PREDICTION OF VISCOSITY OF COBALT FERRITE/SAE50 ENGINE OIL BASED NANOFLUIDS USING WELL TRAINED ARTIFICIAL NEUTRAL NETWORK (ANN) AND RESPONSE SURFACE METHODOLOGY (RSM)

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INTRODUCTION
Nanofluid is a form of fluid formed by dispersing nano-sized particles in a base fluid [1].These nanofluids have gotten a lot of interest in the last few decades for their applications in microelectronics, transportation, solar, nuclear, and space technology [2].Base fluids such as motor oil, water, and ethylene glycol were commonly employed as heat transporting fluids in a variety of industries [3].By distributing nanoparticles in a normal fluid such as water, motor oil, and ethylene glycol, high heat conductive nanofluids can be formed, according to Choi [4].The most important attribute of a nanofluid is its viscosity, which is related with heat transfer.It is obvious that when the volume percentage of nanoparticles increases, convective heat transmission increases [5].As a result, accurate numbers for nanofluid viscosity are critical for industrial nanofluid demand [6].
Einstein created analytical methods for forecasting a mixture's viscosity in 1906, Brinkman in 1952, and Batchelor in 1977, but those models, which are based on the colloidal theory and contain particles on the order of micrometre, failed to predict the viscosity of the mixture numerous times.As a result, a new model based on nanofluid viscosity has been proposed.The majority of them were based on nanoparticle interfacial layers [7] and Brownian nanofluids nanoparticles in ordinary liquids [8].Brownian motion has been discovered to be the cause of additional energy transmission of nano particles.Convection explains the relative mobility between nanoparticles and based fluids, according to Jang and Choi's first model, which is based on Brownian motion.Ravi Prasher, on the other hand, demonstrated that Choi and Jang's correlation is inaccurate, and he produced a new viscosity of nanofluid correlation [9].Masoumi et al. construct an enhanced correlation [10] for nanofluid viscosity using the Ravi Prasher Correlation [11].Yang et al. found a temperature influence on the viscosity of nanofluids.They experimented using graphene as a nanomaterial.They discovered that when temperature rises, viscosity decreases [12].Chen et al. investigated the similar impact of MWCNT-distilled water nanofluid at temperatures ranging from 278 K to 338 K and discovered that beyond 338 K, the viscosity ratio increases dramatically [13].
He and colleagues observed that the viscosity of nanofluid increased with particle size.However, Lu and Fan observed that as particle radius grows, so does the viscosity of the nanofluid decreases [14,15].Chevalier et al. evaluated
the viscosity of SiO2-Ethanol nanofluid for particle sizes and discovered that the viscosity increases as the diameter of the nanoparticles decreases [16].According to [17] Chevalier et al. experimentally investigated that viscosity increases abnormally with increasing volume concentrations.The viscosity of nanofluid grows as the volume concentration increases, after the volume concentration of 0.4%, according to Lu and Fan.Chen et al. discovered that viscosity increases as the volume concentration increases [18].According to Mahbubul et al. no correlation can estimate viscosity values across a wide range of particle volume concentrations [19].
Using various modelling tools, some researchers anticipated the rheological behavior of nanofluid [20] To synthesize and assess nanofluid thermophysical characteristics such as viscosity [21] (Fig. 1), special equipment and experiments, as well as a significant amount of time and money, are required [22].

Figure 1. Special apparatus for the preparation of nanofluids
There are numerous research studies that may be utilized to determine the viscosity of nanofluids.Hajir-Karimi et al. investigated the viscosities of several nanoparticles in the temperature range 238.15-343.15K, using a total number of eight nanoparticles, with a nanoparticle volume fraction of up to 9.4%.An effective and precise artificial neural network based on genetic algorithm (GA) is modelled for forecasting nanofluid viscosity using computational intelligence approaches.To optimize the neural network variables, the genetic algorithm (GA) is applied.As input data for computational intelligence models, they employed nanofluid temperature, nanoparticle size, nanoparticle percentage and nanofluid density.The nanofluid viscosity was the resulting data.The findings demonstrate that the GA-NN model matches the actual data effectively, with an absolute deviation of 2.48 % and a high degree of correlation value (R = 0.98).[23].Majid Gholizadeh et al. properly calculated the viscosity of thermodynamic nanofluids using a robust artificial intelligence technique known as random forest (RF).Temperature, solid volume percentage, base fluid viscosity, nanoparticle size, and nanoparticle density were used to build the model.In addition, 2890 data points were gathered.They utilised (R = 0.989, RMSE = 0.139, MAPE = 4.758 %) rather than the MLP (R = 0.915, RMSE = 0.377, MPE = 16.194%) and the SVR (R = 0.941, RMSE = 0.315, MAPE = 7.895 %) for model accuracy.They produced an effective model based on comparative findings with other approaches [24].Praveen Kanti et al. used a modern computational intelligence strategy, ANN and MGGP, to enhance experimentally recorded dynamic viscosity data of nanofluids.This study looked at the dynamic viscosity of a water-based stable fly-ash nanofluid and a fly ash-Cu (80-20 % by volume) hybrid nanofluid at temperatures ranging from 30 to 60°C.The viscosity of flue-ash nanofluid is determined utilizing MGGP modeling (R = 0.99988, RMSE = 0.0019, and MAPE = 0.25 %).Furthermore, experiment also showed that the MGGP approach excels at predicting flue ash-Cu/Water hybrid nanofluid viscosity (R = 0.9975, RMSE = 0.0063, and MAPE = 0.664 %) [25].Abdullah et al. examined the viscosity of MWCNT-COOH nanoparticles in water at temperatures ranging from 20 to 50° C and solid volume fractions ranging from 0 to 0.2%.As a result of the experimental results, the unique connection that predicts the relative thermophysical properties of the nanofluids was established.An adaptive neuro-fuzzy inference system (ANFIS) and the finest artificial neural network (ANN) were built in addition to nonlinear regression for the least prediction error.120 experimental measurements were submitted to the model.Several theoretical models, predicted outcomes, and experimental findings were all compared.ANN has an RMSE of 0.46618, but ANFIS has an RMSE of 0.49062, and the mean absolute percentage error (MAPE) of ANN and ANFIS is 0.00023 and 0.00047, respectively [26].To predict the viscosity of nanoparticles, Ahmedi et.al. used optimization techniques to simulate the fluid viscosity of silver (Ag)-water nanofluid: multivariable polynomial regression (MPR), artificial neural network-multilayer perceptron (ANN-MLP), and multivariate adaptive regression splines (MARS).Size of the particles, temperature, and silver nanoparticle concentration are the most essential input elements examined in the modelling approach.The ANN-MLP, MARS, and MPR techniques have R² values of 0.9998, 0.9997, and 0.9996, respectively.[27] By forecasting thermophysical qualities, scholars utilized artificial neural network simulation to perform their researches by the least amount of money and time feasible.A summary regarding the various authors have done the work using the nanofluids with different mathematical model are shown in Table 1.
In their investigation the artificial neural network model employed by Baranitharan et al. is presented schematically in (Fig. 2).An artificial neural network (ANN) is a computing approach that understands the relationship between input and output by using neurons and their connections.Input neurons send data to buried layer neurons for processing.The data is then sent from the hidden neurons to the output neurons for processing.The letters "w" and "b" in this image reflect the amount of weight and bias, respectively (Fig. 2).

Scholar
Nanofluid Technique Objective Bahirai et al. [30] Several Nanofluids (analysis) ANN and hybrid Al algorithm Nanofluids thermal characteristics.Zhao et al. [31] Several Nanofluids (analysis) ANN Predicting the viscosity of a substance in order to use it in a radiator.Vakili et al. [32] Water based grapheme.MLP-genetic algorithm Viscosity Vakili et al. [33] Water based CNT.

ANN Viscosity
Alirezai et al. [  Many models for determining effective viscosity values have been established in the past.Some researchers, such as Einstein [42] provided a theoretical model for forecasting nanofluid relative viscosity.When SVF is less than 0.20 percent, the Einstein model (Eq.1) yields more accurate findings, and it is based on the notion that solid suspended particles in the base fluid are spherical: Where 'μ' stands for viscosity, 'φ' for SVF, and the abbreviations "nf" and "bf" stand for nanofluid and base fluid, respectively.Wang et al. [21] also gave the model for estimating relative viscosity shown below Also, H. De Bruijin [43] proposed a model to predict the relative viscosity of nanofluids containing spherical nanoparticles: On the other hand, current theoretical models fail to detect the viscosity of nanoparticles.Nanofluids were predicted by Wang et al (1999) as a function of nanoparticle kind, particle size, volume percent, and temperature.A laboratorybased study is presented in this paper to analyze the viscosity of a Cobalt Ferrite (40-80°C)/SAE 50 Engine oil based nanofluid.Temperature and solid volume fraction (SVF) were employed as inputs in an ANN with two related hidden layers, and viscosity was used as an output.The ANN findings and the experimental results are likewise at variance.After this, the trial outcomes were compared to the RSM model and the ANN approach.

METHODOLOGY 2.1. X-Ray diffraction and Scanning electron Microscopy
To do this, the sol-gel method [44] was used to create cobalt ferrite nanoparticles (CoFe 2 O 4 ).The structure was confirmed using X-Ray diffraction analysis (Fig. 3) [45].The composition of prepared Cobalt spinel ferrite is confirmed by the EDX [46].Using the Scherer formula (eq.4), the particle size was measured to be 15 nm.The form and size of the particles were determined using scanning electron microscopy and the grain size of the particles is analyzed by histogram (Fig. 4) [47].
where "β" is the full width and half maximum, "λ" is the X-ray wavelength, and "θ" is the angle suspended.

Surface Modification
To begin, mill the cobalt ferric oxide nanoparticles and then make an 80 ml orthoxylene in a 20 ml oleic acid solution volume by volume ratio.The Stirring was done of the prepared solution for a few hours to achieve a homogeneous condition.On the other hand, 2 gm of milled particles, were added to 98 gm of orthoxylene, stirred continuously for surface modification, and placed on a heated plate.The modified particles are filtered away, and then particles are added to the oleic acid solution.

Preparation of Nanofluids
The dried powder is then mixed with SAE 50 engine oil in predetermined proportions to make different samples with varied solid volume fractions, such as 0, 0.25, 0.50, 0.75, and 1.0% solid volume fraction.To make the concentrated solutions that are necessary, the weight of solid Cobalt nanoparticles and the oil SAE 50 is specified in (Table 2), which were calculated by using the relation given in (Eq.5).Stir all the solution samples to obtain the stability of cobalt-based nanoparticles in engine oil.The experimental work was summarized in a flow chart that was supplied in order to acquire the greatest understanding of it (Fig. 5).∅ = × 100.
(5)  Finally, using the free-falling technique, the viscosity of the prepared samples is determined experimentally by using relation given in (Eq.6).ƞ =   −  .(6) where "k" is the proportionality constant, "T" is the average time taken by the free fall body through the fluid between two fixed points, and "ρ 1 ", "ρ 2 " are the densities of ball and sample fluid respectively.The experimental viscosity is found to be correlated with the input parameters temperature and solid volume percent in (Fig. 6).

Artificial Neural Network (ANN)
One of the technologies used to study human brain activity is artificial neural networks.Many numerical methods inspired by the human brain have been presented in the subject of Artificial Neural Networks.Many industries have used the models provided to tackle a wide range of scientific and practical issues.There are many other ANN architectures, such as the well-known multilayer perceptron (MLP).This strategy was used to develop the present neural network.Many training approaches may be employed to train the ANN, and one of the most prevalent (the Levenberg-Marquardt approach) is used in this work.
In systems with various input parameters, neural networks are also utilized to anticipate output data.The viscosity of Cobalt Ferrite/SAE 50 Engine oil based nanofluids was investigated in this research using two input parameters which are SVF and Temperature.The ANN approach predicts output data by obtaining the problem's input parameters and training neurons based on a number of inputs and calculating their weight and bias; errors are gathered during the testing and validation stages.The most optimal ANN structure is shown in (Fig. 7).The ideal structure contains two inputs, nine neurons in the first hidden layer, five neurons in the second hidden layer, and one output.The formulas in Eq. 7, 8 and 9 may be used to compute the most efficient number of hidden layers, neuron counts in each layer, neuron weighting, and the optimal combination of transfer functions.

MSE =
− P , ( 7) where T ij and P ij are the expected and estimated values, and the total number of observations is N.

Mathematical Correlation Model
The exact viscosity of nanofluid cannot be predicted using theoretical models.As a result of analyzing the experimental data and applying the RSM method, a new quadratic equation for predicting viscosity has been constructed (Eq.10).Experimental data was used to predict viscosity changes when SVF and temperature varied, as well as curve fitting rates.The correlation coefficient R 2 of this equation is 0.9663, indicating that the prediction is correct based on the experimental results.
The results acquired by analysis variance indicate the correctness of the expected model using response surface technique.In the recommended equation (Eq.7), the relevance of each variable is shown in (Tables 4 and 5).The parameter's relevance in the equation is high if the p-value is less than 0.05; if the p-value is more than 0.05, the parameter's importance in the equation is low, and the parameter's effect can be removed from the equation.

ANN Accuracy Evaluation
The coefficients were obtained using the Levenberg-Marquardt learning procedures, which were utilized to train the network.In this case, the neural network repeats the prediction cycle, altering the weight and bias as well as the training stage to achieve the desired error rates.In this study, the error value is fully provided in (Table 3), which shows the relationship between eq. 7 and 9.The fact that R 2 is so near to 1 (0.9999) demonstrates the constructed neural network's exceptional accuracy (Fig. 9).The experimental data is compared to the ANN's predicted data in the Fig. 10.In this comparison, the trial, train, and total network data were compared.The ANN's projected values are well-trained, resulting in appropriate test data, validation, and total data correctness, as shown in this diagram.

Prediction Accuracy of Artificial Neural network against Mathematical Model
The validation of the ANN and RSM techniques in estimating viscosity at different temperature and solid volume fractions is compared in this section.The ANN forecast, on the other side, closely matches the patterns of experimental results.It can be concluded that the prediction of ANN method is better than the RSM prediction with experimental results.The outcomes of the ANN and RSM are compared in (Fig. 11) Eq. 11 specifies the number of experiments (N), experimental calculated viscosity (exp), and expected viscosity (pre).Calculations revealed that the AAD% is 1.7112%, indicating that the results are accurate.Fig. 12 (a) depicts the experimental data that back up ANN predictions.Maximum margin of deviation (MOD) percent reported (-7% and 9%).The symbol placement on the bisector line also indicates whether the experimental data matches the neural network's predicted outcomes.Fig. 12 (b) depicts the experimental data that back up RSM predictions, that's confirmed the RSM prediction is correlated with the experimental values.Maximum margin of deviation (MOD) percent reported (-8% and 10%) for RSM.The comparison of MOD% for ANN was observed less than the MOD% observed in RSM, indicates that the ANN model much better than RSM.
Another method for comparing experimental data with data produced from the suggested correlation is to use Eq.12 to calculate the percentage of data deviation from experimental data.
Another comparison chart for nf versus temperature and Solid volume fraction is shown in 3D space to evaluate the trained ANN method for estimating the viscosity µ nf .(Fig. 13a).Fig. 13b depicts another 3D space for estimating viscosity using the RSM model.We may deduce from the diagram that a well-trained ANN can be utilized to simulate viscosity.Furthermore, solid volume fraction has a larger impact on viscosity than temperature, which has a smaller impact on the output values.

CONCLUSION
Under this research, 25 experimental results for the viscosity of cobalt ferrite/SAE 50 engine oil based nanofluids in all temperature ranges from 40, 50, 60, 70, and 80°C, at SVFs of 0, 0.25, 0.50, 0.75, and 1.0%, were tried to compare with the simulated values by the neural network, with their insignificant difference (-7%, +9%) representing a precise model for forecasting nanofluid viscosity.The sample's viscosity is significantly influenced by the parameters of the nanoparticle's temperature and solid volume fraction (SVF), therefore an increase in SVF across the range results in a notable increase in viscosity.For all SVF ranges, rising temperature will result in a decrease in dynamic viscosity.From a collection of 25 ANN data, the best optimum structure was chosen after analysis by two hidden layers that each had 9 and 5 neurons.For the first and second hidden layers, respectively, logsig and tansig are the ideal transfer functions.Another appropriate technique to use the RSM method was to build a mathematical relationship between the input parameters temperature and solid volume percentage.The correlation model's accuracy (R 2 = 0.9663) was lower than the neural network model's (R 2 = 0.9941).Furthermore, the experimental findings were compared to the data collected from the RSM and neural network data.The gap between experimental and anticipated model data is quite small, with the greatest difference occurring at temperature 50°C and SVF of 1.0.The MOD% for ANN was observed to be lower than the MOD% for RSM suggests that ANN is a much better model than RSM for predicting the viscosity.

Figure 2 .
Figure 2. A schematic diagram of an artificial neural network

Figure 5 .
Figure 5. Flow chart to represents the preparation of cobalt spinel ferrite-based engine oil based nanofluids in two steps methods

Figure 6 .
Figure 6.Experimental values of viscosity using various volume fractions of cobalt ferrites based nanofluids with effect of (a) temperature and (b) solid volume fraction

Figure 7 .
Figure 7.The design of the most ideal ANN network

Fig. 8 (
Fig.8 (a)  shows the excellent agreement between the experimental and predicted daya using the RSM developed model which reveal the accuracy of the developed model.

Figure 8 .
Figure 8. Experimental validation with RSM results

Fig. 8 (
Fig.8(b) represent the graph between the deviation bwteen the reference point and viscosity.This graph is provide the central point (O) of the deviation which ultemetialy gives the overall influence of all process factors on the response function.The contrast effect of two factors such as solid volume fraction and temperature at the referece point provides the operating range's of the perturbation presented graph.The residual graph based on run number nad data can be seen in Fig.8 (c).Only one data points at runs 2 is out from the other data points in between the red lines which is clear evidence the developed theoretical model has a significant and well adapted to predict the viscosity of the nanofluids.No abnormality in the random distribution of residuals can be seen in Fig.8 (d)3.RESULTS AND DISCUSSION 3.1.ANN Accuracy Evaluation The coefficients were obtained using the Levenberg-Marquardt learning procedures, which were utilized to train the network.In this case, the neural network repeats the prediction cycle, altering the weight and bias as well as the training stage to achieve the desired error rates.In this study, the error value is fully provided in (Table3), which shows the relationship between eq. 7 and 9.The fact that R 2 is so near to 1 (0.9999) demonstrates the constructed neural network's exceptional accuracy (Fig.9).

Figure 9 .
Figure 9. Confirmation of ANN results with experimental results

Figure 10 .
Figure 10.The correlation of intended ANN outputs with the experimental set of data during training, testing, and all data phases

Figure 11 .
Figure 11.RSM and ANN predictions of viscosity compared with experimental valuesThe relationship average absolute percent deviation (AAD) is used to compare expected and observed data in (Eq.11).AAD% = ∑ 100 .(11)

Figure 12 .Figure 13 .
Figure 12.Margin of deviation for RSM and ANN projected data compared with experimental data

Table 2 .
The composition weights for the preparation of different volume fractions of sample

Table 5 .
The present numerical model's evaluation of variance

Table 3 .
The results of an ANN model to measure viscosity of cobalt ferrite / SAE 50 Engine Oil