On evaluation of thermophysical properties of transformer oil-based nanofluids: A comprehensive modeling and experimental study

Journal Pre-proof On evaluation of thermophysical properties of transformer oilbased nanofluids: A comprehensive modeling and experimental study

Ahmadreza Ghaffarkhah, Masoud Afrand, Mohsen Talebkeikhah, Ali Akbari Sehat, Mostafa Keshavarz Moraveji, Farzaneh Talebkeikhah, Mohammad Arjmand PII:

S0167-7322(19)35722-8

DOI:

https://doi.org/10.1016/j.molliq.2019.112249

Reference:

MOLLIQ 112249

To appear in:

Journal of Molecular Liquids

Received date:

14 October 2019

Revised date:

27 November 2019

Accepted date:

30 November 2019

Please cite this article as: A. Ghaffarkhah, M. Afrand, M. Talebkeikhah, et al., On evaluation of thermophysical properties of transformer oil-based nanofluids: A comprehensive modeling and experimental study, Journal of Molecular Liquids(2019), https://doi.org/10.1016/j.molliq.2019.112249

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© 2019 Published by Elsevier.

Journal Pre-proof

On Evaluation of Thermophysical Properties of Transformer Oil-based Nanofluids: A Comprehensive Modeling and Experimental Study

Ahmadreza Ghaffarkhah1, Masoud Afrand2,3,*, Mohsen Talebkeikhah4, Ali Akbari Sehat1, Mostafa Keshavarz Moraveji5, Farzaneh Talebkeikhah6, Mohammad Arjmand1,*

School of Engineering, University of British Columbia, Kelowna, BC V1V 1V7, Canada.

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1

2

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Laboratory of Magnetism and Magnetic Materials, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam 3

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Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam

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Department of Chemical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran 15875-4413, Iran

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5

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Department of Petroleum Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran 15875-4413, Iran

6

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Department of Chemical Engineering, École Polytechnique Fédérale de Lausanne EPFL, CH‐1015 Lausanne, Switzerland

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*Corresponding authors

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Corresponding author at: Ton Duc Thang University, Ho Chi Minh City, Vietnam

Emails: [email protected] (M. Arjmand) [email protected] (m. Afrand)

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Journal Pre-proof Abstract Transformer oil-based nanofluids are known to have higher thermal conductivity and heat transfer performance compared to conventional transformer oils. In this study, four different types of transformer oil-based nanofluids are synthesized using the well-known two-step method. The first nanofluid contains pure multi-walled carbon nanotubes (MWCNTs), while other samples consist of 20 Vol% of MWCNTs and 80 Vol% of different oxide nanoparticles (i.e., Al2O3, TiO2, and SiO2). The dynamic viscosity and thermal conductivity of prepared samples are investigated in seven different volume fractions of 0.001, 0.0025, 0.005, 0.01, 0.025, 0.05, and

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0.1%. Besides, the breakdown voltage of the pure transformer oil and nanofluids containing 0.05

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and 0.1 Vol% of nanoparticles is investigated. The outcomes show that dielectric properties of hybrid carbon-based nanofluids are far better compared to those properties of the pure MWCNTs

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nanofluids. Finally, eight different soft computing approaches, including group method of data

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handling (GMDH), support vector machine (SVM), radial basis function (RBF) neural network, multilayer perceptron (MLP), and MLP and RBF models optimized with bat and grasshopper

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optimization algorithm (GOA), are used to model the viscosity and thermal conductivity of synthesized nanofluids. The outcomes show that the GMDH approach significantly outperforms

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all other models in terms of predicting the thermal conductivity and dynamic viscosity of transformer oil-based nanofluids.

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Breakdown voltage

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Keywords: Nanofluid, Transformer oil, Soft computing, Thermal conductivity, Viscosity,

1. Introduction It is well-known that conventional transformer oils have relatively low thermal conductivity and heat transfer property [1-3]. From a practical point of view, improving the thermal conductivity of transformer oils increases the rate of heat transfer, which in turn results in reducing the size of equipment, improving the performance of electrical transformers, and a considerable extension 2

Journal Pre-proof of the transformer lifetime [1, 4, 5]. Therefore, several pieces of research have been conducted to improve the heat transfer performance of this type of conventional oils [2, 6-9]. However, developing transformer oil with high thermal conductivity and acceptable values of viscosity and maximum breakdown voltage is still one of the priorities of heat transfer engineering. Dispersing nanoparticles in conventional coolants such as water, ethylene glycol, and oil could effectively improve their heat transfer properties [10-14]. The idea of preparing the

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nanoparticles-liquid mixture with enhanced thermophysical properties was first proposed by

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Chio et al. [15] at the Argon National Laboratory (ANL) in 1995. Since then, several pieces of

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research have been conducted to investigate the effect of adding nanoparticles on improving the

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heat transfer characteristics of conventional heat transfer fluids. Ahmadi et al. [16] reviewed the

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valuable and recent studies on the thermal conductivity of nanofluids. Zyła [12] showed that adding MgO nanoparticles to the ethylene glycol effectively increases its thermal conductivity.

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Zyła and Fal [17] demonstrated that the thermal conductivity of aluminum nitride–ethylene

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glycol nanofluid increases linearly by increasing the concentration of nanoparticles. Despite the importance of improving the thermal conductivity of transformer oil, the number of researches

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that investigate the thermal conductivity of transformer oil-based nanofluids is significantly lower compared to those researches that study the heat transfer properties of water-based or ethylene glycol-based nanofluids. A review of the available literature on thermal conductivity of transformer oil-based nanofluids is presented in Table 1. Table 1: A review of the available literature on the thermal conductivity of transformer oil-based nanofluids. Author

Used nanoparticles

Volume/Mass percentage of nanoparticles

Choi et al. [1]

Al2O3, AlN

0.5 to 4 Vol%

3

Range of temperature (°C) Room temperature

Maximum enhancement of thermal conductivity (%) 20

Journal Pre-proof Beheshti et al. [6] Amiri et al. [7]

Oxidized MWCNTs HexylaminMWCNTs

0.001 and 0.01 Wt%

20 to 80

7.6

0.001 and 0.005 Wt%

30 to 70

9.8

Al2O3

0.1 to 1 Vol%

20 to 50

19.2

Fontes et al. [19]

MWCNTs and nano diamond

0.005, 0.01 and 0.05 Vol%

Room temperature

27 % for MWCNTs and 23% for nano diamond

Aberoumand and Jafarimoghaddam [20]

Ag-WO3 hybrid nanoparticles

1, 2 and 4 Wt%

40-100

41

Bhunia et al. [21]

Amorphous graphene

0.0012 to 0.01 Wt%

35-55

30

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Singh and Kundan [18]

Among all types of nanoparticles, carbon nanostructures (i.e., carbon nanotube, carbon

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nanofiber, diamond, and graphene) could be considered as the best option for improving the heat

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transfer performance of conventional coolants [22-30]. However, although carbon nanostructures

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effectively improve the heat transfer of conventional coolants, their cost is considerably higher

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compared to the other types of nanoparticles [27, 31]. Due to this significant limitation, several researchers have worked on hybrid carbon-based nanofluids as an economical alternative to the

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pure carbon-based nanofluids [32-38]. This type of nanofluids consists of carbon nanostructures

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and other types of nanomaterials, including chemically stable metals, metal oxides, and ceramic oxide nanoparticles. Hybrid carbon-based nanofluids exhibit desirable thermal conductivity and

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acceptable pressure drop characteristics, which contribute to their use in a wide range of applications [39-41].

Most of the previous researches on investigating the thermal conductivity of nanofluids focused on the colloidal suspensions that contained a single type of nanoparticles. Besides, those researches on hybrid nanofluids mostly used water or ethylene glycol as the base fluid. However, few studies focused on the thermal conductivity of hybrid oil-based nanofluids. Asadi et al. [42] prepared engine oil-based nanofluids with MWCNT and MgO nanoparticles in six different solid volume fractions of 0.25, 0.5, 0.75, 1, 1.5, and 2%. They observed about 65% enhancement in 4

Journal Pre-proof the thermal conductivity at the temperature of 50 ºC and the solid volume concentration of 2%. Asadi et al. [43] investigated the heat transfer capability of hybrid engine oil nano-lubricants that contain MWCNT and Mg(OH)2 nanoparticles in various temperatures and solid concentrations. Their results indicated the maximum enhancement of about 50% on the thermal conductivity of engine oil. Wei et al. [44] fabricated an oil-based hybrid nanofluid containing SiC and TiO2 nanoparticles. In their study, nanoparticles were dispersed in diathermic oil. They concluded that

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the thermal conductivity of the prepared nano-lubricants increases by increasing the temperature

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and solid volume fraction of nanoparticles. However, to the best of our knowledge, there are no

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researches that focused on fabricating the hybrid transformer oil-based nanofluids consist of

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carbon nanostructures. Therefore, investigating the heat transfer characteristics of this type of

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transformer oil-based nano-lubricants is chosen as one of the main topics of the present study. Dynamic viscosity is another fundamental thermophysical properties of nanofluids that directly

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affects different parameters, including the Reynolds number, pumping efficiency, and friction

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factor. Fontes et al. [19] analyzed the viscosity of diamond and MWCNT mineral oil-based nanofluids, while Jin et al. [45] studied the effect of adding SiO2 nanoparticles on dynamic

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viscosity of mineral oils. Beheshti et al. [6] investigated the rheological properties of transformer oil-oxidize MWCNT nanofluids. Their results demonstrated that the nanofluids containing 0.001 and 0.01 mass percentage of nanoparticles display Newtonian behavior in various temperatures. Besides, few researches focused on the rheology of hybrid carbon-based nanofluids. For example, Asadi and Asadi [46] studied the dynamic viscosity of an engine oil hybrid nanofluid containing MWCNTs and ZnO nanoparticles. Afrand et al. [47] conducted several experiments on MWCNTs-SiO2 hybrid nano-lubricant to evaluate its rheological properties. Using their

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Journal Pre-proof experimental data, they also proposed a new correlation to predict the relative viscosity of this type of nano-lubricants. Breakdown voltage is another crucial factor that directly affects the performance of transformer oils. This parameter is defined as the dielectric strength of transformer oils [2, 48-50]. Routinely, the breakdown voltage of transformer oils is measured by detecting the voltage that causes a spark between two electrodes with a precise gap located in the oil [6, 7, 51, 52]. Du et al. [53]

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found that adding TiO2 nanoparticles to transformer oil increases its dielectric strength. They

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suggested that adding nanoparticles to transformer oil increases the trapping and de-trapping of

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electrons, which in turn results in the increasing dielectric strength of the oil. This theory has also

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been employed by Rafiq et al. [54] to explain the significant insulating performance of

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transformer oil-based nanofluids containing Al2O3 nanorods. Lv et al. [55] compared the effect of adding SiO2, TiO2, and Al2O3 on the AC breakdown voltage of mineral oil. They concluded

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that TiO2 nanoparticles increase the breakdown strength, while SiO2 and Al2O3 nanoparticles

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reduce the breakdown strength of nanofluids. It was also shown that adding magnetic nanoparticles such as Fe3O4 can upgrade the breakdown voltage of transformer oils. This type of

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nanoparticles could act as electron scavenger and reduce the rate of free electron production, which in turn results in enhancing the dielectric performance of transformer oils [56]. Besides, from several pieces of research, it has been found that dispersing MWCNT to transformer oil reduces the breakdown voltage of nanofluids [6, 7, 19]. Although several studies focused on the breakdown voltage of nanofluids that contain a single type of nanoparticles, the breakdown voltage of hybrid carbon-based nanofluids has not yet been investigated. However, adding any impurities to transformer oil may change its electrical performance [7]. Therefore, one of the

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Journal Pre-proof objectives of the present study is to evaluate the breakdown voltage of the hybrid carbon-based nanofluids. Several pieces of research have been used different computer-aided models, including Artificial Neural Network (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), Random forest, and Decision tree for predicting various thermophysical properties of nanofluids. In recent years, these types of numerical methods received considerable attention from researchers who studied

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nanofluids. This is mainly because experimental measurements for calculating the

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thermophysical properties of various nanofluids containing different nanoparticles in various

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temperatures and solid volume fractions are time-consuming, cumbersome, and expensive [57].

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A literature review of the modeling works on the thermophysical properties of nanofluids is

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presented in Table 2. As can be seen, only a few studies compared the accuracy of different numerical approaches in terms of predicting the thermophysical properties of nanofluids, and

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most of them only used one numerical model in their study.

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In this study, four different nanofluids have been prepared using two-step methods. One of the

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prepared samples contained pure MWCNTs, while other nanofluids contained 20 Vol% of MWCNTs and 80 Vol% of different oxide nanoparticles (i.e., SiO2, Al2O3, and TiO2). The dynamic viscosity, thermal conductivity, and breakdown voltage of prepared samples were evaluated experimentally. The outcomes showed that dielectric properties of hybrid carbonbased nanofluids are far better compared to those properties of the pure MWCNTs nanofluids. Besides, eight different soft computing approaches, including GMDH, SVM, RBF, BAT-RBF, GOA-RBF, MLP, BAT-MLP, and GOA-MLP, were employed to model the dynamic viscosity and thermal conductivity of prepared transformer oil-based nanofluids.

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Journal Pre-proof Table 2: A review of the available literature on modeling the thermophysical properties of nanofluids. Base fluid

Nanoparticles

Investigated thermophysical properties

Numerical models

Rostamian et a1. [58]

Water and ethylene glycol (60:40)

Hybrid of CuO and SWCNT

Thermal conductivity

MLP

Esfe [59]

Water

CuO

Thermal conductivity

ANFIS

Alade et al. [60]

Water, ethylene glycol and transformer oil

Al, Cu, Al2O3 and CuO

Thermal conductivity

Support Vector Regression (SVR)

Alrashed et al. [61]

Water

Diamond and COOHfunctionalized MWCNT

Mineral oil

Ag, Cu and TiO2

Viscosity, density, and thermal conductivity Viscosity and thermal conductivity

10W40 engine oil Ethylene glycol

Hybrid of SiO2 and MWCNTs Hybrid of MWCNT and SiO2

Ahmadi et al. [65]

Ethylene glycol

Al2O3

Zhao et al. [66]

Water

Ghaffarkhah et al. [31]

SAE 40 engine oil

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ANFIS

Viscosity

MLP

Thermal conductivity

MLP

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Al2O3 and CuO Hybrid COOHfunctionalized MWCNTs and different oxide nanoparticles (SiO2, Al2O3, MgO, and ZnO)

ANFIS and MLP

Thermal conductivity Viscosity

Viscosity

Least Squares Support Vector Machine (LSSVM) optimized with genetic algorithm RBF

Decision tree, Random forest, SVM and RBF

2. Experimental

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Esfe et al. [64]

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Esfahani et al. [62] Nadooshan et al. [63]

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Author

2.1 Materials MWCNTs, Al2O3, TiO2, and SiO2 nanoparticles were obtained from US Research Nanomaterials, Inc. (Houston, USA). The physical properties of the used nanomaterials were provided by the manufacturer and summarized in Table 3. Besides, Field Emission Scanning Electron Microscopy (FESEM) picture of SiO2, Scanning Electron Microscope (SEM) picture of Al2O3, and Transmission Electron Microscopy (TEM) pictures of MWCNTs and TiO2

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Journal Pre-proof nanoparticles are shown in Figure 1. Well-refined transformer oil was purchased from Nynas, Stockholm, Sweden. The most important physical properties of this transformer oil were provided by the manufacturer and presented in Table 4. Table 3: Physical properties of the used nanoparticles. Value Al2O3

TiO2

SiO2

MWCNTs

Purity (%)

99+

99+

98+

Average Particle Size (APS) (nm)

50

20

60-70

97+ Outside diameter: 10-20 nm Inside diameter: 5-10 nm Length: 10-30 µm

>19

10-45

160-600

3.95 White

4.23 White

2.40 White

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>200

2.1 Black

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Specific Surface Area (SSA) (m2/g) True density (gr/cm3) Color

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Specifications

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Value 9.1 2.3 0.890 150 -57 49 <20

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Characteristics Viscosity at 40°C (cP) Viscosity at 100°C (cP) Density at 15°C (gr/cm3) Flash point (°C) Pour point (°C) Interfacial tension at 25°C (mN/m) Water content (mg/kg)

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Table 4: Physical properties of the used transformer oil.

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2.2 Preparation of nanofluids

In this study, the two-step method was used to produce the nanofluids [31, 67, 68]. The nanoparticles were first dispersed in the transformer oil using a high-speed homogenizer (T25 digital ULTRA-TURRAX, IKA, China) for two hours. The prepared samples were then sonicated by an ultrasonic processor (UP 200 St, Hielscher, Germany) for four hours. It should be noted that sonicating the prepared samples reduces the agglomeration of nanoparticles and eventually increases the stability of nanofluids [69, 70].

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Journal Pre-proof Four different types of nanofluids were prepared in this study. The first one only contained MWCNTs. Other prepared samples contained 20 Vol% of MWCNTs and 80 Vol% of oxide nanoparticles (i.e., SiO2, Al2O3, and TiO2). As a result, in this study, we can compare the thermophysical properties of pure and hybrid transformer oil-based nanofluids. Here, all types of nanofluids were synthesized in seven different volume fractions of 0.001, 0.0025, 0.005, 0.01, 0.025, 0.05, and 0.1. As can be seen in Figure 2, all prepared samples are stable, and no obvious

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sedimentation can be observed after 72 hours.

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2.3 Experimental apparatus

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Brookfield LVDV-III viscometer was used for measuring the viscosity of the pure transformer

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oil and prepared nanofluids. In this study, the SC4-18 spindle was used for all experiments.

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Before conducting the experiments, this viscometer was calibrated using the Brookfield standard

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fluid. For each sample, the viscosity was measured three times, and the mean value was reported. The thermal conductivity of the base transformer oil and prepared samples was measured using

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the KD2 thermal properties analyzer (Decagon Devices, Inc., USA). Experiments were

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conducted at different temperatures ranging from 25 to 75 °∁. It is worth noting that in this study, the thermal conductivity of each sample was measured five times, and the mean value was reported. Besides, the breakdown voltage of the pure transformer oil and the samples containing 0.05 and 0.1 Vol% of nanoparticles is measured using the ultra-light insulating oil tester (Model BA75, b2 electronic GmbH, Austria). The maximum breakdown voltage of prepared nanolubricants measured 12 hours after preparation. All experiments were conducted using lockable mushroom electrodes at room temperature. This type of electrodes significantly reduces the possibility of electrode moving during handling or testing. The gap between electrodes was set to be 1 mm, and the voltage build-up rate was 1 kV/s. For all samples, the breakdown voltage was 10

Journal Pre-proof measured 60 times, and the corresponding mean breakdown voltage was calculated based on the IEC 156 standard. 3. Modeling 3.1 GMDH GMDH is a feed-forward neural network that can be used to solve extremely complex nonlinear

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problems [71]. This algorithm consists of a set of self-organized neurons. In this structure,

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different pairs of neurons in each layer are connected through a quadratic polynomial equation

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and produce a neuron in the next layer [72, 73]. The GMDH algorithm automatically determines the number of neurons and layers, the effect of input variables, and the optimum structure of the

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model [71].

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The GMDH model defines a function (𝑓̂) that estimates the actual value of output (𝑓) for any

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given input vector (𝑥⃗). The actual value and estimated value of M observations of multi-input-

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single-output data pairs are shown in Equation 1 and 2, respectively [72, 73]. 𝑦𝑖 = 𝑓(𝑥𝑖1 , 𝑥𝑖2 , 𝑥𝑖3 , … , 𝑥𝑖𝑛 ), 𝑖 = 1, 2, … , 𝑀

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(1)

𝑦̂𝑖 = 𝑓̂(𝑥𝑖1 , 𝑥𝑖2 , 𝑥𝑖3 , … , 𝑥𝑖𝑛 ), 𝑖 = 1, 2, … , 𝑀

(2)

The main objective of the GMDH algorithm is minimizing the square of the difference between the actual output and the estimated value as follows: ∑𝑀 ̂𝑖 − 𝑦𝑖 ]2 → 𝑚𝑖𝑛 𝑖=1[𝑦

(3)

The Volterra series can represent the connection between input and output parameters in a GMDH algorithm in the form of the following equation [71-73]:

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Journal Pre-proof 𝑦 = 𝑎0 + ∑𝑛𝑖=1 𝑎𝑖 𝑥𝑖 + ∑𝑛𝑖=1 ∑𝑛𝑗=1 𝑎𝑖𝑗 𝑥𝑖 𝑥𝑗 + ∑𝑛𝑖=1 ∑𝑛𝑗=1 ∑𝑛𝑘=1 𝑎𝑖𝑗𝑘 𝑥𝑖 𝑥𝑗 𝑥𝑘 + …

(4)

This connection can be shown as a system of partial quadratic polynomials consisting of two variables in the form of: 𝐺(𝑥𝑖 , 𝑥𝐽 ) = 𝑎0 + 𝑎1 𝑥𝑖 + 𝑎2 𝑥𝑗 + 𝑎3 𝑥𝑖 2 + 𝑎4 𝑥𝑗 2 + 𝑎5 𝑥𝑖 𝑥𝑗

(5)

This partial quadratic polynomial equation is used in the network of interconnected neurons of

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the GMDH algorithms in order to estimate the output value based on the input vector. It should

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be noted that the coefficients of 𝑎1 to 𝑎5 in Equation 5 are optimized using the regression

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technique to minimize the difference between the actual and estimated values of each pair of 𝑥𝑖

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and 𝑥𝑗 [71-73].

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3.2 SVM

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SVM is a robust classifying method that is useful in various branches of science, including industrial and medical engineering [74, 75]. Unlike other types of neural networks, the SVM

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does not suffer over-fitting and under-fitting [76, 77]. SVM efficiently performs linear and

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nonlinear classifications and regressions by constructing hyperplanes among the data. In this structure, inputs are mapped into a higher space dimension using the kernel function. Mapping data into a higher dimensional space will create a clear separation between data classes and make it possible to construct the hyperplane with the most substantial distance to the data margins. A detailed description of the SVM structure can be found in Scholkopf and Smola [78]. 3.3 MLP MLP is the most common type of ANN routinely used to model different thermophysical properties of nanofluids. An MLP is a classifier that contains several layers (i.e., input, output, 12

Journal Pre-proof and hidden layers) [49]. The first layer is called the input layer. The number of neurons in the input layer is equal to the number of input variables. The last layer in the structure of an MLP is called the output layer. In many problems, this layer contains a single neuron [79, 80]. In addition, the intermediate layers between the input and output layers are called hidden layers. In this structure, the number of hidden layers and their neurons should be optimized in order to achieve a desirable connection between the inputs and model outputs.

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For calculating the value of each neuron in the output and hidden layers, the value of each

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neuron in the previous layer is multiplied in specific weight. Then, a bias term is added to the

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sum of these values. Finally, the resulted value is passed through a nonlinear activation function

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[79, 80]. This procedure can be defined as below:

𝑦 = 𝜑(∑𝑛𝑖=1 𝑤𝑖 𝑥𝑖 ) + 𝑏

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(6)

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where, 𝜑 is the activation function, b is the value of the bias, 𝑥𝑖 is the value of ith neuron in the previous layer, and 𝑤𝑖 is the specific weight corresponding to 𝑥𝑖 . The most important activation

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𝑃𝑢𝑟𝑒𝑙𝑖𝑛: 𝑓(𝑥) = 𝑥

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functions are as follows [49]:

𝑆𝑖𝑔𝑚𝑜𝑖𝑑: 𝑓(𝑥) =

1

1+𝑒 −𝑥

𝑆𝑖𝑢𝑠𝑖𝑑: 𝑓(𝑥) = sin(𝑥) 𝑇𝑎𝑛𝑠𝑖𝑔: 𝑓(𝑥) =

𝑒 𝑥 −𝑒 −𝑥 𝑒 𝑥 +𝑒 −𝑥

(7)

(8)

(9)

(10)

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Journal Pre-proof It should be mentioned that, the bat and GOA optimization algorithms were used to optimize the value of weights and biases. The details of these optimization methods are described in the following sections. 3.4 RBF RBF is a type of feed-forward neural network, which is used in both classification and regression

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problems [81]. RBF contains three layers of input, hidden, and output layers [57]. In this

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approach, the input layer is connected to the output layer through a single hidden layer [66]. The

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output space has a higher dimension compared to the input space.

Each point in the hidden layer is located in a space with a specific center and radius. In each

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neuron, the distance between the input vector and its corresponding center is calculated. Then,

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the calculated distances are transferred from hidden neurons to the output neurons by using a

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radial basis transfer function (kernel function). The kernel functions, along with specific weights, create a linear connection between the hidden layer and the output layer. The output of the RBF

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is defined as follows [57, 82]:

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𝑓(𝑥𝑖 ) = ∑𝑁 𝑖=1 𝑤𝑖 ∅𝑘𝑖 (||𝑥𝑘 − 𝑐𝑖 ||)

𝑖 = 1, … , 𝑁

𝑘 = 1, … , 𝑀

(11)

where 𝑐𝑖 is the center of the radial function, ||𝑥𝑘 − 𝑐𝑖 || is the distance between the vector of inputs and the center of the radial function, 𝑤𝑖 is the weight parameter, N is the number of neurons in the hidden layer, M is the number of inputs, and ∅𝑘𝑖 is the kernel function. In this study, the Gaussian function (Equation 12) is used as the kernel function of the developed RBF [57].

∅(𝑟) = 𝑒𝑥𝑝 (

𝑟2

2𝜎 2

)

(12)

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Journal Pre-proof here, 𝜎 is the spread coefficient. The value of the spread coefficient and the number of neurons in the hidden layer of the RBF structure should be optimized in order to achieve acceptable accuracy. In this study, the bat and GOA algorithms were used to calculate the optimum values of these parameters. The details of these optimization algorithms are described in the following sections.

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3.5 Optimization techniques

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3.5.1 Bat algorithm

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Bat algorithm is a nature-inspired optimization technique proposed by Yang [83]. This method is

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routinely used for optimizing different engineering problems and increasing the overall

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computational efficiency [84-86]. This optimization technique imitates the echolocation activities of bats. Each bat in the initial population releases ultrasonic waves and pays attention

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to echoes that return from different objects [84-86]. This sensing system helps bats locate their prey and adjust their positions. In this algorithm, the frequency, velocity, and position of each bat

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in the population are adjusted based on Equations 13 to 15, respectively [84-86]. (13)

𝑡 𝑣𝑖𝑡 = 𝑣𝑖𝑡−1 + (𝑥𝑖𝑡−1 − 𝑥𝑔𝑏𝑒𝑠𝑡 )𝑓𝑖

(14)

𝑥𝑖𝑡 = 𝑥𝑖𝑡−1 + 𝑣𝑖𝑡

(15)

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𝑓𝑖 = 𝑓𝑚𝑖𝑛 + (𝑓𝑚𝑎𝑥 − 𝑓𝑚𝑖𝑛 )𝛽

here, 𝛽 is a random number in the range of [0, 1], 𝑓𝑖 is the frequency of the ith bat, 𝑣𝑖𝑡 is the velocity of the ith bat at the time step t, 𝑥𝑖𝑡 is the location of the ith bat at the time step t, and 𝑡 𝑥𝑔𝑏𝑒𝑠𝑡 is the current global best position at the time step t.

15

Journal Pre-proof In order to optimize the MLP and RBF models, the weights and biases in the MLP structure and the value of the spread coefficient and the number of neurons in the hidden layer in the RBF structure are determined using the bat algorithm. For this purpose, the frequency, velocity, location, pulse rate, and loudness of bats are initialized. Then, new solutions are produced by adjusting the frequency and updating the velocities and locations of bats. After that, the best global solution for initial values is selected based on the objective function. In the next step, a

of

local solution is created around the best global solution. An iterative algorithm is then developed

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to generate new solutions by flaying randomly. This algorithm is terminated after reaching

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specific stop criteria. Finally, the current best solution is chosen by ranking the bats based on

re

their objective function [84-86].

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3.5.2 GOA algorithm

GOA algorithm is a new and novel optimization technique proposed in 2017 by Saremi et al.

na

[87]. This nature-inspired optimization algorithm imitates the swarm behavior of grasshopper

ur

insects, which includes nymphs and adults [88]. In this optimization method, adults are

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characterized by long-range and abrupt movement, while slow movement and small steps are the main characteristics of nymphs. Therefore, in this methodology, adults are used for exploring the entire search space while nymphs are encouraged to move locally during explorations [87, 89]. In this approach, a set of random solutions is generated to initialize the artificial swarm. Then, the best agent (grasshopper) in the current swarm is chosen based on the fitness values, and all other agents move toward it. The movement of the ith grasshopper toward the best agent (target) is formulated as follows [90]: 𝑋𝑖 = 𝑆𝑖 + 𝐺𝑖 + 𝐴𝑖

(16)

16

Journal Pre-proof where 𝑆𝑖 is the social interaction of the ith agent, 𝐺𝑖 is the gravity strength on the ith agent, and 𝐴𝑖 shows the wind advection of the ith agent. The social interaction is formulated as follows: ̂ 𝑆𝑖 = ∑𝑁 𝑗=1 𝑠(𝑑𝑖𝑗 )𝑑𝑖𝑗

(17)

𝑗≠𝑖

where, 𝑁 is the number of agents or grasshoppers, 𝑑𝑖𝑗 is the distance between the ith and jth agent, 𝑑̂𝑖𝑗 is the unit vector between the ith and jth agent, and 𝑠 is the function that defines the strength of

− 𝑒 −𝑟

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−𝑟 𝑙

(18)

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𝑠(𝑟) = 𝑓𝑒

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social forces as shown in the following equation:

𝐺𝑖 = −𝑔 × ̂ 𝑒𝑔

na

(19)

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𝐺𝑖 in Equation 16 is formulated as follows:

re

here, 𝑓 is the intensity of attraction and 𝑙 is the attractive length scale.

here, g is the gravitational constant and ̂ 𝑒𝑔 is the unit vector in the vertical direction of the

ur

surface.

𝐴𝑖 = 𝑢 × 𝑒̂ 𝑤

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𝐴𝑖 in Equation 16 is shown as follows: (20)

where, 𝑢 represents the constant drift and 𝑒̂ 𝑤 shows the unit vector in the direction of the wind. Equation 16 can be re-written based on Equations 17 to 20 as follows [91]: 𝑋𝑖 = ∑𝑁 𝑗=1 𝑠(|𝑥𝑗 − 𝑥𝑖 |) 𝑗≠𝑖

𝑥𝑗 −𝑥𝑖 𝑑𝑖𝑗

−𝑔×̂ 𝑒𝑔 + 𝑢 × 𝑒̂ 𝑤

17

(21)

Journal Pre-proof However, Equation 21 cannot be used for optimization problems since the agents will rapidly reach the comfort region [87, 91]. Saremi et al. [87] proposed an improved version of Equation 21 to solve optimization problems:

𝑋𝑖𝑑 = 𝑐 (∑𝑁 𝑗=1 𝑐 𝑗≠𝑖

𝑈𝐵𝑑 −𝐿𝐵𝑑 2

𝑠(|𝑥𝑗𝑑 − 𝑥𝑖𝑑 |)

𝑥𝑗𝑑 −𝑥𝑖𝑑 𝑑𝑖𝑗

̂𝑑 )+𝑇

(22)

of

̂𝑑 is the best solution where, 𝑈𝐵𝑑 and 𝐿𝐵𝑑 are the upper and lower bounds in the Dth dimension, 𝑇 found so far, and 𝑐 is the decreasing coefficient to shrink the comfort, repulsion, and attraction

-p

ro

zones [87].

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4. Results and discussion

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4.1 Viscosity of nanofluids

Before evaluating the dynamic viscosity of nanofluids, the accuracy of the Brookfield LVDV-III

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viscometer has been validated by comparing the dynamic viscosity of pure transformer oil obtained in this work and those that reported by Beheshti et al. [6] and Amiri et al. [7]. As can be

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seen in Figure 3, the results obtained with this viscometer is in good agreement with those data

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provided by Beheshti et al. [6] and Amiri et al. [7]. In order to investigate the rheological behavior of pure transformer oil and prepared samples, the relation between viscosity and shear rate was investigated. For all fluids and at various temperatures, the viscosity is independent of shear rate. This verified the Newtonian behavior of the base fluid and prepared samples. As an example, Figure 4 shows the viscosity of the pure transformer oil and prepared nanofluids containing 0.1 Vol% of nanoparticles at a temperature of 25 °C and shear rates of 105.6 to 237.6 s-1.

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Journal Pre-proof Dynamic viscosity of the pure transformer oil and prepared nanofluids at various temperatures from 25 to 65 ˚C and solid volume fractions from 0.001 to 0.01 is experimentally investigated and shown in Figure 5. As it is evident, for all samples, the viscosity of fluids reduces by increasing the temperature. This could be explained by weakening the intermolecular forces of the transformer oil due to increasing the temperature. This figure also illustrates that the type of nanomaterials has little impact on the dynamic viscosity of prepared transformer oil-based nano-

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lubricants. The samples that contain pure MWCNTs and those contain hybrid nanoparticles have

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nearly similar viscosity at the same temperature and solid volume fraction.

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Figure 5 also shows that the viscosity of transformer oil-based nanofluids slightly enhances with

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an increase in the solid volume fraction of nanoparticles. This is mainly because adding

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nanoparticles to transformer oil causes an interaction between nanoparticles and oil molecules, which in turn results in enhancing the viscosity of transformer oil. Figure 6 shows the amount of

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viscosity enhancement in various solid volume fractions and temperatures. This figure again

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shows that the type of nanoparticles has little impact on the viscosity of prepared nanofluids. The maximum amount of viscosity enhancement for samples that contain pure MWCNTs, hybrid

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MWCNTs/SiO2, hybrid MWCNTs/TiO2, and hybrid MWCNTs/Al2O3 is equal to 11.336, 13.015, 12.559, and 13.618%, respectively. 4.2 Thermal conductivity Thermal conductivity is known as one of the essential thermophysical parameters that affect the heat transfer performance of cooling fluids. Previous experimental studies showed that the enhancement of thermal conductivity of nanofluids depends on various parameters such as thermal conductivity of nanoparticles and base fluids, concentration, shape, and size of nanoparticles, and temperature [6, 7, 92, 93]. Before evaluating the effect of nanoparticles on the 19

Journal Pre-proof thermal conductivity of prepared nanofluids, the accuracy of the KD2 thermal properties analyzer has been validated by comparing the results of this work with those data obtained by Beheshti et al. [6] and Amiri et al. [7]. As can be seen in Figure 7, the thermal conductivity of pure transformer oil in various temperatures is in good agreement with those experimental outcomes that previously reported by Beheshti et al. [6] and Amiri et al. [7]. Thermal conductivity versus temperature for all prepared nanofluids and pure transformer oil is

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presented in Figure 8. The thermal conductivity of prepared nanofluids is higher than that of pure

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transformer oil. The higher thermal conductivity of nanoparticles compared to pure transformer

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oil along with the thermal motion of nanoparticles (Brownian motion) can be used to explain the

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enhancement of thermal conductivity of transformer oil after adding nanoparticles. Figure 8 also

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shows that the thermal conductivity of nano-lubricants enhances by increasing the solid volume fraction of nanoparticles.

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As it is shown in Figure 8-A, the thermal conductivity of the pure transformer oil decreases by

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increasing the temperature. However, the thermal conductivity of transformer oil-based

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nanofluids enhances by increasing the temperature. It is because by increasing the temperature, the surface energy of particles reduces. As a result, the agglomeration of particles and the viscosity of fluid reduce. This means the higher Brownian motion, which in turn results in higher thermal conductivity [31, 94, 95]. Amiri et al. [7] showed that the thermal conductivity of transformer oil-based nanofluids containing oxidized MWCNTs increases up to 60°C and decreases considerably at higher temperatures. They concluded that at temperatures above 60°C, the MWCNTs accumulate, and the thermal conductivity of nano-lubricants tremendously reduces. Nevertheless, the accumulation of nanoparticles and the sudden reduction of thermal conductivity have not been observed in this study. 20

Journal Pre-proof The thermal conductivity ratio versus solid volume fraction for all nanofluids is shown in Figure 9. As can be seen, the thermal conductivity of prepared nanofluids enhances by increasing the solid volume fraction of nanoparticles. This is mainly because by increasing the solid volume fraction of nanoparticles, the ratio of surface to volume, and eventually, the collision between nanoparticles increases [96]. As a result, heat transfer occurs at a higher rate in nanofluids containing higher solid volume fractions of nanoparticles. Besides, the samples containing pure

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MWCNTs have a higher thermal conductivity ratio compared to those of hybrid nanofluids. The

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maximum enhancement of thermal conductivity for samples that contain pure MWCNTs, hybrid

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MWCNTs/SiO2, hybrid MWCNTs/TiO2, and hybrid MWCNTs/Al2O3 is equal to 28.048, 18.013,

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19.309, and 20.471%, respectively.

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4.3 Breakdown voltage

Breakdown voltage is another crucial factor that directly affects the electrical performance of

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transformers oils. Adding any impurities could affect the breakdown voltage of transformer oils.

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Therefore, in this part of the study, the breakdown voltage of pure transformer oil and nanofluids

(Figure 10).

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containing 0.05 and 0.1 Vol% of nanoparticles were measured and compared with each other

Previous studies showed that adding MWCNTs to transformer oil dramatically reduces its breakdown voltage [6, 7, 19]. As can be seen in Figure 10, our experimental outcomes also show a dramatic decrease in the breakdown voltage of nanofluids containing pure MWCNTs. However, the reduction of the breakdown voltage of hybrid nanofluids was much lower compared to those of pure MWCNTs nanofluids. Therefore it could be concluded that hybrid transformer oil-based nanofluids not only have a lower cost compared to the pure MWCNTs nanofluids but also have higher breakdown voltage. 21

Journal Pre-proof The original transformer oil, which is used in this study, was designed for the transformers with a nominal voltage of below 72.5 kV. In this condition, the breakdown voltage should be at least 40 kV [6]. As a result, the nanofluids that contain pure MWCNTs could not be used for this application. As can be seen in Figure 10, all hybrid nanofluids that contain 0.05 Vol% of nanoparticles and the sample that contains 0.1 Vol% of hybrid MWCNTs/TiO2 can be used for the transformers with the nominal voltage of below 72.5 kV. All in all, it is a big success that the

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dielectric properties of hybrid carbon-based nanofluids synthesized in this study are far better

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compared to those properties of the pure MWCNTs nanofluids. Notably, the nanofluid that

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contains 1 Vol% of hybrid MWCNTs/TiO2 has a high thermal conductivity and an acceptable

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breakdown voltage.

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4.4 Modeling of viscosity

In this study, eight different soft computing approaches (i.e., GMDH, SVM, RBF, BAT-RBF,

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GOA-RBF, MLP, BAT-MLP, and GOA-MLP) were selected to model the dynamic viscosity of

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prepared nano-lubricants. As it was mentioned, the experimental outcomes showed that the type

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of nanoparticles has a limited effect on the viscosity of prepared nanofluids. Therefore, for modeling the viscosity of nanofluids, the input data belong to all prepared samples, including pure MWCNTs, hybrid MWCNTs/SiO2, hybrid MWCNTs/TiO2, and hybrid MWCNTs/Al2O3. Table 5 summarizes the statistical parameters of all implemented models, including the Average Percent Relative Error (APRE), Average Absolute Percent Relative Error (AAPRE), Root Mean Square Error (RMSE), and coefficient of determination (R2). APRE measures the relative deviation from experimental data, while AAPRE measures the relative absolute deviation from experimental data. Besides, RMSE measures the data dispersion around the line of best fit (regression line). It should be noted that the lower values of APRE, AAPRE, and RMSE show 22

Journal Pre-proof the higher accuracy of a model. Finally, the coefficient of determination (R2) shows how good the predicted values match the input data [57, 97]. The closer the value of R2 is to 1, the better the regression line matches the data. It should be mentioned that the implemented models were rated mainly based on the AAPRE and R2 parameters. The following equations were used to calculate the above-mentioned statistical parameters [57, 97]: 1

𝐴𝑃𝑅𝐸 = 𝑛 ∑𝑛𝑖=1 𝐸𝑖

of

(23)

𝑦𝑒𝑥𝑝,𝑖 −𝑦𝑝𝑟𝑒𝑑,𝑖 𝑦𝑒𝑥𝑝,𝑖

] ∗ 100 ; 𝑖 = 1, 2, … , 𝑛

(24)

re

𝐸𝑖 = [

-p

experimental value, which is calculated as follows:

ro

where, n is the number of data and 𝐸𝑖 is the related deviation of a predicted value from an

1

AAPRE = 𝑛 ∑𝑛𝑖=1|𝐸𝑖 |

na

(25)

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here, 𝑦𝑒𝑥𝑝 is the experimental value and 𝑦𝑝𝑟𝑒𝑑 is the predicted value.

1

2

𝑅2 = 1 −

Jo

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𝑅𝑀𝑆𝐸 = √𝑛 ∑𝑛𝑖=1(𝑦𝑒𝑥𝑝,𝑖 − 𝑦𝑝𝑟𝑒𝑑,𝑖 ) ∑𝑛 𝑖=1(𝑦𝑒𝑥𝑝,𝑖 −𝑦𝑝𝑟𝑒𝑑,𝑖 ) ∑𝑛 ̅̅̅̅̅̅̅) 𝑒𝑥𝑝 𝑖=1(𝑦𝑒𝑥𝑝,𝑖 −𝑦

2

(26)

2

(27)

where, 𝑦 ̅̅̅̅̅̅ 𝑒𝑥𝑝 is the mean of experimental data. Table 5 clearly shows that the developed model based on the GMDH approach has the highest accuracy in terms of predicting the dynamic viscosity of prepared nano-lubricants. The amount of error and a comparison between experimental data and outcomes of the GMDH model are shown in Figures 11 and 12, respectively. All of these figures clearly show the exceptional accuracy of the GMDH model for predicting the dynamic viscosity of transformer oil-based 23

Journal Pre-proof nanofluids. The SVM model is also quite useful for predicting the dynamic viscosity of prepared samples and can be ranked second among all approaches used for modeling the dynamic viscosity in this work. It can also be concluded that using the GOA algorithm to optimize RBF and MLP models can effectively improve their accuracy. However, the bat algorithm is not a proper optimization technique for RBF and MLP approaches. The implemented models can be ranked according to their predicting performance as follow:

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GMDH> SVM> GOA-MLP> GOA-RBF> MLP> RBF> BAT-RBF> BAT-MLP

Test 1.857 2.697 3.199 8.680 2.733 3.160 6.533 2.92

Total 2.690 3.149 4.897 6.665 3.134 3.141 8.441 3.061

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Total -0.105 0.453 -0.401 5.031 1.416 0.757 4.618 0.764

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Test -1.120 0.883 -1.144 6.993 1.405 0.377 2.041 -0.311

AAPRE Train 2.898 3.058 5.321 6.161 3.234 3.133 8.919 3.096

RMSE Train 0. 232 0.263 0.551 0.685 0.317 0.314 0.881 0.285

Test 0.157 0.301 0.349 0.792 0.273 0.189 0.801 0.304

Total 0.219 0.271 0.517 0.708 0.301 0.317 0.866 0.289

R2 Train 0.9968 0.9956 0.9830 0.9749 0.9939 0.9943 0.9542 0.9957

Test 0.9987 0.9957 0.9928 0.9539 0.9977 0.9944 0.9675 0.9927

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GMDH SVM RBF BAT-RBF GOA-RBF MLP BAT-MLP GOA-MLP

APRE Train 0.147 0.345 -0.223 4.541 1.418 0.660 5.263 1.033

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Model

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Table 5: Statistical parameters of implemented models for predicting the dynamic viscosity of nano-lubricants.

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4.5 Modeling of thermal conductivity The eight soft computing approaches described before were used to predict the thermal conductivity of prepared nanofluids. In this section, the simulations were performed for each type of nanofluids separately. This means the input data belong to just one type of prepared samples for each case. It should be noted that when the input data belong to all samples, the accuracy of the models in terms of predicting the thermal conductivity of prepared nanofluids reduces slightly.

24

Total 0.9972 0.9958 0.9849 0.9717 0.9949 0.9943 0.9577 0.9952

Journal Pre-proof Tables 6 to 9 summarize the statistical parameters of developed models for predicting the thermal conductivity of the samples that contained pure MWCNTs, hybrid MWCNTs/SiO2, hybrid MWCNTs/TiO2, and hybrid MWCNTs/Al2O3, respectively. The GMDH model outperforms other approaches in terms of predicting the thermal conductivity of transformer oilbased nano-lubricants. Figures 13 and 14 demonstrate the amount of error and a comparison between experimental data and results of the GMDH model for different types of prepared

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nanofluids. The SVM model is the other approach that has high accuracy in terms of predicting

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the thermal conductivity of prepared nano-lubricants. As can be seen in Tables 6 to 9, the

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statistical parameters of this model are close to those of the GMDH approach. The developed

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soft computing approaches can be ranked according to their accuracy as follows:

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Pure MWCNTs: GMDH> SVM> GOA-MLP> GOA-RBF> MLP> BAT-MLP> BAT-RBF> RBF

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Hybrid MWCNTs/SiO2: GMDH> SVM> GOA-RBF> MLP> GOA-MLP> BAT-RBF> BAT-

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MLP> RBF

BAT-RBF

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Hybrid MWCNTs/TiO2: GMDH> SVM> MLP> GOA-RBF> BAT-MLP> RBF> GOA-MLP>

Hybrid MWCNTs/Al2O3: GMDH> SVM> GOA-MLP> RBF> GOA-RBF> MLP> BAT-MLP> BAT-RBF Table 6: Statistical parameters of implemented models for predicting the thermal conductivity of nano-lubricants containing pure MWCNTs. Model GMDH SVM RBF

APRE Train -0.116 -0.126 -0.018

Test 0.133 0.398 -0.136

Total -0.064 -0.017 -0.043

AAPRE Train 0.526 0.519 1.062

Test 0.180 0.501 0.906

Total 0.454 0.516 1.029

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RMSE Train 8.92e-4 8.57e-4 1.56e-3

Test 2.97e-4 8.18e-4 1.38e-3

Total 8.05e-4 8.49e-4 1.53e-3

R2 Train 0.9776 0.9693 0.9295

Test 0.9961 0.9867 0.9289

Total 0.9803 0.9781 0.9295

Journal Pre-proof BAT-RBF GOA-RBF MLP BAT-MLP GOA-MLP

-0.223 0.145 -0.644 -0.105 0.030

0.371 -0.365 -0.068 0.149 -0.108

-0.099 0.039 -0.553 0.001 -0.052

1.006 0.801 1.010 0.830 0.902

1.258 0.776 0.261 1.051 0.812

1.058 0.795 0.963 0.876 0.883

1.48e-3 1.37e-3 1.52e-3 1.52e-3 1.29e-3

1.61e-3 1.22e-3 1.13e-3 1.14e-3 1.30e-3

1.50e-3 1.34e-3 1.45e-3 1.45e-3 1.29e-3

0.9299 0.9394 0.9340 0.9331 0.9458

0.9319 0.9552 0.9507 0.9454 0.9600

0.9314 0.9456 0.9366 0.9361 0.9497

Test 0.198 0.313 0.662 0.692 0.357 0.142 0.512 0.465

Total 0.324 0.329 0.619 0.567 0.463 0.499 0.555 0.461

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Total -0.007 -0.086 -0.065 -0.042 0.121 -0.074 -0.099 -0.161

RMSE Train 6.57e-4 6.77e-4 8.72e-4 8.50e-4 7.39e-4 7.78e-4 8.97e-4 7.63e-4

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Test 0.145 0.254 -0.291 -0.169 0.154 0.073 0.071 0.003

AAPRE Train 0.357 0.333 0.608 0.534 0.491 0.518 0.567 0.460

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GMDH SVM RBF BAT-RBF GOA-RBF MLP BAT-MLP GOA-MLP

APRE Train -0.048 -0.176 -0.006 -0.009 0.112 -0.151 -0.144 -0.205

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Model

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Table 7: Statistical parameters of implemented models for predicting the thermal conductivity of nano-lubricants containing hybrid MWCNTs/SiO2. Test 2.74e-4 4.90e-4 8.80e-4 8.87e-4 4.86e-4 3.31e-4 7.80e-4 6.62e-4

Total 5.98e-4 6.43e-4 8.74e-4 8.57e-4 6.94e-4 7.40e-4 8.74e-4 7.43e-4

R2 Train 0.9667 0.9598 0.9281 0.9364 0.9541 0.9461 0.9336 0.9503

Test 0.9865 0.9798 0.9467 0.9247 0.9752 0.9406 0.9343 0.9591

Total 0.9690 0.9642 0.9338 0.9363 0.9583 0.9525 0.9338 0.9521

Test 0.163 0.160 0.206 -0.005 -0.320 0.047 -0.294 -0.079

Total -0.051 0.027 0.036 0.266 -0.084 -0.083 -0.078 -0.020

AAPRE Train 0.391 0.404 0.773 0.636 0.520 0.630 0.658 0.625

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GMDH SVM RBF BAT-RBF GOA-RBF MLP BAT-MLP GOA-MLP

APRE Train -0.107 -0.007 -0.008 0.337 -0.022 -0.143 -0.021 -0.005

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Model

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Table 8: Statistical parameters of implemented models for predicting the thermal conductivity of nano-lubricants containing hybrid MWCNTs/TiO2. Test 0.310 0.307 0.654 0.683 0.672 0.158 0.687 0.545

Total 0.375 0.384 0.749 0.646 0.552 0.598 0.668 0.608

RMSE Train 7.01e-4 7.25e-4 9.96e-4 1.08e-3 8.53e-4 9.31e-4 9.47e-4 1.01e-3

Test 4.40e-4 3.86e-4 9.40e-4 9.83e-3 9.27e-4 4.06e-4 9.38e-4 9.04e-4

Total 6.55e-4 6.69e-4 9.85e-4 1.06e-3 8.69e-4 8.89e-4 9.45e-4 9.88e-4

R2 Train 0.9616 0.9599 0.9184 0.9025 0.9372 0.9274 0.9270 0.9162

Test 0.9804 0.9794 0.9253 0.9239 0.9334 0.9403 0.9176 0.9333

Total 0.9648 0.9633 0.9207 0.9073 0.9338 0.9354 0.9269 0.9202

Table 9: Statistical parameters of implemented models for predicting the thermal conductivity of nano-lubricants containing hybrid MWCNTs/Al2O3. Model GMDH SVM RBF BAT-RBF

APRE Train -0.089 -0.195 -0.006 0.180

Test 0.132 0.160 -0.275 -0.101

Total -0.043 -0.121 -0.062 0.121

AAPRE Train 0.383 0.361 0.674 0.611

Test 0.208 0.391 0.701 0.717

Total 0.346 0.367 0.680 0.633

26

RMSE Train 7.14e-4 7.31e-4 9.04e-4 1.10e-3

Test 2.99e-3 5.76e-3 9.80e-3 1.20e-3

Total 6.49e-3 7.01e-3 9.20e-3 1.10e-3

R2 Train 0.9679 0.9596 0.9295 0.9135

Test 0.9860 0.9795 0.9295 0.9017

Total 0.9696 0.9646 0.9307 0.9110

Journal Pre-proof GOA-RBF MLP BAT-MLP GOA-MLP

0.034 0.195 -0.076 -0.022

-0.219 -0.126 -0.232 0.348

-0.018 0.075 -0.108 0.054

0.567 0.629 0.724 0.689

0.752 0.215 0.771 0.509

0.605 0.632 0.734 0.651

9.27e-3 9.14e-3 1.06e-3 9.81e-3

1.20e-3 5.97e-3 1.20e-3 7.46e-3

9.83e-3 9.41e-3 1.09e-3 9.37e-3

0.9332 0.9191 0.9197 0.9375

0.9179 0.9449 0.8915 0.9298

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5. Conclusions

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In this study, four different types of transformer oil-based nano-lubricants were prepared. The

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thermal conductivity, dynamic viscosity, and breakdown voltage of prepared samples were

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experimentally evaluated. In addition, eight different soft computing approaches, including GMDH, SVM, RBF, BAT-RBF, GOA-RBF, MLP, BAT-MLP, and GOA-MLP, were selected to

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model the dynamic viscosity and thermal conductivity of prepared samples. The most important

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outcomes of this study are as follows:

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1. The viscosity of prepared nano-lubricants enhances with an increase in the solid volume fraction. However, increasing the temperature results in a substantial reduction of the

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dynamic viscosity of prepared nano-lubricants. 2. The nanofluids containing pure MWCNTs and those containing hybrid nanoparticles exhibit an almost similar rheological behavior in the same solid volume fraction and temperature. 3. The thermal conductivity of transformer oil-based nano-lubricants enhances by increasing the solid volume fraction and temperature. 4. The nanofluids containing pure MWCNTs have a higher thermal conductivity ratio compared to those containing hybrid nanoparticles. 27

0.9306 0.9276 0.9141 0.9368

Journal Pre-proof 5. The dielectric properties of hybrid carbon-based nanofluids are far better than those of the pure MWCNTs nanofluids. 6. The GMDH approach significantly outperforms all other models in terms of predicting the thermal conductivity and dynamic viscosity of nanofluids.

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Acknowledgment

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The authors are grateful for the financial support of the ARAM Company. We would also like to

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thank Mr. Mohsen Fasih (ARAM Company) for analyzing the breakdown voltage. We would also like to thank Dr. Alireza Nasiri, Mr. Majid Valizadeh, and Mr. Farough Agin from the

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Research Institute of Petroleum Industry for their valuable discussion in the experimental part of

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References

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Figure 1: SEM (A), FESEM (B) and TEM (C and D); pictures of A) Al2O3, B) SiO2, C) TiO2 and D) MWCNTs.

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0.098 30

40

50

60

70

80

-p

20

ro

Thermal conductivity (W/m.°C)

0.108

re

Temperature (°C)

Figure 7: A comparison between the thermal conductivity of pure transformer oil that obtained in

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na

lP

this study and those that reported by Beheshti et al. [6] and Amiri et al. [7].

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Thermal conductivity (W/m.°C)

0.129 0.124

Pure oil ϕ=0.001%

0.119

ϕ=0.0025% ϕ=0.005%

0.114

ϕ=0.01% ϕ=0.025%

0.109

ϕ=0.05% ϕ=0.1%

0.099 20

30

40

50

ro

of

0.104

60

70

80

-p

Temperature (°C)

re

(A)

lP

0.122

0.116

0.112

0.108

ϕ=0.0025% ϕ=0.005% ϕ=0.01%

ur

0.114

0.11

ϕ=0.001%

na

0.118

ϕ=0.025% ϕ=0.05%

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Thermal conductivity (W/m.°C)

0.12

ϕ=0.1%

0.106 20

30

40

50

Temperature (°C)

(B)

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60

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Thermal conductivity (W/m.°C)

0.122 0.12 0.118 ϕ=0.001% 0.116

ϕ=0.0025% ϕ=0.005%

0.114

ϕ=0.01% 0.112

ϕ=0.025% ϕ=0.05%

0.11

ϕ=0.1%

of

0.108

20

30

40

50

ro

0.106 60

70

80

-p

Temperature (°C)

re

(C) 0.125

lP

0.121

0.117

0.113

0.109 0.107

ϕ=0.0025% ϕ=0.005% ϕ=0.01%

ur

0.115

0.111

ϕ=0.001%

na

0.119

ϕ=0.025% ϕ=0.05%

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Thermal conductivity (W/m.°C)

0.123

ϕ=0.1%

0.105 20

30

40

50

60

70

80

Temperature (°C)

(D) Figure 8: Thermal conductivity versus temperature for transformer oil and pure MWCNTs (A), hybrid MWCNTs/SiO2 (B), hybrid MWCNTs/TiO2 (C), and hybrid MWCNTs/Al2O3 (D).

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Thermal conductivity ratio

1.25

1.2

T=25°C T=35°C

1.15

T=45°C T=55°C

1.1

T=65°C T=75°C

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1.05

0

0.02

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1 0.04

0.06

0.08

0.1

-p

Solid volume fraction (%)

re

(A)

lP

T=25°C

na

1.15

T=45°C

ur

1.1

T=35°C

1.05

T=55°C T=65°C

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Thermal conductivity ratio

1.2

T=75°C

1 0

0.02

0.04

0.06

Solid volume fraction (%)

(B)

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0.08

0.1

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1.16 1.14 T=25°C

1.12

T=35°C 1.1

T=45°C

1.08

T=55°C

1.06

T=65°C

1.04

T=75°C

1.02 1 0.02

0.04

0.06

0.08

0.1

ro

0

of

Thermal conductivity ratio

1.18

-p

Solid volume fraction (%)

re

(C)

lP

T=25°C

na

1.15

T=45°C

ur

1.1

T=35°C

1.05

T=55°C T=65°C

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Thermal conductivity ratio

1.2

T=75°C

1 0

0.02

0.04

0.06

0.08

0.1

Solid volume fraction (%)

(D) Figure 9: Thermal conductivity ratio versus solid volume fraction for pure MWCNTs (A), hybrid MWCNTs/SiO2 (B), hybrid MWCNTs/TiO2 (C), and hybrid MWCNTs/Al2O3 (D).

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MWCNT/Al2O3-0.1 Vol%

39.0515

MWCNT/Al2O3-0.05 Vol%

42.7123

MWCNT/SiO2-0.1 Vol%

37.0214

MWCNT/SiO2-0.05 Vol%

40.9956

MWCNT/TiO2-0.1 Vol%

44.2301

MWCNT/TiO2-0.05 Vol%

49.2112

MWCNT-0.1 Vol%

24.3333

MWCNT-0.05 Vol% Pure Oil 10

20

30

ro

0

of

29.7307

40

58.2351 50

60

-p

Breakdown voltage (kV)

re

Figure10: The breakdown voltage of the base oil and prepared nanofluids containing 0.05 and

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0.1 Vol% of nanoparticles.

Figure 11: The amount of error of the GMDH model for dynamic viscosity of prepared nanofluids. 48

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Figure 12: A comparison between experimental data and results of the GMDH model for

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dynamic viscosity of prepared nanofluids.

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Figure 13: The amount of error of the GMDH model for thermal conductivity of pure MWCNTs

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(A), hybrid MWCNTs/SiO2 (B), hybrid MWCNTs/TiO2 (C), and hybrid MWCNTs/Al2O3 nanofluids(D).

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Figure 14: A comparison between experimental data and results of the GMDH model for thermal

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conductivity of pure MWCNTs (A), hybrid MWCNTs/SiO2 (B), hybrid MWCNTs/TiO2 (C), and hybrid MWCNTs/Al2O3 nanofluids (D).

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Conflicts of Interest Statement

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The authors of this article certify that they have NO affiliations with or involvement in any organization or entity with any financial interest or nonfinancial interest in the subject matter or materials discussed in the manuscript entitled “On Evaluation of Thermophysical Properties of Transformer Oil-based Nanofluids: A Comprehensive Modeling and Experimental Study”.

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Highlights Preparing four different types of transformer oil-based nanofluids using two-step method



Examination of dynamic viscosity and thermal-conductivity of samples with different nanoparticles concentration



Examination of the breakdown voltage of the pure transformer oil and nanofluids samples



Using different soft computing approaches to model viscosity and thermal-conductivity of nanofluids

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

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