International Communications in Heat and Mass Transfer

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Modeling of thermal conductivity of ZnO-EG using experimental data and ANN methods☆

Mohammad Hemmat Esfe

^a,

⁎ , Seyfolah Saedodin

^b

, Ali Naderi

^b

, Ali Alirezaie

^b

, Arash Karimipour

^a

, Somchai Wongwises

^c,

⁎ , Marjan Goodarzi

^d

, Mahidzal bin Dahari

^e

aDepartment of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Isfahan, Iran

bFaculty of Mechanical Engineering, Semnan University, Semnan, Iran

cFluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of Mechanical Engineering, Faculty of Engineering, King Mongkut's University of Technology Thonburi, Bangmod, Bangkok 10140, Thailand

dYoung Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran

eDepartment of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia

a b s t r a c t a r t i c l e i n f o

Available online 7 February 2015 Keywords:

Thermal conductivity MgO-EG

Artiﬁcial neural network Nanoﬂuid

In the present study, the thermal conductivity of the ZnO-EG nanofluid has been investigated experimentally. For this purpose, zinc oxide nanoparticles with nominal diameters of 18 nm have been dispersed in ethylene glychol at different volume fractions (0.000625, 0.00125, 0.005, 0.01, 0.015, 0.02, 0.03, 0.04, and 0.05) and temperatures (24–50 °C). The two-step method is used to disperse nanoparticles in the basefluid. Based on the experimental data, an experimental model has been proposed as a function of solid concentration and temperature. Then, the feedforward multilayer perceptron neural network has been employed for modeling thermal conductivity of ZnO-EG nanofluid. Out of 40 measured data obtained from experiments, 28 data were selected for network training, while the remaining 12 data were used for network testing and validating. The results indicate that both model and ANN outputs are in good agreement with the experimental data.

1. Introduction

It was 20 years ago when, for thefirst time, nanoparticles were used in commonfluids as additives to increase their heat transferring[1]. Since then, a wide range of studies have been done in this area and different nanoparticles have been used in heat-transferringfluids. Therefore, a col- lection of data has been obtained to produce thefluids commercially and to use them in the industrial systems. However, after spending so much money and doing a lot of research in this area, some scholars have claimed that studies done on nanoparticles do not have a necessary cohesion, and the obtained results are very different from each other in some cases.

Most of the research done in this area has focused on thermal conductivity in the calculation of nanoﬂuids because the scholars believe that when thermal conductivity of nanoﬂuids increases, their heat transferring increases too[2–5].

However, the studies have not stopped here, and some scholars have investigated other features of thesefluids. The viscosity of nanofluids is the second important issue from the scientists' point of view because adding solid particles to thefluid will cause a pressure drop in the system,

and the power consumption of the pump will increase. Hemmat Esfe et al.

[6]have studied the heat transferring of functionalized COOH DWCNTs- water nanofluids and obtained the friction factor and pressure drop for different Reynolds numbers in the experiment. Fuoc et al.[7]have also studied MWCNT nanofluids, which were suspended by chitosan. They presented their result based on the cut rate and concluded that this nanofluid shows non-Newtonian behavior. A lot of different studies have been conducted about the issue[8–10].

Diameter size of the nanoparticles is one of the other factors that has been noticed in the studies of nanoﬂuids. The investigations[11–14]indicate that the smaller the diameter of the nanoparticles, the larger the thermal conductivity. Nasiri et al.[15]reported that in carbon nanotubes, when the diameter size of nanotubes is smaller, the nanoﬂuid shows greater thermal conductivity.

Additionally, the effect of temperature on the thermal conductivity of nanoﬂuids has been studied in some studies[16–20], and most of them proved that there is a direct relationship between thermal conductivity fraction and temperature.

The volume fraction of the solid particles is also another feature that has been investigated by the researchers[21–23]. Thermal conductivity of nanoﬂuids increases in a non-linear way by an increase in solid volume fraction.

Simultaneously, in experimental studies, analytical and numerical studies have been done on nanoﬂuids, as well[24–26]. Different models

☆ Communicated by W.J. Minkowycz.

⁎ Corresponding authors.

E-mail addresses:[email protected](M. Hemmat Esfe), [email protected](S. Wongwises).

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International Communications in Heat and Mass Transfer

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have, thus far, been proposed for predicting thermal conductivity and viscosity of nanofluids. The other method of predicting nanofluids behaviors involves using an artificial neural network for conductivity fraction and viscosity of nanofluids. Hojjat et al.[27]conducted an experimental study on thermal conductivity of three different nanofluids, alumina, titania, and CuO. Then, they modeled the experimental data using the neural network. They used three factors—temperature, volume fraction of nanoparticles, and thermal conductivity of nanoparticles. In another study, Hemmat Esfe et al.[28]measured the thermal conductivity of magnesium oxide-ethylene glycol nanofluids and modeled experimental data by an artificial neural network. Their variables in this experiment were temperature, volume fraction, and the diameter of the nanoparticles. They attained a model that is very accurate.

2. Experimental 2.1. Nanoﬂuid preparation

Measuring thermal conductivity, ZnO-EG nanoﬂuid was provided by two-step methods. Furthermore, the XRD pattern and a transmission of a microscope electron image of the particles, which take from the com- pany, are displayed inFig. 1.

First, the ZnO nanoparticles required for the desired volume concentrations (i.e., 0.05 (5.0%), 0.04 (4.0%), 0.03 (3.0%), 0.02 (2.0%), 0.015 (1.5%), 0.01 (1.0%), 0.005 (0.5%), 0.0025 (0.25%), 0.00125(0.125%), and 0.000625 (0.0625%)) were weighed and then added with the baseﬂuid.

After mixing the ZnO nanoparticles with ethylene glychol, the samples were subjected to an ultrasonic vibrator(400 W, 20 KHz) for about 3–5 h.

2.2. Thermal conductivity of the nanoﬂuid

Thermal conductivity of the ZnO-EG nanoﬂuid has been investigated experimentally. The ZnO-EG nanoﬂuid with particle diameters of 18 nm has been examined by the KD2 pro instrument at different volume fractions up to 5% over the temperature ranging from 24 to 50 °C.Fig. 2 shows the thermal conductivity ratio with respect to a solid volume fraction at different temperatures.

2.2.1. Proposed new correlation

In this study, experimental data have been employed as a correlation pattern for the experimental results. The thermal conductivity of the

ZnO-EG nanofluid has been studied by developing a non-linear regression equation that includes the effect of the volume fraction and the fluid temperature. Measuring thermal conductivity of the ZnO-EG nanofluid with average particle diameters of 18 nm has been performed in different volume fractions and temperatures.

The desired relationship in this study is^K_K^{n f}

b ¼f Tð ;φÞ, whichﬁts the thermal conductivity ratio in terms of temperature and volume fraction.

Accordingly, multiple relations were derived. Finally, the best model was selected in terms of accuracy. In order to select the best curve- ﬁtting equation, various criteria can be employed. In this study, the mean squared error (MSE) and the mean absolute error (MAE) were used as the main criteria for investigating the correlated model performance, which is calculated by the following relations:

MSE¼1 N

X^N

i¼1

K_{n f} K_b

Exp−K_{n f} K_b

pred

!2

ð1Þ

MAE¼1 N

X^N

i¼1

K_{n f} K_b

_Exp−K_{n f} K_b

_pred

ð2Þ

whereNis the number of experimental data used in the correlation,

K_{n f}

K_b_Expand^K_K^{n f}

b

_predare thermal conductivity of the experimental results and thermal conductivity of the correlated model results, respectively, whose difference shows the curve-ﬁtting error between the real and predicted values.

In order to select the best curve-ﬁtting equation, the MSE and MAE performance criteria were investigated for multiple curve-ﬁtting equations developed for predicting thermal conductivity in terms of temperature and volume fraction from regression equations. Finally, Eq.(3) was selected as the best correlation equation, which is, indeed, the best equation for the results of the regression analysis of the thermal conductivity data at different temperatures and volume fractions compared to other equations.

K_{n f}

K_b ¼1:00475þ2:26216φþ1:57146Tφ²þ481:646φ² expð−66:7522φÞ−0:0100301Tφcos 1560ð :99φÞ

ð3Þ

2 Theta Scale

Lin(Counts)

20 40 60 80

0 500 1000 1500 2000

Fig. 1.TEM image and XRD patterns of ZnO nanoparticles.

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whereTandφrepresent temperature and volume fraction of the nanoﬂuid, respectively.

Performance criteria for Eq.(3)have been presented inTable 1.

Fig. 3compares the present experimental model prediction with experimental data for thermal conductivity of the ZnO-EG nanoﬂuid at different temperatures and volume fractions. It can be observed that the thermal conductivity ratio obtained from the correlated model is in good agreement with the thermal conductivity ratio measured for all studied temperatures and volume fractions.

Fig. 4compares the experimental results with those obtained by the correlated experimental model. As it can be seen, the correlated model properly predicts the thermal conductivity ratio of the nanoﬂuid. It is determined that the maximum error is about 0.0098 at a volume fraction of 4% and in temperature of 40 °C.

According to the experimental results, a correlation was developed to estimate the thermal conductivity ratio using a regression equation.

A comparison of the results from the experimental data with those of the correlation model shows that there is good agreement between them, indicating the accuracy of the relation provided in this study.

3. Artiﬁcial neural network modeling

Artificial neural network modeling is a non-linear statistical tech- nique that can be used for solving problems that are not solved using conventional statistical methods. Neural networks can be used for modeling complex relations between outputs and inputs orfinding patterns between data. Important benefits of ANN compared to other specialized systems include high speed, simplicity, the capability of modeling multivariate problems for solving complex relations between variables, and the ability to derive non-linear relations through training data.

The proper selection of input parameters plays an important role in the ANN method and can improve the predicting quality. This selection is usually based on the physical background of the problem. In order to predict the thermal conductivity ratio for every type of nanoﬂuid,

temperature and volume fraction variables are considered as inputs to the neural network.Fig. 5depicts the network training process.

In this study, the feedforward multilayer percepetron neural network has been used for modeling the thermal conductivity ratio of the ZnO-EG nanoﬂuid. This network has a good ability in estimating non- linear relations and is one of the most common neural network models used in engineering applications.

The multilayer perceptron neural network consists of multiple layers, each of which has a number of neurons. Each neuron in each layer is connected to the neurons in the next layer by weight coefﬁ- cients. An activation function is determined for the neurons in each layer, which is used for calculating the sum of the input weights and the biases of each neuron in order to produce the output neuron.

Developing an ANN involves three steps. Theﬁrst step is developing the data required for network training. The second step is evaluating different neural network structures in order to select the optimal one. Finally, the third step is testing the neural network using data not previously used in network training. Biased neurons are linked to other neurons in the next layers to develop a constant bias. The most exact and accurate prediction of neural networks is made using the tan-sigmoid function for the hidden-layer neurons and the purelin function for the output-layer neurons. Therefore, the

Data Number

0 10 20 30 40

Thermal Conductivity Ratio

0.9 1.0 1.1 1.2 1.3 1.4

Experimental Results Correlated Model Prediction

Fig. 4.Comparison between experimental results with those obtained by correlated experimental model.

Experimental Results

0.9 1.0 1.1 1.2 1.3 1.4

Fig. 3.Correlation regression diagram.

Table 1

Performance of the correlated model.

Mean square error 1.0829906*10⁻⁵

Mean absolute error 0.0022070592

Maximum error 0.0098439036

Correlation coefﬁcient 0.99949742

Volume Fraction

0.00 0.01 0.02 0.03 0.04 0.05 0.06

0.9 1.0 1.1 1.2 1.3 1.4

Temperature = 24 ôC Temperature = 30 ôC Temperature = 40 ôC Temperature = 50 ôC

Fig. 2.Thermal conductivity ratio via volume fraction in different temperature.

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tan-sigmoid activation function is used in the hidden layer while linear activation functions are used in the output layer. In hidden layers, each neuron calculates the sum of the corresponding bias and the input weights and transfers them via the activation function.Fig. 6 shows a three-layer neural network with two hidden layers consisting of three neurons and one/an output layer.

In training algorithms, training data are given to the network and the network updates the weights and biases repeatedly until the predicted values agree with the desired values in an acceptable and logical man- ner. The back-propagation algorithm and the Levenberg–Marquardt training method have been employed in this modeling.

The performance function is a function that is used for calculating errors during the network training process. Two of the most common performance functions used in feedforward neural networks are the mean squared error (MSE) and the mean absolute error (MAE) (Eqs.(1) and (2)). These two criteria are used for investigating neural network performance in this study, as well.

A multilayer perceptron neural network has been used in which the volume fraction and the temperature have been considered as network inputs for predicting the thermal conductivity ratio (Fig. 5). The thermal conductivity ratio has been measured using the following conditions.

Volume fraction (φ): 0.000625, 0.00125, 0.005, 0.01, 0.015, 0.02, 0.03, 0.04, 0.05

Temperature (T): 24, 30, 40, 50

Out of the 40 data obtained from the experiments, 28 of the data are used for network training, while the remaining 12 data are used for network testing and validating.

The existence of the input parameters in different ranges may lead to inadequate network training. This should be considered regarding the inputs of this study—that is, volume fraction varying from 0.0025 to 0.25 and temperature varying from 24 to 50 °C. To remove this problem, input data are normalized in [−1, 1] intervals.

The number of optimal neurons in the hidden layer is determined trying different networks and comparing their performance functions.

The neural network structure with the lowest MSE and MAE (the performance functions selected in this study) is considered as the most optimal network structure.Table 2presents MSE and MAE values for artiﬁcial neural networks with different structures. According to Table 2, the three-layer structure with two neurons in each hidden layer (Fig. 6) is the most optimal network structure for modeling the thermal conductivity ratio of the ZnO-EG nanoﬂuid in terms of temperature and volume fraction. This structure has been selected based on the smallest difference between the model outputs and the experimental results and predicts a thermal conductivity ratio with MSE and MAE values equal to 6.37 × 10⁻⁶and 1.8 × 10⁻³, respectively.

Fig. 7shows a network regression diagram after training, the value of which is over 0.999 in all cases. This regression value conﬁrms good performance of the trained network.

The experimental data and predicted results of the neural network have been compared with the tested data inFig. 8. As it can be seen, the experimental results and model outputs are in good agreement with each other.

Table 2

Performance of ANN with different structures.

Number of hidden layers

Number of neurons in each hidden layer

MSE MAE

1 2 5.50E−05 0.00703

1 3 5.65E−05 0.0072

1 4 6.70E−05 0.00833

1 5 2.96E−05 0.0043

1 6 7.28E−05 0.00895

1 7 4.45E−05 0.0059

1 8 1.42E−04 0.0164

2 2 4.89E−05 0.00638

2 3 6.37E−06 0.0018

2 4 2.16E−05 0.00344

2 5 8.45E−05 0.0102

2 6 1.02E−05 0.00221

2 7 1.11E−04 0.0131

2 8 3.27E−05 0.00463

Fig. 6.Three layer neural network with two hidden layers and one output layer.

Fig. 5.ANN processﬂowchart.

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Given the above-mentioned points, it can be realized that this model is capable to predict the thermal conductivity ratio with high precision.

In addition, training and test errors are properly close to each other, indicating that the data have been appropriately divided into training and test data.

4. Comparing correlation model and artiﬁcial neural network with experimental results

Fig. 9shows the predicted values for the thermal conductivity ratio of ZnO-EG nanoﬂuid obtained through the correlation method and the ANN, as a function of the volume fraction, in different temperatures.

In order to better visualize the prediction quality of the models used in this study, an experimental parity plot and thermal conductivity ratio prediction for ZnO-EG have been presented inFig. 10. As it can be seen, the predicted values for both models are in good agreement with the experimental thermal conductivity ratio value.

In this study, we aimed at modeling the thermal conductivity ratio of the ZnO-EG nanoﬂuid through an artiﬁcial neural network (ANN) and correlation methods using experimental data in the temperature ranging from 24 to50°C and volume fractions between 0.0625% and 5%. In- vestigating the results of the developed models shows that there is good agreement between them and the experimental data. Therefore,

the thermal conductivity ratio value of the ZnO-EG nanoﬂuid can be properly predicted using the ANN and correlation models.

5. Conclusion

In this paper, we have mentioned that the artificial neural network is one of the approaches to obtain an accurate model in nanofluids. Fur- thermore, to estimate the thermal conductivity of the ZnO-EG nanofluid, a correlation with two parameters (temperature and volume concentration) with a very high accuracy has been provided. For that aim, nine different volume concentrations from 0.0625% to 5% and four various temperatures have considered. The accuracy of the ANN model and the proposed correlation were up to 10⁻⁵and 10⁻⁴, respectively.

Acknowledgment

The authors gratefully acknowledge High Impact Research Grant UM.C/HIR/MOHE/ENG/23 and Faculty of Engineering, University of Malaya, Malaysia for their support in conducting this research work.

The sixth author would like to thank the“Research Chair Grant” from the National Science and Technology Development Agency, the Thailand Research Fund (IRG5780005) and the National Research University Project for the support.

0.9 1.0 1.1 1.2 1.3 1.4

Themal Conductivity Ratio

0.9 1.0 1.1 1.2 1.3 1.4

Correlation ANN Fit Line

Fig. 10.Experimental parity plot and thermal conductivity ratio prediction for ZnO-EG.

Volume Fraction

0.00 0.01 0.02 0.03 0.04 0.05 0.06

0.9 1.0 1.1 1.2 1.3 1.4

Fig. 9.Predicted values for thermal conductivity ratio ZnO-EG nanoﬂuid obtained through correlation method and ANN.

Data Number

0 10 20 30 40

0.9 1.0 1.1 1.2 1.3 1.4

Experimental Results ANN Outputs

Fig. 8.Network regression diagram.

0.9 1.0 1.1 1.2 1.3 1.4

ANN Model Prediction

0.9 1.0 1.1 1.2 1.3 1.4

Fig. 7.ANN regression diagram.

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