15 CuO:40 Fe: 35–45 OD: 3–5 Inner diameter 5–15 TiO2:10 SiC: 30 25

Table 2 A summary of studies conducted on modeling of nanofluids. Author

Purpose

Nanofluid

Algorithm

Accuracy

Ziaei-Rad et al. [43]

Friction factor Nusselt Number Nusselt Number

Al2O3/water

MLP

CuO/water

RPROP

Mehrabi et al. [45]

Nusselt Number Pressure drop

TiO2/water

Saeedan et al. [46]

Pressure drop Nusselt Number

CuO/water Cu/water CNT/water

GA-PNN GMGH NSAG-II Back propagation

Zhao et al. [47]

Dynamic viscosity

Meybodi et al. [19]

Dynamic viscosity

CuO/water Al2O3/water Al2O3/water TiO2/water SiO2/water CuO/water

MRE = 0.19% MRE = 0.36% MRE = 2.5% STDR = 2.46% MAE = 0.835 MRE = 8.9% RMSE = 1.01 MRE = 1.2596% Error = 0.409% MRE = 0.2515% Error = 0.081% R2 = 0.9962 R2 = 0.9992 R2 = 0.998

Santra et al. [44]

nanofluid viscosity is greater than pure fluids. So as nanoparticle value increases or nanofluid temperature decreases, nanofluid viscosity increases [17–24]. Due to the purpose for which nanofluid is used, increase in viscosity can have a negative or positive role. If nanofluid is provided for cooling, base fluid of ethylene glycol and water is commonly used, so increase in viscosity would be a negative point. However, if nanofluid is used for lubrication, in which oil is usually used, increase in viscosity would be desirable. On the other hand, variations in viscosity due to exercising force are of great importance. Shear rate alteration is the fundamental reason of the rheological behavior changes. Also, there is some other reasons like temperature [25], shearing time [26], nanoparticle loading [27], type of the base fluid and nanoparticle shape [28] can affect the rheological behavior combined with shear rate effect [29]. Rheology of flow studies and liquid and solid transformation are in mechanical stress conditions. It is significant whether nanofluid behavior is Newtonian or non-Newtonian since it can affect

RBF LSSVM

nano-lubricant performance and thus the engine performance. Determining nanofluids rheological behavior has been investigated in a few studies. In Table 1, a summary of studies on nanofluids rheological behavior has been presented.

Table 3 Physicochemical property of cupric oxide (CuO) nanopowders. Parameter

Value

Color Purity SSA Diameter Morphology True density Bulk density

Black 99% 20 m2/g 40 nm Nearly spherical 6.4 g/m3 0.79 g/cm3

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The prediction of nanofluids physiochemical properties is important since it can eliminate the need to repetition of experiments and provide the condition for progress of material physics sciences. In the last decade, utilizing software methods for modeling has attracted attention. In the last decade, nanoscience researchers have employed designing a neural network for predicting and modeling nanofluids behavior. A summary of these studies is presented in Table 2. The high production cost of carbon nanofluids that have superior thermal properties in addition to undesirable properties of oxide nanofluids which are cheap and available has encouraged researchers to combine these two types of particles. Hybrid nanofluids has a practical combination of superior properties and reasonable cost and can be introduced as a new generation of practical nanofluids. Research in resources shows that investigating rheological properties of these nanofluids has not been conducted in a systematic and serious way so far, and a specific and practical model of rheological properties and nano-lubricant suspension for engineering applications has not been presented. So, in the present study, viscosity of hybrid nano-lubricant including nanoparticles of copper oxide (CuO) and multi walled carbon nanotube (MWCNTs) dispersed in engine oil has been studied. The effect of volume fraction of CuO-MWCNT nanoparticles and variations of temperature and shear rate on the viscosity of CuO-MWCNT/SAE40 hybrid nano-lubricant has been investigated and good results have been obtained. In order to increase the practical capabilities of this nano-lubricant, the modeling of viscosity by using the proposed

Table 4 Physicochemical characteristics of MWCNTs. Parameter

Value

Color Purity

Black >95 wt% (carbon nanotubes) (from TGA & TEM)>97 wt% (carbon content) 50 lum (TEM) 5–15 nm (from HRTEM, Raman) 3–5 nm <1.5 wt% (TGA) 1500 W/m K >100 s/cm 0.27 g/cm3 2.1 g/cm3 >233 m2/g (BET) CVD

Length Outside diameter Inside diameter Ash Thermal conductivity Electrical conductivity Tap density True density SSA Manufacturing method

Table 5 Engine oil (SAE40) characteristics. Property

Value

Density at 60 °F (15.6 °C) Kinematic viscosity at 100 °F (38 °C) Kinematic viscosity at 210 °F (99 °C) Viscosity index CCS viscosity at 13 °F (25 °C) Flash point Pour Point Sulfated ash Neutralization no. (TBN-E)

827 kg/m3 108.5 cSt 15.4 cSt 149 6270 cP 220 °C 33 °C 0.86% 7.1

(a)

Functionalized COOH-MWCNT

Lin (Counts)

150

100

50

0 20

(b)

40

60

80

2 Theta-scale

1000

CuO (40 nm)

Lin (Counts)

800

600

400

200

0

20

40

60

2 Theta scale Fig. 1. XRD pattern and TEM analysis for (a) MWCNTs and (b) CuO nanoparticles.

80

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MWCNT

CuO nanoparticles

Fig. 2. Photograph of CuO nanoparticles and MWCNTs, SAE40 and nano-lubricant samples.

wMWCNT

þ wCuO

qMWCNT qCuO u ¼ wMWCNT wSAE40 wCuO qMWCNT

Fig. 3. Comparison between EG viscosity data of Zyla et al. study and this study.

correlation and artificial neural network were considered. The results of this research can be useful for lubricating and designing systems that require high viscosity in high temperatures.

2. Experimentation Hybrid nano-lubricant was prepared by dispersing copper oxide (CuO) nanoparticles and multi walled carbon nanotube (MWCNT) in SAE40 oil. These particles were used with proportions of 70– 30%. Properties of particles and SAE40 oil have been presented in Tables 3–5. The required amounts of particles were estimated by Eq. (1).

þq

CuO

þq

ð1Þ

SAE40

In Fig. 1, a XRD pattern and the analysis of Transitional Electron Microscope (TEM) of CuO particles and MWCNTs are shown. According to the figure, diameter of CuO nanoparticles was 40 nm and the internal and external diameters of carbon nanotube were 3–5 and 5–15 nm, respectively. First, CuO nanoparticles and MWCNTs were weighed by a digital scale with precision of 0.001 g. Then particles were mixed with SAE40. The obtained solution was stirred for one hour. Ultrasonic stirrer (produced by KIMIA NANODANESH COMPANY in Iran) was used for six hours with 1200 W and frequency of 20 Hz. The experimentation process was as follows: CuO and MWCNT powders were mixed with each other, finely. No reposition was seen in the mixture. Then, the powder mixture was added to the base oil in several times and stirred after that until an integration can be observed (now, the nanofluid surely will have a long time to be a continuous integration). This helped the powders and base oil combine very well, thus the necessary power and time of sonication decrease. Next, the nano-lubricant was sonicated to break the agglomerations between the particles. Due to preventing harm to the device, the sonication was nonconsecutive. It was done at various time periods as well as temperature control (preventing temperature increment). Nano-lubricant relaxation and resting the device was done after 10 min sonication. Because temperature control was difficult and nano-lubricant stability, surfactant was added to nano-lubricant proportionate to nanoparticle volume fraction. Some samples of SAE oil, CuO nanoparticles, MWCNT and hybrid nano-lubricant after a week are shown in Fig. 2. As can be seen in the figure, none of the nano-lubricant samples have sedimentation or agglomeration after this duration. The viscosity of pure oil and hybrid nano-lubricant in solid volume fraction of 0.0625–1% was measured. The experiments were

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M.A. Moghaddam, K. Motahari / Applied Thermal Engineering 123 (2017) 1419–1433 Table 6 Part of the data obtained from the experiments. Solid volume fraction (%) 1

0.75

0.5

0.25

0.125

0.0625

0

T = 30 °C 1333.3 2666.6 3999.9 5333.2 6666.5

322 314.1 310 306.1 302.6

283 277.5 273.1 270.5 267.4

281 275.6 271.9 269.1 266.2

279 274.7 271.3 268.6 265.9

272 266.2 262.5 259.7 256.5

259 253.1 250.6 246.6 243.4

249 244.7 241.9 239.5 237

T = 40 °C 2666.6 3999.9 5333.2 6666.5 7999.8

170.6 168.1 165.9 164.6 163.8

150.9 149.4 147.2 146.6 144.7

150 148.7 146.7 145.1 143.8

143.4 141.9 140.2 139.1 137.5

143.4 141.3 139.7 138.8 137.5

137.8 136.9 135.5 133.9 132.5

130.6 129.8 128.3 127.2 126.2

T = 50 °C 2666.6 3999.9 5333.2 6666.5 7999.8

104.1 100.6 98 97.1 96.6

88.1 87.2 86.3 85.3 84.6

86.9 85.8 85.1 84.1 83.6

83.8 82.5 82.9 80.9 80.1

83.1 82.5 81.4 80.3 79.6

80.6 79.7 78.8 77.8 77.1

76.3 75.9 75 74.4 73.7

of shear rate on viscosity decreases, in higher temperatures the effect of shear rate on viscosities decreases and viscosity data of the two studies have been closer to each other. In order to minimize repeatability effect, the experiments were repeated in all temperatures, concentrations and different shear rates and the average data were calculated. The viscosity data are presented in Table 6.

o

30

T= 25 C T= 30 oC T= 35 oC o T= 40 C o T= 45 C T= 50 oC

DVE (%)

20

3. Presentation of results 3.1. The effects of concentration and temperature on dynamic viscosity

10

0 0

0.2

0.4

0.6

0.8

1

Solid volume fraction (%) Fig. 4. Dynamic viscosity enhancement versus solid volume fraction.

conducted in shear rates of 666.5–9331 s1 and temperatures of 25–50 °C. For this purpose, Brookfield viscometer with precision and repeatability of ±1% and ±0.2% was used. It is noteworthy that sonication and viscosity measurement were firstly performed on 1 vol.%. After that, specified base fluid was added to the 1 vol.% nano-lubricant. This caused 0.75 vol.% nano-lubricant preparation. Subsequent concentrations were prepared by this procedure. Due to this preparation method, lower concentrations can be sonicated and made stable easier; also, this is more economical.

According to Fig. 4, dynamic viscosity enhancement (DVE) has not changed greatly with an increase in temperature, while DVE has a different behavior in different solid volume fraction. With increasing solid volume fraction from 0.0625% to 0.125% and also from 0.75% to 1%, DVE gradient has greatly increased. According to the figure, in solid volume fraction 1%, the viscosity of hybrid nano-lubricant has been obtained 29.47% higher than that of pure oil. This increase can be applied in industries which require a high viscosity. 3.2. Rheological behavior investigation In Fig. 5, shear tension of hybrid nano-lubricant and pure oil has been shown in terms of shear rate. This figure has been drawn in different solid volume fractions and temperatures. In order to determine nano-lubricant behavior (Newtonian, non-Newtonian or Bingham), two general relations are used. For this purpose, Ostwald de Waele relationship and HerschelBulkley model has been used. These two relations are defined as follows:

2.1. Measurements accuracy

sOW ¼ mc_ n

ð2Þ

The first experiment was conducted on EG fluids in ambient temperature for the calibration. The obtained viscosity data have been compared with the results of study by Zyła et al. [48] and shown in Fig. 3. According to the figure, the viscosities of this study have a good agreement with Zyla viscosity data. The difference observed between the data can be due to the fact that the shear rates selected in Zyla’s study are different from the shear rates in this study. As will be mentioned later, since the effect

sHB ¼ sy þ K c_ t

ð3Þ

In these relations, n shows power law index, m shows consistency index, t and K are the parameters related to structure and sy shows yield stress. Different types of behavior that fluids can show have been shown in Fig. 6. In order to determine the hybrid nano-lubricant behavior precisely, these two relations have been adjusted with experimental

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=0.25%

T=25oC T=30oC o T=35 C T=40oC T=45oC T=50oC

2500

T=25oC T=30oC o T=35 C o T=40 C T=45oC T=50oC

2500

Shear stress (Pa)

Shear stress (Pa)

2000

=1%

3000

1500

1000

2000

1500

1000 500

0

500

0

2000

4000

6000

8000

0

10000

0

2000

Shear rate (1/s) 2500

T=25oC T=30oC T=35ooC T=40oC T=45oC T=50 C

SAE40 Pure oil

1500

1000

500

=0.125%

2500

8000

T=25oC T=30oC o T=35 C T=40oC T=45oC T=50oC

2000

Shear stress (Pa)

Shear stress (Pa)

6000

Shear rate (1/s)

2000

0

4000

1500

1000

500

0

2000

4000

6000

8000

10000

0

0

Shear rate (1/s)

2000

4000

6000

8000

10000

Shear rate (1/s)

Fig. 5. Shear stress in terms of shear rate at various solid volume fractions and temperatures.

data, and the quality of their adjustment has been compared with each other and presented in Tables 7 and 8. These two tables clearly show that Ostwald de Waele relationship shows changes in shear tension in terms of shear rate of hybrid nano-lubricant more precisely. This process shows that hybrid nano-lubricant is a non-Newtonian fluid and follows power-law fluid. In order to obtain the indices of Ostwald de Waele relationship, the logarithm of the two sides of the relationship can be taken and the indices can be calculated:

LnðsÞ ¼ LnðmÞ þ nLnðc_ Þ

ð4Þ

For example, the results obtained from the relationship above, for pure oil and nano-lubricant with solid volume fraction 1% are shown in Fig. 7. In all solid volume fractions and temperatures, the two indices of ‘n’ and ‘m’ have been calculated by logarithmic method and presented in Tables 9 and 10, respectively. By considering the values of ‘n’, hybrid nano-lubricant and pure oil in all solid volume fractions and temperatures are nonNewtonian and shear thinning. Adding MWCNT and CuO to base oil leads to instability in oil structure. As a result, intermolecular connections of base oil break and the particles between oil layers play the role of an intermediary. On the other hand, increasing

shear rate weakens these connections. Therefore, formation of thinning shear behavior of hybrid nano-lubricant would not be far-fetched. In Fig. 8, changes in ‘n’ in terms of solid volume fraction have been shown. According to the figure, with increasing temperature, ‘n’ decreases. On the other hand, increasing solid volume fraction from 0 to 0.25% does not have a noticeable effect on ‘n’. But increasing solid volume fraction from 0.5% to 1% decreases ‘n’. In summary, with increasing temperature and solid volume fraction, nano-lubricant tends more to be nonNewtonian. In temperature 50 °C and solid volume fraction 1%, the greatest deviation of nano-lubricant from Newtonian behavior is observed. In Fig. 9, the effect of temperature and solid volume fraction on ‘m’ has been shown. According to Ostwald de Waele relationship, fluid apparent viscosity is defined as follows:

lApp ¼ mc_ n1

ð5Þ

Changes in ‘m’ have a direct effect on viscosity. Therefore, with increasing m, viscosity increases. Also, increasing concentration up to 0.25 does not have a noticeable effect on m. However, in solid volume fractions higher than 0.5%, ‘m’ increases and this increase is greater in lower temperatures. On the other hand, increasing

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Fluid behaviors

Newtonian Fluid

Shear rate

Non-Newtonian Fluid

Time Dependent Viscosity

Time Independent Viscosity

Bingham

Dilatant (Shear Thickening)

Rheopecc

Thixotropic

Newtonian

Bingham Plasc

Bingham Pseudoplasc

Pseudoplasc (Shear g) Thinning)

Fig. 6. Different types of fluid behaviors.

Table 7 R-squared value of Ostwald de Waele equation fitted on shear stress-shear rate diagram. T (°C)

25 30 25 40 45 50

Solid volume fraction (%) 1

0.75

0.5

0.25

0.125

0.0625

0

1 1 1 1 0.9999 0.9998

1 1 1 1 1 1

1 1 1 0.9999 1 1

1 1 1 1 0.9987 0.9995

1 1 1 1 0.9999 0.9999

1 1 1 0.9999 1 1

1 1 1 1 1 0.9999

Table 8 R-squared value of Herschel-Bulkley equation fitted on shear stress-shear rate diagram. T (°C)

25 30 25 40 45 50

Solid volume fraction (%) 1

0.75

0.5

0.25

0.125

0.0625

0

0.9890 0.9873 0.9899 0.9788 0.9679 0.9444

0.9891 0.9888 0.9899 0.9795 0.9743 0.9500

0.9895 0.9888 0.9899 0.9796 0.9741 0.9518

0.9895 0.9891 0.9899 0.9796 0.9751 0.9642

0.9895 0.9899 0.9899 0.9798 0.9789 0.9709

0.9895 0.9899 0.9899 0.9897 0.9798 0.9621

0.9900 0.9912 0.9874 0.9852 0.9720 0.9564

temperature decreases ‘m’. This decrease in solid volume fraction 1% is slightly less. 3.3. Proposed correlation To obtain a new correlation, curve fitting was conducted on viscosity experimental data. In order to increase the accuracy of the proposed correlation, in each temperature, a correlation in terms of solid volume fraction has been proposed. The general view of the correlation is similar for all temperatures while constant coefficients change in each temperature. The general view of relative viscosity correlation is as follows:

lnf ¼ a0 þ a1 u expðuÞ þ a2 u2 þ a3 u3 lbf

ð6Þ

The obtained constants for each temperature are presented in Table 11. This correlation is able to predict hybrid nano-lubricant viscosity in temperatures 25–50 °C and in solid volume fraction 0.0625– 1% with particle sizes mentioned in Section 2. In Fig. 10, theoretical models such as Wang et al. [49], Einstein [50], Lundgren [51] and Birkman [52] have been used to predict hybrid nano-lubricant viscosity. As is evident in the figure, these models had great errors in prediction of viscosity data. Brinkman model has been presented for fluids with solid volume fraction up to 4%; that is, strong fluids

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T=25oC o T=30 C o T=35 C T=40oC T=45oC o T=50 C

7.5

7.5

7

Ln ( (Pa) )

Ln ( (Pa) )

7

6.5

6

6.5

m=0.2303 n=0.962

m=0.423 n=0.9622

m=0.1848 n=0.9585

m=0.2634 n=0.9524

m=0.4601 n=0.9626

6

m=0.1957 n=0.9498

m=0.6671 n=0.9488

SAE40 Pure oil

T=25oC o T=30 C o T=35 C T=40oC T=45oC o T=50 C

m=0.1494 n=0.9511

m=0.3123 n=0.9609 m=0.1804 n=0.9298

5.5

m=0.3094 n=0.9701

m=0.1081 n=0.9584

5.5 6.5

7

7.5

8

8.5

9

7

7.5

8

-1

8.5

9

-1

Ln ( (s ) )

Ln ( (s ) )

Fig. 7. Shear stress logarithm versus shear rate logarithm at the volume fractions of 0% and 1% and different temperatures. Table 9 Power law indices at all solid volume fractions and temperatures. T (°C)

Solid volume fraction (%)

25 30 25 40 45 50

1

0.75

0.5

0.25

0.125

0.0625

0

0.9488 0.9622 0.9609 0.962 0.9498 0.9298

0.9629 0.9652 0.9683 0.9628 0.9583 0.9516

0.9706 0.967 0.9712 0.9608 0.9592 0.9538

0.9773 0.9706 0.966 0.9625 0.944 0.9493

0.9713 0.9645 0.9627 0.9625 0.9625 0.9472

0.9757 0.9678 0.959 0.9643 0.9589 0.9469

0.9626 0.9701 0.9524 0.9585 0.9511 0.9584

Table 10 Consistency indices at all solid volume fractions and temperatures. T (°C)

Solid volume fraction (%)

25 30 25 40 45 50

1

0.75

0.5

0.25

0.125

0.0625

0

0.6671 0.423 0.3123 0.2303 0.1957 0.1804

0.5199 0.3641 0.2594 0.2029 0.1602 0.1319

0.486 0.357 0.2518 0.205 0.1577 0.1275

0.4606 0.3455 0.2517 0.1932 0.1745 0.1279

0.4663 0.3518 0.2578 0.1928 0.1468 0.1292

0.4197 0.3392 0.2568 0.1833 0.1461 0.1254

0.4601 0.3094 0.2634 0.1848 0.1494 0.1081

1

0.98

Power law index

0.99

Power law index

1

SAE40 Pure oil =0.0625% =0.125% =0.25% =0.5% =0.75% =1%

0.97 0.96 0.95

o

T=25 C T=30oC T=35oC o T=40 C T=45oC T=50oC

0.975

0.95

0.94 0.93 20

0.925

25

30

35

40

Temperature ( oC )

45

50

55

0

0.2

0.4

0.6

0.8

Solid volume fraction (%)

Fig. 8. Power law index in terms of solid volume fraction and temperatures.

1

1427

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0.8

1

SAE40 Pure oil =0.0625% =0.125% =0.25% =0.5% =0.75% =1%

T=25 C T=30oC o T=35 C o T=40 C o T=45 C T=50oC

n

0.8

0.7

Consistency index (mPa.s )

Consistency index (mPa.sn)

o

0.6

0.4

0.6 0.5 0.4 0.3 0.2

0.2 0.1

0 0

0.2

0.4

0.6

0.8

0 20

1

25

30

35

40

45

50

55

Temperature ( oC )

Solid volume fraction (%)

Fig. 9. Consistency index in terms of solid volume fraction and temperatures.

Table 11 Correlation constants at each temperature. Temp. (°C)

a0

a1

a2

a3

R2

25 30 35 40 45 50

0.9554 0.977 0.9985 1.016 1.017 1.017

1.211 1.014 0.6208 0.548 0.5723 0.6471

3.616 3.029 1.791 1.569 1.667 1.886

0.6647 0.5729 0.3798 0.3445 0.3859 0.4045

0.9917 0.9964 0.983 0.9838 0.9806 0.9963

that have similar conditions to those of oil. It is obvious in the figure that the deviation of Brinkman model has been less than that of the other models. The proposed model has estimated viscosity experimental data with a good precision. 3.4. Evaluation of viscosity sensitivity to concentration As expected, by adding nanoparticles to oil, the viscosity of oil increases. On the other hand, adding more nanoparticles to nano-

B %Sensitivity ¼ @

3.5 3

1.2

1.15

1.1

1.05

1

2.5

0.25

0.5

1

After Change

C  1A  100

ð7Þ

Base Condition

0.75

1

T=25 °C T=30 °C T=35 °C T=40 °C T=45 °C T=50 °C

2 1.5 1 0.5 0

0




lnf




lnf



Sensitivity of viscosity (%)

Relative viscosity

1.25

0

T=30 (oC)

Experimental viscosity Proposed correlation Lundgren model Brinkman model Wang et al model Einstein model

1.3

lubricant does not have a similar effect on solid volume fraction viscosity. In other words, the viscosity of each solid volume fraction has a unique sensitivity against solid volume fraction increase. In this section, the sensitivity of different solid volume fraction of nano-lubricant to adding 10% nanoparticle to them has been calculated. By using the following equation, the sensitivity of hybrid nano-lubricant to change in conditions is calculated:

0.0625

0.125

0.25

0.5

0.75

Solid volume fraction (%)

Solid volume fraction (%) Fig. 10. Comparing experimental data with theoretical models.

Fig. 11. Sensitivity of nano-lubricant versus solid volume fraction at various temperatures.

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Entering relave viscosity data

Dividing data to Training data, Validaon data and Test data

Network training using various neurons

Selecng the opmal network considering the minimum MSE and in the absence of over-fing

Fig. 12. The procedure of designing artificial neural network with MLP algorithm.

Specify number of hidden layers and neurons

Calculate MSE, Rsquared, %AARD

Enter inputs

Start to train inputs

Desired error

Specify the number of training data

Best structure achieved

Finish

Comparison of predicted and experimental data Unfavorable error

Fig. 13. The manner of optimal structure selection.

Table 12 Outputs of various configurations of ANN. Case num.

Num. of hidden neurons

R-Squared

MSE

AARD (%)

Transfer function

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

[1] [1] [2] [2] [3] [3] [4] [4] [1 1] [2 2] [3 3] [4 4] [5 4] [4 5] [5 5] [6 6]

0.2362 0.8914 0.2361 0.9701 0.2381 0.9712 0.2390 0.9862 0.9081 0.9804 0.9876 0.9883 0.9966 0.9898 0.9996 0.9951

0.0047 6.7446e04 0.0047 1.8583e04 0.0047 1.7885e04 0.0047 8.5773e05 5.7079e04 1.2204e04 7.6924e05 7.2620e05 2.0819e05 6.3101e05 2.2346e05 3.8731e05

4.5583 0.0757 4.5409 0.0747 4.5388 0.0724 4.5817 0.0300 0.1365 0.0194 0.0324 0.0650 0.0055 0.2347 0.0182 0.0183

[Logsig] [Tansig] [Logsig] [Tansig] [Logsig] [Tansig] [Logsig] [Tansig] [Logsig Logsig] [Logsig Logsig] [Logsig Logsig] [Logsig Logsig] [Logsig Logsig] [Logsig Logsig] [Logsig Logsig] [Logsig Logsig]

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6

6.0E-03

All data

MSE %AARD

5

5.0E-03

4

3.0E-03 2

MSE

AARD (%)

4.0E-03 3

2.0E-03 1

Proposed case

1.0E-03

0

0.0E+00

-1 0

2

4

6

8

10

12

14

16

18

Case num. Fig. 14. The performance of MSE and %AARD for all data.

In this equation, After Change refers to viscosity after changing conditions (adding 10% nanoparticle) and Base Condition refers to viscosity before changing conditions. According to Fig. 11, the general view of diagrams shows that higher solid volume fractions have a greater sensitivity. As is evident in the figure, by adding solid volume fraction, the viscosity sensitivity of temperatures 35–50 °C has increased. Viscosity change and its sensitivity due to change in conditions can affect the way in which the nanofluid is used. Specially in the systems operating with high changes in temperature such as car engines, the investigation of sensitivity in form of viscosity change due to temperature increase or due to nanolubricant solid volume fraction change must be considered by the system designer. 4. Artificial neural network In this study, 447 temperatures, volume fractions and shear rates for neural network input and 149 data of viscosity of hybrid nano-lubricant as goal have been considered. The designed neural network has been planned by using multilayer perceptron algorithm. The function of this algorithm is in a way that by receiving input data and training neurons based on a percentage of inputs and determining weight and bias for them, it produces outputs

Inputs

Hidden layer

Fig. 16. Performance of the artificial neural network training, testing and validation processes.

that is obtained after testing and error validity. In case of difference between this error and the predicted error by user, weight and bias change and training is repeated until network reaches the determined error. This algorithm generally includes three layers of inputs, hidden layer and outputs. The hidden layer can be made up of several layers with different numbers of neurons. This point controls the performance of neural network. The flowchart of designing process of neural network has been shown in Fig. 12. To obtain the best and optimum structure for neural network, the method depicted in Fig. 13 has been adopted. 16 samples from different designs were taken. The results are shown in Table 12. Choosing the most appropriate network was performed by investigating the values of MSE, R-squared and Average Absolute Relative Deviation (AARD). Their correlations have been presented as follows:

MSE ¼

N 1X ðl j  lnf jpred Þ2 N i¼1 nf EXP:

Hidden layer

ð8Þ

Output layer

ANN output

Purelin funcon

Relave viscosity

∑ ∑

Temperature

∑ Shear rate

Solid volume fracon

∑

∑

∑

∑

∑

∑ Bias

Bias Fig. 15. Schematic of the designed ANN.

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1.3

ANN Prediction

was Tansig. Also, the function of output layer was purelin linear function. These functions are defined as follows:

Equality line All data

1.2

1.1

1 1

1.1

1.2

1.3

Experimental data Fig. 17. Comparison between experimental data and ANN outputs.

PN 2

R ¼1

AARD% ¼

i¼1 ð

lnf jEXP:  lnf jpred: Þ2i 2 i¼1 ðlnf jEXP: Þi

ð9Þ

PN




N
100 X
lnf jpred:  lnf jExp:



N i¼1
lnf jExp:

ð10Þ

tan sigðnÞ ¼ 2=ð1 þ expð2nÞÞ  1

ð11Þ

purelinðnÞ ¼ n

ð12Þ

The structure of the designed neural network is shown in Fig. 15. In Fig. 16, MSE of train, test and validation in terms of the number of iterations has been shown. For the designed neural network, 70% of input data were trained randomly. As shown in the figure, as the number of iterations increases, the MSE value of all three operations decreases. For training the network, a goal for neural network has been considered. According to the figure, in iteration number 128, training the network was able to achieve the goal. In this iteration, MSE value was obtained 0.000002081. In Fig. 17, the performance of neural network for estimation of hybrid nano-lubricant viscosity has been shown. According to the figure, all the predicted viscosity data have been located on bisector or in its vicinity. So the maximum error has been calculated around 1.93%. In Fig. 18, histogram and error values for prediction of hybrid nano-lubricant viscosity have been shown. As seen in the figure, the maximum error is located in the vicinity of zero. It is observed that maximum values of error are located around0.7%. This error value shows that viscosity estimation by neural network has a good precision. 5. ANN and correlation accuracy

i

where lnf shows nano-lubricant relative viscosity and N shows the number of data. In Fig. 14, AARD and MSE of all data for different samples have been shown. According to the figure, in the samples including two hidden layers (after sample 9), increasing neurons has led to decreasing MSE and AARD. So in sample 13, MSE and AARD have reached their minimum amount. In next samples, increasing neuron has not caused a noticeable change in neural network performance. Therefore, for designing neural network, two hidden layers were used. One of the layers included five neurons and the other one had four neurons and the transfer function of both of them

In Fig. 19, the relative viscosity that predicted by ANN method and correlation have been compared with data of experimental viscosity. As can be seen, ANN and correlation have predicted viscosity of hybrid nano-lubricant with a good accuracy. Despite in ANN method the shear rate has been considered, the outputs of this method have higher resolution in viscosity prediction. As can be seen, at T = 25 °C and T = 30 °C, there is no increase or decrease in viscosity when volume fraction increases from 0.25% to 0.75%. This event is clearly depicted in Fig. 20. This figure shows dynamic viscosity of nano-lubricant versus solid volume fraction at certain shear rate. As can be seen, the concentrations between 0.25 and 0.75 vol.% at all temperatures (the dot-dashed box) have

0.04

0.02

Error

+0.7%

0

-0.7%

-0.02

-0.04 0

25

50

75

Data num. Fig. 18. Histogram and error of ANN predictions versus number of data.

100

125

150

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M.A. Moghaddam, K. Motahari / Applied Thermal Engineering 123 (2017) 1419–1433

o

o

T=25 C

Relative viscosity

Relative viscosity

1.3

1.2

1.1

T=30 C

1.3

Experimental viscosity Correlation Outputs ANN Outputs

Experimental viscosity Correlation Outputs ANN Outputs

1.2

1.1

1

0

0.2

0.4

0.6

0.8

1

1

0

0.2

Solid volume fraction (%)

0.6

0.8

Experimental viscosity Correlation Outputs ANN Outputs

Experimental viscosity Correlation Outputs ANN Outputs

Relative viscosity

1.3

1.2

1.1

1.2

1.1

1 0

0.2

0.4

0.6

0.8

1 0

1

0.2

Solid volume fraction (%)

0.4

0.6

0.8

o

Experimental viscosity Correlation Outputs ANN Outputs

1.3

Relative viscosity

Relative viscosity

T=50 C

Experimental viscosity Correlation Outputs ANN Outputs

1.3

1

Solid volume fraction (%) T=45oC

1.2

1.1

1

1

T=40oC

T=35oC

1.3

Relative viscosity

0.4

Solid volume fraction (%)

1.2

1.1

0

0.2

0.4

0.6

Solid volume fraction (%)

0.8

1

1

0

0.2

0.4

0.6

Solid volume fraction (%)

Fig. 19. Experimental data of relative dynamic viscosity compared to predictions of the ANN.

0.8

1

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M.A. Moghaddam, K. Motahari / Applied Thermal Engineering 123 (2017) 1419–1433

T=25oC T=30oC o T=35 C T=40oC T=45oC o T=50 C

Dynamic viscosity (mPa.s)

500

Shear rate (s -1) = 6666.5

400

300

200

100

0

0.2

0.4

0.6

0.8

1

Solid volume fraction (%) Fig. 20. Dynamic viscosity versus solid volume fraction at various temperatures.

6. Conclusion In this project, rheological changes of hybrid nano-lubricant were experimentally modeled and evaluated. The mixture of 70% nanoparticles of CuO and 30% MWCNT was dispersed in SAE40 engine oil. The viscosity of solid volume fractions 0625.0–1% of nano-lubricant at temperatures 25–50 °C and different shear rates was measured. The results showed that nano-lubricant viscosity in 1 vol.% is 29.47% greater than viscosity of pure oil. By investigating the effect of shear rate on viscosity, it turned out that hybrid nanolubricant and pure oil follow Ostwald de Waele relationship and they have non-Newtonian behavior with tendency of shear thinning. A new relationship in terms of solid volume fraction for each temperature was proposed. The sensitivity of hybrid nanolubricant to concentration increase was calculated. For viscosity prediction, a MLP network was proposed which had two hidden layers. The first layer included 5 neurons and the second one had 4 neurons. Comparison between ANN predictions and correlation outputs and experimental data revealed that the designed ANN can accurately predict the viscosities over wide ranges of operating parameters. Acknowledgements

MOD of correlation outputs (%)

2

2 +1.75 %

0

0

-1.75 %

-2

-2

-4

0

10

20

30

MOD of ANN outputs (%)

4

4

-4

Data num. Fig. 21. MOD of correlation and ANN calculated by Eq. (13).

no significant viscosity enhancement. The reason is that in the first three concentrations the nano-lubricant is shocked under the new condition, so the viscosity increases. For the next three concentrations, there is an interdiction-like force between molecules and nanoparticles against cohesion increasing. Finally, at the last concentration or the highest concentration, the interdiction-like force is broken down and the viscosity enhancement resumes. Also, it can be seen in Fig. 9 that at mentioned concentrations the consistency index was almost constant. This illustrates that the viscosity can be constant. Using Eq. (13), margin of deviation (MOD) predicted data by ANN and correlation are calculated and displayed in Fig. 21.




MOD ¼ 1 

lrel
Pred
lrel
Exp

ð13Þ

As can be seen in Fig. 21, the average MOD of correlation outputs is higher than the MOD of ANN output. The average MOD of ANN and correlation are approximately obtained ±0.5% and ±1%, respectively. This result demonstrated that the outputs of ANN method are more adaptable with experimental data.

Authors acknowledge funding support from the Chemical Engineering Department, Faculty of Engineering, Arak University for the financial supports providing the equipment and research implementation to perform the sample preparation and also helping to complete the paper in time. References [1] G. Wang, J. Zhang, Thermal and power performance analysis for heat transfer applications of nanofluids in flows around cylinder, Appl. Therm. Eng. 112 (2017) 61–72, http://dx.doi.org/10.1016/j.applthermaleng.2016.10.008. [2] M.K. Abdolbaqi, W.H. Azmi, R. Mamat, K.V. Sharma, G. Najafi, Experimental investigation of thermal conductivity and electrical conductivity of bioglycol water mixture based Al2O3 nanofluid, Appl. Therm. Eng. 102 (2016) 932–941, http://dx.doi.org/10.1016/j.applthermaleng.2016.03.074. [3] M. Afrand, K.N. Najafabadi, M. Akbari, Effects of temperature and solid volume fraction on viscosity of SiO2-MWCNTs/SAE40 hybrid nanofluid as a coolant and lubricant in heat engines, Appl. Therm. Eng. 102 (2016) 45–54, http://dx.doi. org/10.1016/j.applthermaleng.2016.04.002. [4] G.A. Oliveira, E.M. Cardenas, Contreras, E.P. Bandarra Filho, Experimental study on the heat transfer of MWCNT/water nanofluid flowing in a car radiator, Appl. Therm. Eng. 111 (2017) 1450–1456. [5] M. Xing, J. Yu, R. Wang, Thermo-physical properties of water-based singlewalled carbon nanotube nanofluid as advanced coolant, Appl. Therm. Eng. 87 (2015) 344–351, http://dx.doi.org/10.1016/j.applthermaleng.2015.05.033. [6] M. Mehrali, E. Sadeghinezhad, M.A. Rosen, S. Tahan Latibari, M. Mehrali, H.S.C. Metselaar, S.N. Kazi, Effect of specific surface area on convective heat transfer of graphene nanoplatelet aqueous nanofluids, Exp. Therm. Fluid Sci. 68 (2015) 100–108, http://dx.doi.org/10.1016/j.expthermflusci.2015.03.012. [7] M.A. Akhavan-Behabadi, M. Nasr, S. Baqeri, Experimental investigation of flow boiling heat transfer of R-600a/oil/CuO in a plain horizontal tube, Exp. Therm. Fluid Sci. 58 (2014) 105–111, http://dx.doi.org/10.1016/ j.expthermflusci.2014.06.013. [8] S. Halelfadl, P. Estellé, T. Maré, Heat transfer properties of aqueous carbon nanotubes nanofluids in coaxial heat exchanger under laminar regime, Exp. Therm. Fluid Sci. 55 (2014) 174–180, http://dx.doi.org/10.1016/ j.expthermflusci.2014.03.003. [9] S. Halelfadl, T. Maré, P. Estellé, Efficiency of carbon nanotubes water based nanofluids as coolants, Exp. Therm. Fluid Sci. 53 (2014) 104–110, http://dx.doi. org/10.1016/j.expthermflusci.2013.11.010. [10] M. Khoshvaght-Aliabadi, F. Hormozi, A. Zamzamian, Experimental analysis of thermal-hydraulic performance of copper-water nanofluid flow in different plate-fin channels, Exp. Therm. Fluid Sci. 52 (2014) 248–258, http://dx.doi.org/ 10.1016/j.expthermflusci.2013.09.018. [11] D. Madhesh, R. Parameshwaran, S. Kalaiselvam, Experimental investigation on convective heat transfer and rheological characteristics of Cu-TiO2 hybrid nanofluids, Exp. Therm. Fluid Sci. 52 (2014) 104–115, http://dx.doi.org/ 10.1016/j.expthermflusci.2013.08.026. [12] A.A. Altohamy, M.F. Abd Rabbo, R.Y. Sakr, A.A.A. Attia, Effect of water based Al2O3 nanoparticle PCM on cool storage performance, Appl. Therm. Eng. 84 (2015) 331–338, http://dx.doi.org/10.1016/j.applthermaleng.2015.03.066.

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