Increasing the accuracy of estimating the dynamic viscosity of hybrid nano-lubricants containing MWCNT-MgO by optimizing using an artificial neural network

Mohammad Hemmat Esfe; Saeed Esfandeh; Fatemeh Amoozadkhalili; Davood Toghraie

doi:10.1016/j.arabjc.2022.104405

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Original article

02 2022

:16;

104405

doi:

10.1016/j.arabjc.2022.104405

Increasing the accuracy of estimating the dynamic viscosity of hybrid nano-lubricants containing MWCNT-MgO by optimizing using an artificial neural network

Mohammad Hemmat Esfe^{^a,⁎}, Saeed Esfandeh^{^a}, Fatemeh Amoozadkhalili^{^a}, Davood Toghraie^{^b,⁎}

a Nanofluid Advanced Research Team, Tehran, Iran

b Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran

⁎Corresponding authors. m.hemmatesfeh@gmail.com (Mohammad Hemmat Esfe), Toghraee@iaukhsh.ac.ir (Davood Toghraie)

Received: 2022-6-27, Accepted: 2022-11-6,

Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

ANN is used to predict the $μ_{nf}$ of the MWCNT-MgO/SAE40 nano-lubricant experimental data set.
To predict the $μ_{nf}$ of the data by ANN, an MLP network with LM algorithm is used.
From 400 different ANN structures for nano-lubricant, the optimal structure is selected.
The margin of deviation for all ANN data is in the range of less than −1% <MOD <+ 1 %.
It's good because the ANN model is more accurate and has a great ability to predict $μ_{nf}$ .

Abstract

Artificial neural network (ANN) is utilized as efficient models to forecast the nanofluids (NFs) viscosity ( $μ_{nf}$ ). In this examination, ANN is used to forecast the $μ_{nf}$ of the MWCNT-MgO (25 % −75 %) / SAE40 nano-lubricant (NL) experimental data set. Experimental evaluation of NLs is taken in volume fraction of nanoparticles (NPs) $φ =$ 0.0625 % −1% and temperature range of T = 25 to 50 °C. To predict the $μ_{nf}$ of the data using ANN, a multilayer perceptron (MLP) ANN with the algorithm of Levenberg-Marquardt (LM) is utilized. For ANN modeling, temperature, $φ$ and shear rate ( $\dot{γ}$ ) are determined as inputs and $μ_{nf}$ is determined as output. From 400 various ANN samples for NL, the optimal sample (OS) is selected, comprising two hidden layers (HLs) with the OS of 8 and 5 neurons in the primary and second layer, respectively. Eventually, for the OS, the amount of the regression coefficient (RC) and the mean square error (MSE) are set equal to 0.9999882 and 0.001453292, respectively. The margin of deviation (MOD) for all ANN information is in the range of less than −1% <MOD <+1%. It's good because the ANN pattern is more precise and has a great ability to forecast $μ_{nf}$ . The main goal of this research is to model and estimate the $μ_{nf}$ of MWCNT-MgO (25:75)/SAE40 NL through ANN and also to select the optimal structure from the set of predicted ANN structures and manage time and cost.

Keywords

ANN

Experimental data

Hybrid nano-lubricants

Dynamic viscosity

nanolubricant

Levenberg-Marquardt

multilayer perceptron

Show Related Articles from PubMed

ANN: artificial neural network
MoD: Margin of deviation
NF: Nanofluid
NP: Nanoparticle
HL: hidden layers
LM: Levenberg-Marquardt
MSE: mean square error
OS: optimal sample

1 Introduction

The flourishing time of nanoscience can be seen in the last two decades, where the research of researchers regarding nanoscience has found a significant improvement in all fields of science. Researchers are continuously investigating various aspects of this branch of technology (Doaa Domyati et al., 2022), (Azin et al., 2021), (Zhang.et al., 2015), (Wang et al., 2022), (Anqi et al., 2022). Investigating the rheological properties of fluids has always been one of the subjects of researchers' research, and the reduction of viscosity to reduce pumping power has always become one of the subjects of researchers' research Zhang et al., (2022a), Zhang et al., (2022b). Also, fluids are used in various applications such as lubrication, heat transfer, etc. and optimizing their properties, such as increasing the thermal conductivity and reducing the viscosity, can increase their efficiency Bagheri et al., 2020; Esfe, 2017; Keshtegar et al., 2020; Li et al., 2022; Putra, 2020; Rikani, 2021; Tang et al., 2022; Yang et al., 2017 . The particles that are added to fluids in old research had micrometer sizes. These particles do not have the necessary stability in the suspension and the settling speed of these materials is high, and this causes the fluid passages to be blocked quickly. But over time, nanofluids (NFs) were obtained by distributing particles with nano dimensions in conventional fluids. NFs are new materials that are a combination of nanoparticles (NPs) with a size of 0–100 nm in the base fluid Hosseini and Dehaj, 2021a,b; Mousavi et al., 2021; Sheikholeslami, 2017; Valipour et al., 2017 while that NFs form a much more stable suspension and their low sedimentation speed minimizes the problem of clogging and blockage of ducts. These particles are made of metal particles such as copper (Cu), magnesium (Mg) or metal oxides such as Al₂O₃ and CuO and Khanafer et al., (2012), Saidur et al., (2011), Haddad et al., (2012). NFs originate from heat transfer (HT) and nanotechnology. NFs have superior properties, and this has led to an increase in cooling power, a reduction in the power required for fluid pumping, the development of more compact NF-based systems, a reduction in the ratio of cooling fluids, a reduction in friction coefficient, and miniaturization of heat exchangers. size and improved wear resistance (see Fig. 1).

One of the main advantages of NFs can be sought in heat exchangers. Since thermal conductivity (TC) augmentation is much more significant in NFs Azman et al., (2021), Öğüt and Kahveci, (2016), Jamei et al., 2021; Ruhani, 2022; Yang et al., 2021 , the HT coefficient of NFs passing through the heat exchanger tubes is expected to enhance significantly Nfawa et al., (2021). Studies have proven that the addition of NPs to fluids, can enhance the $μ_{nf}$ Banisharif et al., 2021; Dezfulizadeh et al., 2021; Esfe and Sarlak, 2017; He, 2020; Hosseini and Dehaj, 2021a,b; Shahsavar et al., 2021 . If two or more NPs are added to the fluid, then hybrid NFs will be created that can have better properties than NFs with a single NP. This NF is generally prepared by dispersing two different NPs in the base fluid and appears as new nanotechnology. One of the pioneers in the field of hybrid NFs that has worked on many NFs is the Hemmat Esfe research team, which has examined thermophysical features like $μ_{nf}$ and $TC$ Hemmat Esfe et al., 2022, Esfe and Arani, 2018; Fontes et al., 2015; Kotia and Ghosh, 2015 . Hybrid NFs are used in various fields such as heat exchangers and electric coolers, the automotive industry, medicine and defense Jamil et al., (2020), Alidoust et al., (2022). Table 1 lists the studies on $μ_{nf}$ and TC of NFs.

Table 1 Some of the recently examinations on the NFs.

Ref.	NPs	Base Fluid	T (˚C)	$φ$ (%)	The purpose of the Experiment
Akhavan-Behabadi et al., (2016)	Al₂O₃	Gear oil (SAE EP-90)	15–40	0–2	Distribution of size and stability with varying temperatures and $φ$
Binu et al., (2015)	Diamond & MWCNT	Oil	20 & 25	0.005–0.05	$k_{nf}$ , $μ_{nf}$ and breakdown voltage of NFs with varying $φ$
Aberoumand et al., (2016)	CuO	Oil	20–80	0.5–1.5	Thermophysical features and convective HT rate
Barati-Harooni et al., (2016)	TiO₂	Oil	10–80	0.05–2.5	Correlation and $μ_{nf}$
Çolak et al., (2021)	Ag	oil	40–100	0–0.72	$μ_{nf}$ with varying $φ$ .

For utilization of the properties of NFs in the needed calculations in industrial system designs, it is necessary to present these properties in form of mathematical equations or software. Some studies have provided some theoretical and experimental equations, based on temperature and $φ$ . These studies are listed in Tables 2 and 3. Also, researchers used software methods for the prediction of these properties. Their results indicate the high precision of these methods and their flexibility to changing conditions Goudarzi et al., (2009), Goudarzi et al., (2008), Ashrafi et al., (2018).

Table 2 Some of the theoretical models.

Ref.	$φ Φ$ (%)	Correlation
Einstein(1905)	--------	$\frac{μ_{nf}}{μ_{bf}} = e^{(\frac{2.5 φ}{1 - k φ})}$ 1.35 < k < 1.91
Krieger and Dougherty (1959)	--------	$\frac{μ_{nf}}{μ_{bf}} = \frac{1}{{(1 - φ)}^{2.5}}$
Nielsen(1970)	< 2	$\frac{μ_{nf}}{μ_{bf}} = (1 + 2.5 φ)$
Lundgren(1972)	--------	$\frac{μ_{nf}}{μ_{bf}}$ = [1 − $φ_{m}$ ] − 2.5 $φ_{m} {0.495 < φ}_{m} < 0.54$
Wanget al., (1999)	< 2	$\frac{μ_{nf}}{μ_{bf}} = (1 + 1.5 φ) e^{(\frac{1}{1 - φ_{m}})}$
Tsenget al., (2003)	< 4	$\frac{μ_{nf}}{μ_{bf}}$ = (1 + 2.5 $φ$ + 6.25 $φ^{2}$ )
Meybodiet al., (2016)	--------	$\frac{μ_{nf}}{μ_{bf}} = (1 + 7.3 φ + 123 φ^{2}$ )

Table 3 Some of the experimental models.

Ref.	NF	$φ$ (%)	Correlation
Esfe et al. (2014)	Al₂O₃, TiO₂, SiO₂ and CuO/Water	< 4	$\frac{μ_{nf}}{μ_{bf}} = \frac{133.546 - 343.824 e^{(\frac{φ}{s})} + 290.118 ({e^{(\frac{φ}{s})})}^{2} - 78.993 ({e^{(\frac{φ}{s})})}^{3}}{0.911 + 32.3301 \times \frac{\ln s}{T} - 11.732 \times \frac{({\ln s)}^{2}}{T}}$
Esfe and Saedodin (2014)	ZnO/EG	Up to 2	$\frac{μ_{nf}}{μ_{bf}} = (0.9118 e^{5.49 φ - 0.00001359 T^{2}} + 0.0303 \ln (T))$
Afrand et al., (2016)	Mg(OH)₂/ EG	< 2	$\frac{μ_{nf}}{μ_{bf}} = (15.89 + 614.4 φ - 14526 φ^{2})$
Shaddel et al., (2016)	Ag/Oil	0–0.72 (wt)	$\frac{μ_{nf}}{μ_{bf}} = (1.15 + 1.061 φ - 0.5442 φ^{2} + 0.1181 φ^{3}$ )
(Hemmat Esfe et al., 2022)	MWCNT-MgO	up to 1	μ_nf = +1439.18463–74.55874T + 680.60734φ-0.023008SR-18.93092Tφ +9.20862E-004TSR+1.41458T²-335.84851SVF²+1.64364E-007SR²+0.14964T²φ-1.03952E-005 T²SR+3.83013 Tφ²-9.38513E-003 T³ + 68.56743φ³

The rheological behavior of fluids is a science that deals with the deformation of materials due to the exerted forces on them. Determination of $φ$ and temperature that affects on properties of NFs is one of the aspects of rheology science that was the subject of some studies in recent years. NFs have two Newtonian and non-Newtonian behaviors depending on the type of used materials in them. Aberoumand et al. Aberoumand et al., (2016) measured the $μ_{nf}$ of Ag/oil NL at T = 25 to 60 ˚C and $φ =$ 0.12 % to 0.72 %. The outcomes display that with an increase in $φ$ , the $μ_{nf}$ changes shift from linear to non-linear modes; in other words, the NL’s behavior becomes non-Newtonian. Also, at T < 35 ˚C, NFs show non-Newtonian behavior but at T > 35 ˚C, it begins to show Newtonian behaviors. A review of past research shows that the need for high accuracy in the process of estimating the $μ_{nf}$ , especially hybrid NFs, is of great importance. Therefore, recently the use of ANNs and other post-processing methods were widely studied by researchers. In recent years, ANN was used in various applications such as solar cells, memristors, thermistors, and supercapacitors, in medicine, including data prediction in the covid-19 virus, etc that can be find in Shakeri et al., (2016), Sutar et al., (2021), Dongale et al., (2015), Yan et al., (2020), Zhang et al., (2021), , Safa et al., (2020) studies and some of them are shown in Fig. 2.

Various applications of anns in various industries.

In recent years, increasing the accuracy in predicting the rheological behavior of NFs and nano-particles was one of the most important fields of study in the field of HT. Considering that the behavior of NFs and NLs should be studied separately, it is necessary to define a wide range of targeted studies to increase the accuracy of predicting the rheological and thermal behavior by different researchers and its results in industrial and engineering simulations. For this reason, using experimental data, $μ_{nf}$ of MWCNT-MgO(25:75)/SAE40 is presented in terms of temperature, $φ$ and $\dot{γ}$ variables by ANN. It should be noted that all experimental data were taken from (Hemmat Esfe et al., 2022). The complex rheological behavior of this NL and the presence of different parameters reduce the accuracy of common relationships for predicting $μ_{nf}$ . The optimal ANN is selected after examining a large number of neurons and different transfer functions in a large number of different ANNs. According to the authors, no published research has been presented in this area so far.

2 ANN training

An ANN is fabricated of a set of nodes named artificial neurons that are like biological neurons in the brain of a human. Any connection among neurons can transfer a signal from one neuron to another Esfe et al., 2018; Rezaee et al., 2018. Signals and then the signal neurons are connected to their process by the receiving neuron. In the ordinary implementation of ANNs, a signal of the synapse is an actual number, and each neuron output is computed using a nonlinear function of its input. Synapses and neurons have weights that are regulated as learning progress Shirani et al., (2015), Aghaei et al., (2018), Ghazvini et al., (2020), Dianati Tilaki et al., (2020), Rustamovich Sultanbekov et al., (2020), Tan et al., (2022), Ruhani et al., (2019a), Ruhani et al., (2019b). In this research, ANN modeling to predict the $μ_{nf}$ of MWCNT-MgO (25 %-75 %)/SAE40 in $φ$ , temperature and $\dot{γ}$ are determined as inputs and $μ_{nf}$ is determined as output. An example of an ANN structure is a structure with two hidden layers (HLs), in which there are 10 neurons in each HL and using transfer functions (TFs) (4 modes) which are composed of a total of 400 topologies. The ANN pattern is a multilayer perceptron (MLP) and the utilized algorithm for the training section is Levenberg-Marquardt (LM). The sigmoid transfer function is utilized in each of the HLs. To choose, the most optimal sample (OS) of ANN, a set of 400 various ANN samples was investigated, which vary in the neurons number in the primary and second HLs and the mixture of exerted TFs to the HLs. In the examined samples, various mixtures of tan-sigmoid and log-sigmoid tangent TFs in HLs were utilized. Out of 400 different ANN structures, the OS is formed, which includes two HLs with the OS of 8 and 5 neurons in the primary and second layers, respectively. In each section, the number of HLs, the neuron number in each HL, and the related TFs to the HLs were put on the agenda to determine the structure of the set of ANN structures. The technique of weighting exerted on neurons is also assessed randomly. Finally, to attain the OS and by the training process of ANN, 174 sets of information were utilized, which were allocated to three stages, information to train (70 %), validation step to optimize the neurons number, and HLs (15 %) and test step to the modality of performance of ANN (15 %). The best-choose sample from the 400 examined samples to forecast the $μ_{nf}$ of MWCNT-MgO (25:75) / SAE40 NL is plotted in Fig. 3. Fig. 4 shows the flowchart for choosing and gaging the 400 structures' performance of the examined ANN. Gaging the amount of R and reaching the number 1 is one of the chief measures for choosing the finest ANN sample. A higher R-amount is a symbol that ANN outcomes are more consonant with laboratory outcomes.

The proposed algorithm to attain the OS of ANN.

Given that the ANN alone cannot use all the modeled structures, it is necessary to assess ANN's performance. Therefore, the ANN regression coefficient (RC) factors R for the three steps are presented in Table 4 and the best amount of the RC based on the information in Table 4 is equal to 0.9999882, which is related to the eleventh structure in Table 4. It must be mentioned that the eleventh structure in Table 1 is the OS among the 400 samples with maximum RCs compared to other examined samples. The neuron's number and the kind of TFs are given in Table 4.

Table 4 Features of top 11 ANN structures.

Candidate Topology No.	Structure	Function1	Function2	R	Train R	Val R	Test R
1	[2 2]	tansig	tansig	0.9999282	0.9999531	0.9999695	0.9998892
2	[2 4]	tansig	tansig	0.9999611	0.9999725	0.9999321	0.999487
3	[2 5]	tansig	tansig	0.9999651	0.9999742	0.9999254	0.9999670
4	[2 6]	logsig	tansig	0.9999668	0.9999766	0.9999556	0.9999264
5	[2 8]	tansig	logsig	0.9999753	0.9999800	0.9999703	0.9999626
6	[3 4]	logsig	tansig	0.9999754	0.9999781	0.9999683	0.9999624
7	[4 2]	tansig	tansig	0.9999757	0.9999762	0.9999766	0.9999702
8	[4 5]	logsig	tansig	0.9999836	0.9999883	0.9999734	0.9999766
9	[4 6]	tansig	logsig	0.9999843	0.9999888	0.9999839	0.9999642
10	[7 4]	tansig	tansig	0.9999851	0.9999956	0.9999704	0.9999519
11	[8 5]	tansig	logsig	0.9999882	0.9999962	0.9999712	0.9999709

3 Results and discussion

After determining the OS and neuron number and HLs from the set of different samples of the ANN, in this section, it is essential to examine the performance of the forecasted information from different aspects. The amount of the RC close to 1 indicates a close connection between the laboratory and the forecasted information from the ANN. The correlation relationship for different stages including training, testing, and validation and all information is drawn in Fig. 5 in four separate sections. Note that the RC for all information in the current pattern is higher than 0.999. Although the RC occurred in the ninth or eighth topologies during the training and validation steps, here, the results of the RC survey are more important for all data, which is 0.9999882 and belongs to the 11th proposed topology.

The performance of the selected sample from ANN samples in terms of Mean-Square Error (MSE) in three stages (Train, test, and validation) and all information analysis is displayed in Fig. 6. The MSE in the training phase compared to the other phases is the lowest MSE, which according to Eq. (1) is equal to 0.001453292.

(1)

MSE = \frac{1}{N} \sum_{i = 1}^{N} (μ_{rel} {|_{EXP} - μ_{rel} |_{pred})}^{2}

The evaluation of the forecasted information of the designated ANNs with the outcomes of the experimental information in four sectors (All information, training, validation, and test) is drawn in Fig. 7. According to Fig. 7, there is a very good homogeneity among the outputs of ANN data and experimental data, and the modeled data accurately predicts the laboratory values.

Comparison among forecasted information with ANN-according to empirical information.

A comparison between experimental data predicted by ANN is shown in Fig. 8. This was done numerically in three stages including training, testing, and validation. If adequate accuracy is achieved in the data, the ANN training is complete and provides an acceptable output. According to the curves in Fig. 8, There is a close correlation between the data, which indicates the high accuracy of the ANN data from the experimental data.

Fig. 9 shows another comparison between the experimental and the forecasted information using the ANN in different temperature ranges and for each $φ$ separately. As shown in the curves of Fig. 9, all points predicted using ANN are associated with points of experimental, which indicate the high precision and appropriate ANNs performance in forecasting laboratory information.

Comparison of ANN by experimental information.

Fig. 10 shows the associated error with the predicted data of different phases of the train, validation, and testing for the data set separately. As shown in Fig. 10, the maximum error is between ± 2 and this indicates the accuracy of predicted viscosities from the ANN model. According to Fig. 10, it was observed that the highest error in all data and test phases is seen at T = 250 ⁰C and less than 5±. The least error in the validation phase is less than ± 1.

A histogram diagram of data prediction errors of the three phases in ANN modeling is shown in Fig. 11. Most of the data errors are positioned near the line passing through zero and in the range of ± 1. However, for the test and validation phases, the frequency of data was considered in the range of more than ± 1.5. According to Fig. 11, the least error with the highest frequency belongs to the training phase which is equal to −0.152232464. Also to check the accuracy of the ANN prediction, the margin of deviation (MOD) is calculated and depicted in Fig. 12.

The margin of deviation (MOD) for the experimental information is reported with the predicted data for the different phases in Eq. (2).

(2)

M O D (%) = \frac{μ_{pre -} μ_{\exp}}{μ_{\exp}} \times 100

Fig. 11 displays the MOD of this information at various $φ$ . According to Fig. 11, the MOD does not surpass 1 %±, which shows a satisfactory precision of the association accuracy of the proposed data for forecasting the $μ_{nf}$ of MWCNT-MgO (25:75) / SAE40 NL. The highest MOD in all information phase at T = 40 ⁰C was observed in the range of less than −2%. In other phases, it has the lowest MOD.

To predict the $μ_{nf}$ of MWCNT-MgO (25:75)/SAE40 NL, the Batchelor relation (Eq. (3) was offered, which is according to the $φ$ and the base fluid viscosity and estimates the $μ_{nf}$ . This relationship is defined as follows Batchelor (1977):

(3)

μ_{nf} = (1 + 2.5 φ + 6.5 φ^{2}) μ_{f}

Fig. 13 displays the ultimate comparison of the study, which is very significant. In this sector, the outputs of the reported relationship, the ANN prediction data and the $μ_{nf}$ of the experimental data at different $φ$ and T = 25, 30, 40 and 50 °C and $\dot{γ}$ = 3999 s⁻¹ are compared. Comparisons show that there is satisfactory compatibility between the considered ANN outputs and the experimental results. ANN accuracy proves the consistency of the $μ_{nf}$ of ANN data and experimental data. In addition, the obtained values from the presented relationship to predict the $μ_{nf}$ at high $φ$ are close to the outcomes of laboratory data, but their precision is less than the ANN.

Comparison among empirical information (Zhang et al., 2022b) and modeling outputs of ANN and association.

4 Conclusion

Examining laboratory data for $μ_{nf}$ takes a lot of time and money. As a result, several techniques were proposed to predict the $μ_{nf}$ . One of the best methods is data modeling by ANN. In this work, $μ_{nf}$ of MWCNT-MgO/SAE40 NL was evaluated using ANN. Also, 174 laboratory data in terms of temperature, $\dot{γ}$ and $φ$ were used for ANN modeling. Temperature, $\dot{γ}$ and $φ$ were considered as input variables and predicted $μ_{nf}$ as output variables in ANN. In this research, the MLP model with an LM algorithm with two transfer functions was used to design ANN. The RC and MSE for the ANN operating system were 0.9999882 and 0.001453292, respectively. The operating system is selected from among 400 ANN samples that have two HLs and 8 and 5 neurons in the first and second HLs. The highest frequency of MOD Amounts was in the range of −1 < MOD> +1, indicating a very low error of ANN data for $μ_{nf}$ . In the final part, the comparison of three groups of data, i.e., Experimental data, correlation output and ANN predicted data show that ANN performed better in predicting $μ_{nf}$ than the presented relationship. Therefore, the predicted data are more accurate than the calculated data. The main goal of the present work is to design, model, and estimate the viscosity of MWCNT-MgO/SAE40 NL through ANN artificial neural network and Choosing the best and most suitable optimal structure from the set of ANN predicted structures is financially and laboratory work time wise.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Introduction

ANN training

Results and discussion

Conclusion

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[42] Li H., Zhang Y., Li C., Zhou Z., Nie X., Chen Y., Sharma S., . Extreme pressure and antiwear additives for lubricant: academic insights and perspectives. Int. J. Adv. Manuf. Technol. 2022:1-27.
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[46] Nfawa S.R., Basri A.A., Masuri S.U., . Novel use of MgO nanoparticle additive for enhancing the thermal conductivity of CuO/water nanofluid. Case Stud. Therm. Eng.. 2021;101279
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[47] Nielsen L.E., . Generalized equation for the elastic moduli of composite materials. J. Appl. Phys.. 1970;41(11):4626-4627.
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[48] Öğüt E.B., Kahveci K., . Mixed convection heat transfer of ethylene glycol and water mixture based Al2O3 nanofluids: effect of thermal conductivity models. J. Mol. Liq.. 2016;224:338-345.
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[49] Putra A.B.W., . Computer technology simulation towards power generation potential from coproduced fluids in South Lokichar oil fields. Int. J. Commun. Computer Technologies. 2020;8(2):9.
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[50] Rezaee M.J., Jozmaleki M., Valipour M., . Integrating dynamic fuzzy C-means, data envelopment analysis and artificial neural network to online prediction performance of companies in stock exchange. Physica A: Statistical Mech. its Applications. 2018;489:78-93.
[Google Scholar]

[51] Rikani A.S., . Investigation of turbulent fluid flow in the presence of a magnetic field induced dynamic motion of the vessel. J. Res. Sci. Eng. Technol.. 2021;9(01):74-94.
[Google Scholar]

[52] Ruhani B., Toghraie D., Hekmatifar M., Hadian M., . Statistical investigation for developing a new model for rheological behavior of ZnO–Ag (50%–50%)/Water hybrid Newtonian nanofluid using experimental data. Physica A: Statistical Mech. its Applications. 2019;525:741-751.
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[53] Ruhani B., . Statistical modeling and investigation of thermal characteristics of a new nanofluid containing cerium oxide powder. Heliyon 2022e11373
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[54] Ruhani B., Barnoon P., Toghraie D., . Statistical investigation for developing a new model for rheological behavior of Silica–ethylene glycol/Water hybrid Newtonian nanofluid using experimental data. Physica A: Statistical Mech. its Applications. 2019;525:616-627.
[Google Scholar]

[55] Rustamovich Sultanbekov I., Yurievna Myshkina I., Yurievna Gruditsyna L., . Development of an application for creation and learning of neural networks to utilize in environmental sciences. Caspian J. Environ. Sci.. 2020;18(5):595-601.
[Google Scholar]

[56] Safa M., Ahmadi M., Mehrmashadi J., Petkovic D., Mohammadhassani M., Zandi Y., Sedghi Y., . Selection of the most influential parameters on vectorial crystal growth of highly oriented vertically aligned carbon nanotubes by adaptive neuro-fuzzy technique. Int. J. Hydromechatronics. 2020;3(3):238-251.
[Google Scholar]

[57] Saidur R., Leong K.Y., Mohammad, . A review on applications and challenges of nanofluids. Renew. Sustain. Energy Rev.. 2011;15:1646-1668.
[Google Scholar]

[58] Shaddel M., Javan D.S., Baghernia P., . Estimation of hourly global solar irradiation on tilted absorbers from horizontal one using Artificial Neural Network for case study of Mashhad. Renew. Sustain. Energy Rev.. 2016;53:59-67.
[Google Scholar]

[59] Shahsavar A., Jamei M., Karbasi M., . Experimental evaluation and development of predictive models for rheological behavior of aqueous Fe3O4 ferrofluid in the presence of an external magnetic field by introducing a novel grid optimization based-Kernel ridge regression supported by sensitivity analysis. Powder Technol. 2021
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[60] Shakeri S., Ghassemi A., Hassani M., Hajian A., . Investigation of material removal rate and surface roughness in wire electrical discharge machining process for cementation alloy steel using artificial neural network. Int. J. Adv. Manuf. Technol.. 2016;82(1–4):549-557.
[Google Scholar]

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Increasing the accuracy of estimating the dynamic viscosity of hybrid nano-lubricants containing MWCNT-MgO by optimizing using an artificial neural network

Abstract

Abstract

Keywords

ANN

Experimental data

Hybrid nano-lubricants

Dynamic viscosity

nanolubricant

Levenberg-Marquardt

multilayer perceptron

Abbreviations

1 Introduction

2 ANN training

3 Results and discussion

4 Conclusion

Declaration of Competing Interest

References

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