Journal of Thermal Analysis and Calorimetry https://doi.org/10.1007/s10973-017-6895-y
Prediction of rheological behavior of MWCNTs–SiO2/EG–water nonNewtonian hybrid nanofluid by designing new correlations and optimal artificial neural networks Hamed Eshgarf1 • Nima Sina2 • Mohammad Hemmat Esfe3 • Farhad Izadi2 • Masoud Afrand2 Received: 21 August 2017 / Accepted: 3 December 2017 Akade´miai Kiado´, Budapest, Hungary 2017
Abstract In this paper, at the first, new correlations were proposed to predict the rheological behavior of MWCNTs–SiO2/EG–water non-Newtonian hybrid nanofluid using different sets of experimental data for the viscosity, consistency and power law indices. Then, based on minimum prediction errors, two optimal artificial neural network models (ANNs) were considered to forecast the rheological behavior of the non-Newtonian hybrid nanofluid. One hundred and ninety-eight experimental data were employed for predicting viscosity (Model I). Two sets of forty-two experimental data also were considered to predict the consistency and power law indices (Model II). The data sets were divided to training and test sets which contained respectively 80 and 20% of data points. Comparisons between the correlations and ANN models showed that ANN models were much more accurate than proposed correlations. Moreover, it was found that the neural network is a powerful instrument in establishing the relationship between a large numbers of experimental data. Thus, this paper confirmed that the neural network is a reliable method for predicting the rheological behavior of non-Newtonian nanofluids in different models. Keywords Non-Newtonian hybrid nanofluid Rheological behavior Shear rate Experimental correlations Artificial neural network
Introduction Conventional fluids such as water, ethylene glycol or a mixture of ethylene glycol, and water are used in many industries as antifreeze agents, especially in heat exchangers and radiators. Due to its low thermal conductivity, this mixture lacks desirable heat transfer efficiency. Compared to such fluids, solid particles have a higher heat transfer coefficient. Therefore, the distribution of solid particles in the base fluid increases the thermal conductivity of the fluid.
& Masoud Afrand
[email protected];
[email protected] 1
Young Researchers and Elite Club, Najafabad Branch, Islamic Azad University, Najafabad, Iran
2
Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
3
Faculty of Mechanical Engineering, Imam Hossein University, Tehran, Iran
Thus, making a suspension of fine solid particles in pure fluids is a new strategy to increase fluid heat transfer properties of the working fluid. However, suspension of particles (metallic, nonmetallic, and polymeric) in the milli- and microscale causes problems such as wear, channel blockage, pipe network erosion, reduced momentum transfer, and increased pressure drop. Instability is also a problem, especially when particles are strongly inclined to settle in the suspension. With advances in nanotechnology, in 1995, Choi [1] in the Oregon Research Institute was the first to use the term ‘‘nanofluids’’ for nanoparticles in a liquid suspension and claimed that such fluids are very different from conventional solid/fluid suspensions and macrofluids both in terms of production and stability and transfer properties. The main difference of nanofluids with conventional suspensions stems from the very small size of dispersed particles (1–100 nm) because many forces that are effective in the macroscale lose their effect in smaller scales and are replaced by inter-molecular forces [2, 3]. It is also clear that adding nanoparticles to the base fluid strongly affects and changes the rheological behavior of the
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fluid [4–8]. Since rheological behavior is an important parameter in determining the pumping power and fluid flow in cooling or heating systems, assessing fluid viscosity is essential [9–11]. In recent years, extensive research has been done on the effect of additives on the viscosity of nanofluids. A number of these studies on nanofluid viscosity are presented in Table 1. These studies have discussed the factors affecting the viscosity and Newtonian or non-Newtonian behavior of nanofluids. Since the experiments for measurement of thermophysical properties of nanofluids are costly, researchers have recently turned to employing computer methods in order to predict nanofluid properties [28–40]. CFD methods are other ways to reduce laboratory costs [41–47]. Inspired by the neural network in the human brain, artificial neural network (ANN) is one of these methods which was developed to further simulate humans using computers and have appropriately advanced so far. For instance, Hojat et al. [28] conducted a numerical study on nonNewtonian fluids and eventually presented a model using experimental results as well as neural network modeling. In their study, they used nanoparticles of c - Al2O3, TiO2, and CuO at different volume fractions of 0.1, 0.2, 0.5, 2.3, and 4% with carboxymethyl cellulose (CMC) of 0.5 mass% as the base fluid at temperatures of 5–45 C. The results indicated that thermal conductivity of the resulting nanofluid was greater than its base fluid and, additionally, the thermal conductivity of the nanofluid increased as the volume fraction increased. Moreover, for
higher concentrations of the nanoparticles, thermal conductivity of the nanofluid increased as the temperature was increased. Ultimately, a neural network model, which was a function of temperature, volume fraction of nanoparticles, and nanofluid thermal conductivity, was presented. The model revealed that the experimental data were consistent with the neural network model and that the Hamilton–Crosser model was acceptable for low volume fractions. Hemmat Esfe et al. [29] used an ANN model to study the heat transfer of MgO nanofluid mixed with water and ethylene glycol with a ratio of 60:40 based on experimental data. Nanofluid properties were measured at different volume fractions of 0.1, 0.2, 0.5, 1, 2, and 3% at temperatures of 20–50 C. The results showed that the ANN model was able to predict thermal conductivity to a great extent and that the results were in good agreement with experimental results. Finally, two correlations were proposed to predict nanofluid thermal conductivity. Ahamadloo and Azizi [30] conducted a research on prediction of thermal conductivity of different nanofluids using ANNs. They considered a five-input ANN model to predict the ratio of thermal conductivity of nanofluid to that of the base fluid for different nanofluids with water, ethylene glycol, and transformer oil as the base fluid. They designed an ANN trained with 766 experimental data obtained from 21 tests. The mean particles’ diameter, volume fraction, thermal conductivity of nanoparticles, and temperature as well as some of the values assigned to both nanoparticle and base fluid were considered as the input to
Table 1 Brief review of previous researches on the viscosity of nanofluids References
Nanoadditives
Base fluid
Temperature range/oC
[12]
TiO2
Water
25
[13]
CuO
Gear oil
10–80
[14]
SiO2
EG:Water
(- 35) to 50
0–10
Newtonian
Nanoadditives concentration/% 5–12 0.5–2.5
Nanofluid behavior Newtonian Non-Newtonian
[15]
CuO
EG:Water
(- 35) to 50
0–6.12
Newtonian
[16]
Ag
Water
50–90
0–0.9
Newtonian
[17] [18]
TiO2 Al2O3 and TiO2
EG EG:Water
10–50 15–40
0–25 1–8
Non-Newtonian Newtonian
[19]
MgO
Water
24–60
0–1
Newtonian
[20]
MWCNT
Water
25–55
0–1
Newtonian
[21]
DWCNT
Water
27–67
0–0.4
Newtonian
[22]
Fe3O4–Ag
EG
25–50
0–0.3
Newtonian
[23]
Fe–CuO
EG:Water
25–50
[24]
Fe3O4
Water
20–55
0–3
Newtonian
[25]
Al2O3–MWCNTs
SAE40
25–50
0–1
Newtonian
[26]
SiO2–MWCNTs
SAE40
25–50
0–1
Newtonian
[27]
ZnO
SAE50
25–50
0–1.5
Newtonian
0.6–1.2 0–0.1 0.25–1.5
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Non-Newtonian Newtonian Non-Newtonian
Prediction of rheological behavior of MWCNTs–SiO2/EG–water non-Newtonian hybrid nanofluid by…
range of 25–50 C at different shear rates. Their results showed that the non-Newtonian behavior of nanofluid follows the power law model at all volume fractions. They reported 198 experimental data in the form of shear stressshear rate as shown in Fig. 1. Knowing that nanofluid has a power law behavior according to Eq. (1), consistency and power law indices were obtained through curve fitting. Results are shown in Fig. 2. s ¼ mc_n ;
ð1Þ
where s and c_ are respectively the shear stress in Pa and shear rate in s-1. Moreover, m and n denote consistency index and the power law index, respectively.
New empirical correlations Model I In this section, a correlation is presented in order to predict the viscosity of nanofluids as a function of volume fraction, temperature, and shear rate using experimental data. The Marquardt–Levenberg algorithm was used to find the constant in the proposed correlation. The proposed correlation with R2 = 0.987 is as follows: lnf ¼ 15:88u0:8514 T 1:189 c_0:5639 ;
ð2Þ
where u is volume fraction in %, T is temperature in C, c_ is shear rate in s-1, and l is viscosity in mPa s. Figure 3 displays the compatibility of the proposed correlation with the experimental data. As observed, some points are on the equality line, while some of them have
700 600 500
Viscosity/mPa s
the network, while the ratio of the thermal conductivity of the respective nanofluid to that of the base fluid was selected as the output. The developed ANN model indicated that prediction of the experimental results was logically consistent with the mean absolute error (MAE) and the coefficient of correlation in training and testing of the data. Afrand et al. [31] experimentally studied the heat transfer of Fe3O4 nanoparticles in water as the base fluid and presented a new correlation and ANN. The sample nanofluid was prepared using a two-stage method by dispersion of Fe3O4 nanoparticles in water with volume fractions of 0.1, 0.2, 0.4, 1, 2, and 3%. The coefficient of thermal conductivity was measured at different temperatures ranging from 20 to 55 C using KD2 software package employed in analysis of thermal properties. Then, using experimental data, a new correlation was proposed for optimal prediction of the ratio of thermal conductivity for a magnetic nanofluid. Ultimately, an ANN was designed for optimal prediction of the ratio of thermal conductivity for a magnetic fluid. According to the experimental results, the maximum increase in the nanofluid thermal conductivity was 90%, occurred at a concentration of 0.3% and temperature of 55 C. The results revealed deviances of 1.5 and 0.5%, respectively, for ANN and the proposed correlation from the measurements. Because of various applications of EG–water mixture (antifreeze), the evaluation of its rheological behavior seems very essential. However, inadequate works have been done on the rheological behavior of non-Newtonian nanofluids. On the other hand, literature review discloses that there is a few works in the field of predicting the viscosity of non-Newtonian nanofluid. In addition, it was found that there is no any reported work about modeling of rheological behavior of MWCNTs–SiO2/EG–water nonNewtonian hybrid nanofluid using artificial neural network. Since the rheological behavior of non-Newtonian nanofluids is influenced by various parameters, modeling it by neural network is attractive. Therefore, for the first time, new correlations have been proposed to predict the rheological behavior of MWCNTs–SiO2/EG–water non-Newtonian hybrid nanofluid using different sets of experimental data for the viscosity, consistency and power law indices. Then, precise and optimal artificial neural networks have been designed to model the rheological behavior of the non-Newtonian hybrid nanofluid.
ϕ = 0.0625% ϕ = 0.25% ϕ = 0.5% ϕ = 0.75% ϕ = 1% ϕ = 1.5% ϕ = 2%
400 300 200
Experimental In the present research, experimental data for hybrid nanofluids that have been previously reported are used. Eshgarf and Afrand [10] measured viscosity of different samples with different volume fractions at the temperature
100
0
50
100
150
200
Data number Fig. 1 Categorized data set from experimental report
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0.6
ϕ = 0.0625% ϕ = 0.25% ϕ = 0.5% ϕ = 0.75% ϕ = 1% ϕ = 1.5% ϕ = 2%
0.4
0.9
0.3
0.2
ϕ ϕ ϕ ϕ
ϕ = 1% ϕ = 1.5% ϕ = 2%
= 0.0625% = 0.25% = 0.5% = 0.75%
0.8
Power law index
Consistency index/Pa sn
0.5
1
0.7 0.6 0.5
0.1
0.4
0 25
30
35
40
45
50
0.3 25
30
Temperature/°C
35
40
45
50
Temperature/°C
Fig. 2 Consistency and power law indices obtained through curve fitting on experimental data
Model II 700
Given that the values of m and n have been reported by Eshgarf and Afrand [10], the Marquardt–Levenberg algorithm for empirical correlations can be used to predict the parameters as a function of temperature and volume fraction. The correlations are provided in Eqs. (3) and (4): 1:083 mnf ¼ 0:02048 þ 2:189exp 0:03327T ; ð3Þ u
Predicted viscosity/mPa s
600 500 400 300
nnf ¼ 0:6868uð0:09060:001474T Þ 0:006267T:
ð4Þ
200 100 0
0
100
200
300
400
500
600
700
Experimental viscosity/mPa s Fig. 3 Comparison between experimental viscosity and that obtained from proposed correlation
considerable distance from the equality line. In fact, because of the large number of experimental data (198 data), it seems that the curve-fitting method is associated with a noteworthy error. Curve fitting becomes more difficult when the number of data increases. In this case, the artificial neural network can be used to predict the viscosity. Thus, in the ‘‘Artificial neural network’’ section, we use ANN modeling to predict the viscosity of the nanofluid by employing temperature, concentration, and shear rate as input variables.
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The accuracy of the proposed correlations can be evaluated using Fig. 4. As seen in this figure, some points are near the equality line, while some of them are far from the equality line. It means that these correlations are not very accurate because of the large number of data in two independent variables including temperature and concentration. In this case, the artificial neural network also can be useful to predict the consistency and power law indices.
Artificial neural network Artificial neural network is a computational model in machine learning to prediction data, and it is based on the biological neural network. It consists of simple processing elements named neurons that can learn and predict the data based on the learning algorithms. In this section, two ANN models have been designed for prediction of viscosity of the nanofluid.
0.6
0.9
0.5
0.8
Power law index (Correlation)
Consistency index (Correlation)
Prediction of rheological behavior of MWCNTs–SiO2/EG–water non-Newtonian hybrid nanofluid by…
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0.1 0.3
0
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Consistency index (Experimental)
Fig. 4 Comparisons between experimental data and that obtained from proposed correlations for m and n
Model I In the Model I, the input data in the artificial neural network consist of temperature, concentration, and shear rate, and the target was viscosity. There were 198 experimental data, in which 40 data considered as test and 158 data considered as train data in the artificial neural network. Calculating the neuron number is important to reach the number on neurons in the hidden layer. The optimal neural network is generated by changing the architecture of different neural networks. In a loop, the number of neurons in the hidden layer changed and the performance of the network is calculated during each step. It should be regarded that the best network selection is based on the two important criteria. Firstly, its performance and secondly its over fitting. Over fitting is a state that the artificial neural network can predict the data only in the trained data, but it fails during predicting data that are not trained. By changing the number of neurons, from 10 to 120, the best network had 12 neurons. In addition, we know that the procedure of generating a neural network is random. Therefore, it is better to apply a certain number of neurons for several times. This method leads to reach a better understanding of the performance of the certain neuron numbers in the neural network, which is called inner iteration. In the current study, the inner iteration is 10 and training algorithm is Marquardt–Levenberg. The flowchart of the model is presented in Fig. 5. In this model, the activation function in the hidden layer is tansig which is introduced in Eq. (5) and the activation function in the output layer is a linear transfer function:
tan sigðnÞ ¼
2 1: 1 þ e2n
ð5Þ
If the input parameter was considered as x, the predicted parameter is y and the output of neural network is f; in a good artificial neural network, the difference between f and y should be tiny so the goal is to minimize this difference which is introduced by Eq. (6): C¼
N 1X ðf ðxi Þ yi Þ2 : N i¼1
ð6Þ
For better understanding the model, the topology of this model is shown in Fig. 6. Figure 7 displays a comparison between experimental viscosity and that predicted by ANN Model I. Training data and test data are distinguished from each other. As observed in this figure, there is a great match between the experimental viscosity and data predicted by ANN Model I. The match can be seen in the training data and test data concurrently. Therefore, it can be argued that the neural network is a powerful instrument in establishing the relationship between a large numbers of data. To demonstrate this capability, data derived from neural networks (Model I) have been compared with experimental viscosity against the results obtained from the proposed correlation in Fig. 8. This figure shows that ANN Model I is much more accurate than proposed correlation presented in Eq. (2). It confirmed that the neural network is a reliable method for the large number of data compared to curvefitting method.
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H. Eshgarf et al. Fig. 5 Flowchart of the ANN models
Start
Enter experimental data Dividing experimental data to Train (80%) and Test (20%)
Setting the stopping criterion during training process Setting the minimum number of neurons in the hidden layer Setting the minimum number of neurons in the hidden layer number of Inner Iteration = 10
Inner Iteration = 0
Training artificial neural network and calculating performance Storing mean performance of this architecture
Inner Iteration = Inner Iteration + 1 Inner Iteration > number of Inner Iteration?
Yes
No
Yes
Number of neurons < Maximum number of neurons? No Selecting the best architecture of ANN based on the performance
End
Model II In this model, the input data in the artificial neural network are temperature and concentration, and the outputs are consistency and power low index. Here, there were 42 experimental data including test data (20%) and training data (80%). The procedure of calculation of the best neuron number was like the Model I, while by changing the
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number of neurons from 10 to 120 the best network had 10 neurons. Moreover, as there are two outputs, the number of neurons in the hidden layer is 2. The training algorithm is like the previous model (Fig. 5) and was Marquardt– Levenberg. In addition, Fig. 9 shows the topology of this model. Figure 10 presents a comparison of experimental consistency and power law indices with those obtained from
Prediction of rheological behavior of MWCNTs–SiO2/EG–water non-Newtonian hybrid nanofluid by… Fig. 6 Topology of ANN Model I
Output Layer Neuron = 1
Solid Volume Fraction
Hidden Layer Optimal neurons = 12
Mass
+ Bias
Mass
+
Bias
Temperature
Mass
+
Viscosity
Shear rate
Bias
Mass
+ Bias
Equality line Training data
600
Test data
500 400 300 200 100
0
Experimental Correlation ANN
700
Predicted viscosity/mPa s
Predicted viscosity/mPa s
800
700
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0
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200
300
400
500
600
700
Experimental viscosity/mPa s
0
0
50
100
150
200
Data number
Fig. 7 Comparison between experimental viscosity and that obtained from ANN Model I
Fig. 8 Comparison between data derived from ANN Model I, experimental viscosity and that obtained from proposed correlation
ANN Model II. As seen in this figure, there is an excellent agreement between the experimental viscosity and data predicted by ANN Model II. Consequently, the ability and accuracy of the artificial neural network to predict the behavior of two completely independent parameters become clear. To establish this capability, Fig. 11 shows the consistency and power law indices obtained from
neural network (Model II) compared with experimental data against the results obtained from the proposed correlations. This figure shows that ANN Model II is much more accurate than proposed correlations presented in Eqs. (3) and (4).
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H. Eshgarf et al. Fig. 9 Topology of ANN Model II
Hidden Layer Optimal neurons = 10
Solid Volume Fraction
Mass
Output Layer Neurons = 2
+ Mass
Mass
+
Consistency index
Bias
+
Bias
Power law index
Temperature
Bias
Mass
+ Bias Mass
+
0.6
0.9
0.5
0.8
Power law index (ANN)
Consistency index (ANN)
Bias
0.4
0.3
0.2
0.7
0.6
0.5
0.4
0.1 0.3
0
0
0.1
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Consistency index (Experimental)
0.3
0.4
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0.8
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Power law index (Experimental)
Fig. 10 Comparison of experimental consistency and power law indices with those obtained from ANN Model II
Conclusions In this study, based on reported experiential data, new correlations were proposed to predict the viscosity, consistency and power law indices of MWCNTs–SiO2/EG– water non-Newtonian hybrid nanofluid. Then, based on minimum prediction errors, two optimal artificial neural
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network models (ANNs) were designed to forecast the rheological behavior of the non-Newtonian hybrid nanofluid. The optimal models were obtained by varying the number of neurons in the hidden layer. For Model I, temperature, shear rate, and solid volume fraction were considered as input variables and viscosity was the output parameter. For Model II, solid volume fraction and
Prediction of rheological behavior of MWCNTs–SiO2/EG–water non-Newtonian hybrid nanofluid by…
Experimental Correlation ANN
0.5
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Power law index
Consistency index/Pa s–n
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40
0
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10
Data number
15
20
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40
Data number
Fig. 11 Comparison of ANN (Model II) outputs with experimental data and correlations outputs
temperature were input variables, and consistency and power law indices were obtained by ANN. The results revealed that there was a great match between the experimental viscosity and data predicted by ANN Model I. It was claimed that ANN modeling is a powerful instrument in establishing the relationship between a large numbers of data. Comparing the ANN Model II with correlations showed the ability and accuracy of the artificial neural network for predicting the behavior of the nanofluid. Finally, it can be found that the optimal artificial neural network models were more accurate compared to experimental correlations.
References 1. Choi S. Enhancing thermal conductivity of fluids with nanoparticles. ASME Publ Fed. 1995;231:99–106. 2. Shamaeil M, Firouzi M, Fakhar A. The effects of temperature and volume fraction on the thermal conductivity of functionalized DWCNTs/ethylene glycol nanofluid. J Therm Anal Calorim. 2016;126:1455–62. 3. Esfe MH, Naderi A, Akbari M, Afrand M, Karimipour A. Evaluation of thermal conductivity of COOH-functionalized MWCNTs/water via temperature and solid volume fraction by using experimental data and ANN methods. J Therm Anal Calorim. 2015;121:1273–8. 4. Esfe MH, Saedodin S, Yan W-M, Afrand M, Sina N. Study on thermal conductivity of water-based nanofluids with hybrid suspensions of CNTs/Al2O3 nanoparticles. J Therm Anal Calorim. 2016;124:455–60. 5. Afrand M. Experimental study on thermal conductivity of ethylene glycol containing hybrid nano-additives and development of a new correlation. Appl Therm Eng. 2017;110:1111–9. 6. Soltanimehr M, Afrand M. Thermal conductivity enhancement of COOH-functionalized MWCNTs/ethylene glycol–water
7.
8.
9.
10.
11.
12.
13. 14.
15.
16.
17.
18.
nanofluid for application in heating and cooling systems. Appl Therm Eng. 2016;105:716–23. Sina N, Moosavi H, Aghaei H, Afrand M, Wongwises S. Wave dispersion of carbon nanotubes conveying fluid supported on linear viscoelastic two-parameter foundation including thermal and small-scale effects. Phys E Low Dimens Syst Nanostruct. 2017;85:109–16. Toghraie D, Chaharsoghi VA, Afrand M. Measurement of thermal conductivity of ZnO–TiO2/EG hybrid nanofluid. J Therm Anal Calorim. 2016;125:527–35. Esfe MH, Afrand M, Rostamian SH, Toghraie D. Examination of rheological behavior of MWCNTs/ZnO-SAE40 hybrid nano-lubricants under various temperatures and solid volume fractions. Exp Therm Fluid Sci. 2017;80:384–90. Eshgarf H, Afrand M. An experimental study on rheological behavior of non-Newtonian hybrid nano-coolant for application in cooling and heating systems. Exp Therm Fluid Sci. 2016;76:221–7. Ghahdarijani AM, Hormozi F, Asl AH. Convective heat transfer and pressure drop study on nanofluids in double-walled reactor by developing an optimal multilayer perceptron artificial neural network. Int Commun Heat Mass Transf. 2017;84:11–9. Tseng WJ, Lin K-C. Rheology and colloidal structure of aqueous TiO2 nanoparticle suspensions. Mater Sci Eng A. 2003;355:186–92. Kole M, Dey T. Effect of aggregation on the viscosity of copper oxide–gear oil nanofluids. Int J Therm Sci. 2011;50:1741–7. Namburu P, Kulkarni D, Dandekar A, Das D. Experimental investigation of viscosity and specific heat of silicon dioxide nanofluids. Micro Nano Lett. 2007;2:67–71. Namburu PK, Kulkarni DP, Misra D, Das DK. Viscosity of copper oxide nanoparticles dispersed in ethylene glycol and water mixture. Exp Therm Fluid Sci. 2007;32:397–402. Godson L, Raja B, Lal DM, Wongwises S. Experimental investigation on the thermal conductivity and viscosity of silverdeionized water nanofluid. Exp Heat Transf. 2010;23:317–32. Cabaleiro D, Pastoriza-Gallego MJ, Gracia-Ferna´ndez C, Pin˜eiro MM, Lugo L. Rheological and volumetric properties of TiO2ethylene glycol nanofluids. Nanoscale Res Lett. 2013;8:286. Yiamsawas T, Mahian O, Dalkilic AS, Kaewnai S, Wongwises S. Experimental studies on the viscosity of TiO2 and Al2O3
123
H. Eshgarf et al.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
nanoparticles suspended in a mixture of ethylene glycol and water for high temperature applications. Appl Energy. 2013;111:40–5. Esfe MH, Saedodin S, Mahmoodi M. Experimental studies on the convective heat transfer performance and thermophysical properties of MgO–water nanofluid under turbulent flow. Exp Therm Fluid Sci. 2014;52:68–78. Esfe MH, Saedodin S, Mahian O, Wongwises S. Thermophysical properties, heat transfer and pressure drop of COOH-functionalized multi walled carbon nanotubes/water nanofluids. Int Commun Heat Mass Transf. 2014;58:176–83. Esfe MH, Saedodin S, Mahian O, Wongwises S. Heat transfer characteristics and pressure drop of COOH-functionalized DWCNTs/water nanofluid in turbulent flow at low concentrations. Int J Heat Mass Transf. 2014;73:186–94. Afrand M, Toghraie D, Ruhani B. Effects of temperature and nanoparticles concentration on rheological behavior of Fe3O4– Ag/EG hybrid nanofluid: an experimental study. Exp Therm Fluid Sci. 2016;77:38–44. Bahrami M, Akbari M, Karimipour A, Afrand M. An experimental study on rheological behavior of hybrid nanofluids made of iron and copper oxide in a binary mixture of water and ethylene glycol: non-Newtonian behavior. Exp Therm Fluid Sci. 2016;79:231–7. Toghraie D, Alempour SM, Afrand M. Experimental determination of viscosity of water based magnetite nanofluid for application in heating and cooling systems. J Magn Magn Mater. 2016;417:243–8. Dardan E, Afrand M, Meghdadi Isfahani AH. Effect of suspending hybrid nano-additives on rheological behavior of engine oil and pumping power. Appl Therm Eng. 2016;109(Part A):524–34. Afrand M, Najafabadi KN, Akbari M. 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. 2016;102:45–54. Sepyani K, Afrand M, Hemmat Esfe M. An experimental evaluation of the effect of ZnO nanoparticles on the rheological behavior of engine oil. J Mol Liq. 2017;236:198–204. Hojjat M, Etemad SG, Bagheri R, Thibault J. Thermal conductivity of non-Newtonian nanofluids: experimental data and modeling using neural network. In J Heat Mass Transf. 2011;54:1017–23. Esfe MH, Rostamian H, Afrand M, Karimipour A, Hassani M. Modeling and estimation of thermal conductivity of MgO–water/ EG (60:40) by artificial neural network and correlation. Int Commun Heat Mass Transf. 2015;68:98–103. Ahmadloo E, Azizi S. Prediction of thermal conductivity of various nanofluids using artificial neural network. Int Commun Heat Mass Transf. 2016;74:69–75. Afrand M, Toghraie D, Sina N. Experimental study on thermal conductivity of water-based Fe3O4 nanofluid: development of a new correlation and modeled by artificial neural network. Int Commun Heat Mass Transf. 2016;75:262–9. Esfe MH, Razi P, Hajmohammad MH, Rostamian SH, Sarsam WS, Arani AAA, Dahari M. Optimization, modeling and accurate prediction of thermal conductivity and dynamic viscosity of stabilized ethylene glycol and water mixture Al2O3 nanofluids by NSGA-II using ANN. Int Commun Heat Mass Transf. 2017;82:154–60. Rostamian SH, Biglari M, Saedodin S, Esfe MH. An inspection of thermal conductivity of CuO–SWCNTs hybrid nanofluid
123
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43. 44.
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versus temperature and concentration using experimental data, ANN modeling and new correlation. J Mol Liq. 2017;231:364–9. Vafaei M, Afrand M, Sina N, Kalbasi R, Sourani F, Teimouri H. Evaluation of thermal conductivity of MgO–MWCNTs/EG hybrid nanofluids based on experimental data by selecting optimal artificial neural networks. Phys E Low Dimens Syst Nanostruct. 2017;85:90–6. Afrand M, Esfe MH, Abedini E, Teimouri H. Predicting the effects of magnesium oxide nanoparticles and temperature on the thermal conductivity of water using artificial neural network and experimental data. Phys E Low Dimens Syst Nanostruct. 2017;87:242–7. Vakili M, Karami M, Delfani S, Khosrojerdi S, Kalhor K. Experimental investigation and modeling of thermal conductivity of CuO–water/EG nanofluid by FFBP-ANN and multiple regressions. J Therm Anal Calorim. 2017;129:1–9. Esfe MH, Afrand M, Wongwises S, Naderi A, Asadi A, Rostami S, Akbari M. Applications of feedforward multilayer perceptron artificial neural networks and empirical correlation for prediction of thermal conductivity of Mg(OH)2–EG using experimental data. Int Commun Heat Mass Transf. 2015;67:46–50. Zhao N, Li Z. Experiment and artificial neural network prediction of thermal conductivity and viscosity for alumina–water nanofluids. Materials. 2017;10:552. Longo GA, Zilio C, Ortombina L, Zigliotto M. Application of artificial neural network (ANN) for modeling oxide-based nanofluids dynamic viscosity. Int Commun Heat Mass Transf. 2017;83:8–14. Afrand M, Najafabadi KN, Sina N, Safaei MR, Kherbeet AS, Wongwises S, Dahari M. Prediction of dynamic viscosity of a hybrid nano-lubricant by an optimal artificial neural network. Int Commun Heat Mass Transf. 2016;76:209–14. Afrand M, Rostami S, Akbari M, Wongwises S, Esfe MH, Karimipour A. Effect of induced electric field on magneto-natural convection in a vertical cylindrical annulus filled with liquid potassium. Int J Heat Mass Transf. 2015;90:418–26. Afrand M, Toghraie D, Karimipour A, Wongwises S. A numerical study of natural convection in a vertical annulus filled with gallium in the presence of magnetic field. J Magn Magn Mater. 2017;430:22–8. Afrand M. Using a magnetic field to reduce natural convection in a vertical cylindrical annulus. Int J Therm Sci. 2017;118:12–23. Afrand M, Farahat S, Nezhad AH, Sheikhzadeh GA, Sarhaddi F. Numerical simulation of electrically conducting fluid flow and free convective heat transfer in an annulus on applying a magnetic field. Heat Transf Res. 2014;45:749–66. Afrand M, Farahat S, Nezhad AH, Sheikhzadeh GA, Sarhaddi F. 3-D numerical investigation of natural convection in a tilted cylindrical annulus containing molten potassium and controlling it using various magnetic fields. Int J Appl Electromagn Mech. 2014;46:809–21. Afrand M, Farahat S, Nezhad AH, Sheikhzadeh GA, Sarhaddi F, Wongwises S. Multi-objective optimization of natural convection in a cylindrical annulus mold under magnetic field using particle swarm algorithm. Int Commun Heat Mass Transf. 2015;60:13–20. Mahmoodi M, Hemmat Esfe M, Akbari M, Karimipour A, Afrand M. Magneto-natural convection in square cavities with a source-sink pair on different walls. Int J Appl Electromagn Mech. 2015;47:21–32.