Experimental and theoretical investigation of thermal conductivity of ethylene glycol containing functionalized single walled carbon nanotubes

Author’s Accepted Manuscript Experimental and theoretical investigation of thermal conductivity of ethylene glycol containing functionalized single walled carbon nanotubes Mohammad Hemmat Esfe, Masoumeh Firouzi, Masoud Afrand www.elsevier.com/locate/physe

PII: DOI: Reference:

S1386-9477(17)30928-1 http://dx.doi.org/10.1016/j.physe.2017.08.017 PHYSE12897

To appear in: Physica E: Low-dimensional Systems and Nanostructures Received date: 27 June 2017 Revised date: 22 August 2017 Accepted date: 30 August 2017 Cite this article as: Mohammad Hemmat Esfe, Masoumeh Firouzi and Masoud Afrand, Experimental and theoretical investigation of thermal conductivity of ethylene glycol containing functionalized single walled carbon nanotubes, Physica E: Low-dimensional Systems and Nanostructures, http://dx.doi.org/10.1016/j.physe.2017.08.017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Experimental and theoretical investigation of thermal conductivity of ethylene glycol containing functionalized single walled carbon nanotubes

Mohammad Hemmat Esfe1,*, Masoumeh Firouzi2, Masoud Afrand3,* 1

Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran 2 Department of Physics, Kashan Branch, Islamic Azad University, Kashan, Iran 3 Young Researchers and Elite Club, Najafabad Branch, Islamic Azad University, Najafabad, Iran

* Corresponding authors Emails: [email protected] (M. Hemmat Esfe) [email protected] (M. Afrand) Phone number: +989132064001

Abstract In this paper, functionalized single walled carbon nanotubes (FSWCNTs) were suspended in Ethylene Glycol (EG) at different volume fractions. A KD2 pro thermal conductivity meter was used to measure the thermal conductivity in the temperature range from 30 to 50°C. Nanofluids were prepared in solid volume fraction of 0.02, 0.05, 0.075, 0.1, 0.25, 0.5 and, 0.75%. Experimental results revealed that the thermal conductivity of the nanofluid is a non-linear function of temperature and SWCNTs volume fraction in the range of this investigation. Thermal conductivity increases with temperature and nanoparticles volume fraction as usual for this type of nanofluid. Maximum increment in thermal conductivity of the nanofluids was found to be about 45% at 0.75 volume fractions loading at 50oC. Finally, a new correlation based on artificial neural network (ANN) approach has been proposed for SWCNT-EG thermal conductivity in terms of nanoparticles volume fraction and temperature using the experimental data. Used ANN approach has estimated the experimental values of thermal conductivity with the absolute average relative deviation lower than 0.9%, mean square error of 3.67×10-5 and regression coefficient of 0.9989. Comparison between the suggested techniques with various used correlation in the literatures established that the ANN approach is better to other presented methods and therefore can be proposed as a useful means for predicting of the nanofluids thermal conductivity. 1

Graphical Abstract

Keywords: Experimental Study; Thermal conductivity; F-SWCNTs/EG nanofluid; Sensitivity; New correlation; ANN

1. Introduction Today it is obviated that in the fields of thermal and fluid science, better understanding of processes involved in microscale fluid flow and heat transfer has become a major concern [1]. In the convection heat transfer, it is approved that working fluid thermal conductivity has a significant role in the heat transfer efficiency. Concerning to this, a new class of fluids, instead of conventional fluid, named as nanofluids was presented. Nanofluids consisting of nano-sized particles dispersed in 2

fluid [2], having this possibility due to their thermal conductivity that are significantly higher than the conventional fluids. Nanofluids thermal conductivity of suspension containing suspended metallic nanoparticles has been reported to be higher than the average values of the conventional heat transfer fluids [3-11]. Higher thermal conductivity directly affects the heat transfer coefficient in heat exchangers and other thermal systems [12-18]. Physical and chemical characteristics of base fluid and solid nanoparticles will influence the thermal conductivity of suspension. For this reason, using appropriate type of solid nanoparticles has vital role for obtaining a suspension with a high efficiency. Some types of nanoparticles are metallic, metallic oxide and carbon nanotubes that are commonly used in the published research works. Among the most used nanoparticles, single, double, or multi-walled carbon nanotubes (CNTs) have gained particular attention due to their thermophysical properties. Published research work showed that carbon nanotubes (CNTs) were the best nanomaterials to prepare nanofluids. In the present investigation, Single Wall Carbone Nanotubes (SWCNTs) has been used as solid nanoparticles. The thermal conductivity of very low volume fractions of this new type of nanoparticles dispersed in ethylene glycol is measured. Here, a brief review on the experimental investigation for measuring and estimating of thermal conductivity is performed. Hemmat Esfe et al. [19] examined the thermal conductivity of MWCNTs-water nanofluid. Their investigations were done for various temperatures and MWCNTs volume fractions. They reported that the thermal conductivity of MWCNTs-water nanofluid increased with temperature. In addition they observed that temperature has a considerable effect on thermal conductivity at low concentration while opposite behavior was observed at high concentration. In another work by Indhuja et al. [20] experimentally studied the effect of temperature and nanoparticles volume fraction on the thermal conductivity of MWCNTs–water nanofluids. They reported that there is an inextricable connection between temperature and thermal conductivity especially for temperatures above 45 °C. Nasiri et al. [21] conducted an experimental investigation on the effect of dispersion method for thermal conductivity and stability of nanofluid. Utilized nanofluids were five different 3

types of carbon nanotubes (CNTs) including: single-wall CNTs (SWNTs); double-wall CNTs (DWNTs); two multiwall nanotubes (MWNTs); and few-wall CNTs (FWNTs). These differences were created to organize nanofluids with three different dispersion methods. Their results showed that the highest thermal conductivity and best stability of nanofluids are associated with functionalized nanofluids. It is worth to note that in experimental investigation, analytical and numerical techniques have been employed for estimation of nanofluids thermophysical properties [22-27]. Several models have been suggested to predict the dynamic viscosity and thermal conductivity of nanofluids. One of the methods that recently used to predict nanofluids properties is artificial neural network (ANN) [2835]. In this regard, Hojjat et al. [36] firstly examined thermal conductivity of water-based nanofluids of Al2O3, TiO2, and CuO. After that, they correlated their findings emloying the neural network. They considered three parameters including temperature, volume fraction, and thermal conductivity of nanoparticles. Hemmat Esfe et al. [37] measured thermal conductivity of MgO-EG nanofluids and correlated their measurements by ANN. The used variables in their experimental investigation were nanoparticles volume fraction, temperature, and nanoparticles diameter. They reported that the obtained model was very accurate. In the present work, for the first time, the thermal conductivity of single wall carbon nanotubes (SWCNTs)–water is experimentally investigated. In this way, nanofluid with different nanoparticles volume fractions and temperatures has been prepared and tested. In addition to measuring the thermal conductivity, a new correlation for estimating the thermal conductivity of nanofluid based on artificial neural network (ANN) has been proposed.

2. Experiment 2.1. Nanofluids Preparation The first step in each experimental study is preparation of nanofluids. Nanofluids are not simply liquid–solid mixtures. Stable suspension, negligible agglomeration of particles, durable suspension 4

and no chemical change in the fluid are some essential and special requirements for this type of suspension named nanofluids. As it is well known, there are two ways to create sustainable nanofluids containing CNTs: 1- using surfactant, and 2- the functionalization of the CNTs. The use of surfactant may lead to the insertion of undesirable effects on the thermal conductivity of the nanofluids. functionalized carbon nanotubes were used to reach sustainable nanofluid (because of it's important effect on nanofluids' stability [38]). Functionalizing SWCNTs by COOH functional groups makes the carbon nanotubes hydrophilic; subsequently, the stability of the prepared nanofluids is better. The properties of COOH functionalized SWCNT's have been described in Table 1. In this work, nanofluids were prepared by dispersing COOH functionalized SWCNTTs in the ethylene glycol with volume fractions of 0.02, 0.05, 0.075, 0.1, 0.25, 0.5 and, 0.75%. Magnetic stirring was performed for 2 h to mix SWCNTs with water. Next, an ultrasonic processor (power= 400W, frequency=24 kHz) is used for 6 h for breaking down the cluster of the nanotubes. After 16 h, no sedimentation was observed (with the naked eye) in the samples. A TEM and XRD image of SWCNTs are shown in Fig. 1 to display an approximation of the size and shape of the particles and results. It should be noted that by functionalizing the carbon nanotubes with COOH, the dispersion of nanotubes will be better in the base fluid. Therefore; there is no need to use a surfactant to have a stable suspension. In this way, the negative effects of surfactant on the thermophysical properties will not be observed. 2.2. Thermal conductivity measurement Experimental thermal conductivities were done by a KD2 Pro thermal properties analyzer probe instrument manufactured by Decagon Devices, USA. Thermal conductivity measuring principle is based on the transient hot-wire method. In this method, a KS-1 sensor made from stainless steel having 60 mm long and 1.27 mm in diameter is used for measuring the thermal conductivity. It is worth noting that a hot water bath was used in order to stabilize the temperature. The used 5

thermometer has an accuracy of of 0.1 °C. Before using this apparatus and starting the experimental procedure, KD2 was previously checked and calibrated with distilled water. Thermal conductivity has been measured within the range of temperature from 300C to 500C and at nanoparticles volume fraction up to 0.75. In addition, every test at any temperature and nanoparticles volume fraction is repeated three times. For better measuring and evaluating the enhancement of nanofluids, it is important to measure both the nanofluid and base fluid with a unique technique and the same temperature range. For this reason, thermal conductivity of Ethylene Glycol was also measured in the whole range of temperature. It must be noted that the uncertainty related to thermal conductivity measurement is inferior to 3%.

2.3. Thermal conductivity of nanofluids Thermal conductivity of the FSWCNTs-EG nanofluid has been measured. The thermal conductivity values have been measured by the KD2 pro instrument at various nanofluid concentrations over the temperatures ranging from 30°C to 50 °C. Fig. 2 shows the thermal conductivity ratio (TCR) with respect to a solid volume fraction and temperature. According to the figure, in each temperature adding SWCNTs to base fluid has had a non-linear effect on nanofluid TCR, that is, TCR increase has been non-linear. It is observed in the figure that in higher volume fractions and temperatures, there has been a steeper increase in TCR. In these temperatures and volume fractions, the number of SWCNTs in the fluid has increased, that is, heat transfer surface compared to the amount of the volume occupied has increased. In Fig. 3, the percentage of increase in nanofluid thermal conductivity has been illustrated in different volume fractions and temperatures. As seen in the figure, the highest effect of adding SWCNT particles can be found in temperature of 50 degrees and volume fraction of 0.75%. In this volume fraction and temperature, the nanofluid thermal conductivity has been obtained 45% greater than EG thermal conductivity. This value of increase can be useful in processes requiring heat transfer like car radiators. 6

2.4. Proposing new correlation Experimental data, reported in previous sections, have been used as a correlation pattern for predicting the thermal conductivity. To propose the correlation, a non-linear regression has been performed on experimental values of thermal conductivity. Intended equation includes the effect of the fluid temperature and the nanotubes volume fraction. Therefore, it is a function of temperature and solid volume fraction. Consequently, multiple equations have been considered by try and error and the most accurate correlation was selected. It is worth noting that, to choice the best curvefitting equation, several norms must be used. Here, the mean absolute error (MAE) and the mean squared error (MSE) were employed as the key parameter for testing the correlated model performance. MSE and MAE were calculated by the following equations: 1 MSE  N MAE 

1 N

k  nf   kf i 1  N

N

 i 1

k nf kf

k  nf kf Exp .  Exp .

k nf kf

   Pred . 

2

(1)

(2) Pred .

where N is the number of experimental data used for the proposed correlation. Moreover,

and

k nf kf

k nf kf

Exp .

denote thermal conductivity from the measurements and that obtained from the Pred .

correlated model, respectively. As mentioned above, the MSE and MAE performance criteria were employed for multiple curve-fitting correlations. These were developed to predict thermal conductivity in terms of nanoparticles volume fraction and temperature from regression equations. In conclusion, Eq. (3) was chosen as the most accurate correlation.

k nf  1.44947 103  0.96193  0.05759T  0.25780T  0.31723 2  0.047001T kf where φ and T represent respectively the solid volume fraction in % and temperature in oC.

7

2

(3)

A comparison between the used correlation prediction and experimental data is shown in Fig. 4. One can see the TCR obtained from the correlation is in good agreement with the experimental TCR. On the other hand, the theoretical models are unable to predict experimental TCR. It must be noted that the maximum error is approximately 0.0098 at φ=0.75% and T=50°C. Based on the experimental findings, an experimental correlation was presented to predict the TCR using a regression equation. In addition, a comparison between the measured TCRs with those predicted by the correlation model reveals that there is proper agreement, showing the acceptable precision of the correlation presented in this study. 2.5. Sensitivity Thermal conductivity sensitivity of SWCNTs/EG nanofluid to volume fraction variation is calculated through the following relationship [39]: (

(4)

)

In this relationship, after change shows the conditions after adding nanoparticle and base condition illustrates the conditions before adding nanoparticle. To calculate TCS, in each of the volume fractions, 10% of that volume fraction nanoparticle is added to the nanofluid and changes are investigated. In fig. 5, the effect of temperature and volume fraction on TCS has been shown. As seen in the figure, in high volume fractions and temperatures, nanofluid has had the greatest sensitivity. In temperature of 50 and volume fraction of 0.5, nanofluid sensitivity has reached 1.43%.

3. Artificial neural network modeling Artificial neural network (ANN) is an artificial intelligence modeling technique. This technique has a highly interconnected structure similar to human brain neural cells. Artificial neural networks can provide a complex relation between outputs and inputs [40, 41]. Main benefits of ANN modeling are simplicity, high speed, ability of providing difficult relations between parameters, and the 8

capability to develop non-linear relations through training data. Better predicting value by this technique depends on proper selection of input parameters. This selection is based on the comprehension of user from the problem and physical view of the problem. Normally, to forecast the TCR for every type of nanofluid, temperature, concentration and nanoparticles diameter are assumed as input variables to the neural network. ANN includes a large number of elements with simple processing called neurons, which are organized in different layers in the network. Each network has three or more layers, an input layer, an output layer, and one or more hidden layers. Artificial neural network modeling consists of weights, addition function, activation function, and outputs. The neurons are organized in three layers. In the first layer, input data set is provided; in second layer(s), the hidden layer(s), in fact is the brain of the system; and output layer, which dictates the outcome of the system. In each neuron the process of data or signal transfer to the next neuron was done by the transfer function, weight, and bias embedded in the neuron [42]. It is worth noting that the input layer is the layer that was responsible for receiving the input data for the ANN technique and for delivering the data to the next (intermediate) layer (layers). The processes on the input data were done in the hidden layer (layers). In addition this layer (layers) sends it to the (next) output layer. It is evident that the neurons in the hidden layer do not have any (relation) connection with the external environment. Responsible for the output layer is processing the information coming from the intermediate layer and preparing the output data based on the input layer of the network, which sends this to the outside world. One of the important advantages of ANNs technique is having the training set. Training set refers to ability of ANN technique to learn from the sample set, in a supervised or unsupervised learning process. When the architecture of network is defined, using the learning process, weights are calculated in order to present the desired output. In training algorithms, received training data were used in order to update the weights and biases and this process was repeated until the predicted data agreed with the desired data in an adequate and reasonable manner. The Levenberg–Marquardt training method and the back-propagation 9

algorithm have been used in this modeling [43, 44]. The performance function is employed to calculate errors during the process of network training. The mean absolute error (MAE) and the mean squared error (MSE) are two of the most popular performance functions employed in feed forward neural networks (Eqs. (1) and (2)). In this study, these criteria are used for evaluating neural network performance, as well. The multilayer perceptron neural network includes multiple layers [45, 46]. Each layer also consists of several neurons. Each neuron in each layer has been connected to the neurons in the next layer by weight coefficients. In each layer a function named activation function is used to calculate the summation of the input weights and the biases of each neuron for producing the output neuron. Developing an ANNs network includes 3 steps as follows: 1- Developing the data required for network training. 2- Evaluating neural network structures to choice the optimal one. 3- Testing the neural network using data not previously used in network training. Biased neurons are connected to other neurons in the next layers to develop a constant bias. We have used the tan-sigmoid function for the hidden-layer and the purelin function for the outputlayer. In hidden layers, each neuron computes the summation of the relating bias and the input weights and then transfers them through the activation function. A multilayer perceptron neural network has been employed to estimate the thermal conductivity ratio (Fig. 6). The temperature and concentration have been employed as network input variables. TCR has been estimated by the following conditions. Nano particles volume fractions (φ) are: 0.02, 0.05, 0.075, 0.1, 0.25, 0.5 and, 0.75. Temperature (T) are: 30, 35, 40, 45, 50oC. It is worth noting that the different ranges of the input variables may lead to inadequate network training. We know that

and

. To solve this problem, all input variables were

normalized in [−1, 1] breaks. The optimal neurons number in the hidden layer is obtained by trying dissimilar networks and comparing their performance functions with each other. As mentioned, the performance functions, selected in this study, were. Thus, the neural network structure with the 10

lowest values of MAE and MSE was chosen as the optimum network structure. Table 2 represents the values of MAE and MSE for ANNs with various structures. Based on this table, the one-layer structure with four neurons in each hidden layer (Fig. 7) is the optimum network structure to model the TCR of the FSWCNTs-EG nanofluid in terms of concentration and temperature. This construction has been chosen regarding to the lowest difference between the ANN outputs and the experimental data. It estimates a TCR with MSE and MAE values equal to 6.70E-6 and 9.90E03, respectively. Fig. 8 shows a network regression diagram after training and all data, the value of which is over 0.9998 in all cases. This regression value establishes suitable performance of the trained network. The experimental results and predicted values (estimated by ANN) have been compared with the tested data and margin of deviation of the proposed correlation versus data number is presented in Fig. 9. Difference between the thermal conductivity evaluated by predicted value with the ANN method and results obtained from experiment data for SWCNT-EG nanofluid were compared in Fig. 10. This comparison was done as a function of number of data. As seen, the predicted values obtained for ANN method and experimental correlation are in good agreement with each other. The purpose of this study was to model the TCR of the FSWCNTs- EG nanofluid using artificial neural network (ANN) technique and correlation methods in the nanoparticles volume fraction from 0.02 to 0.75 and temperature ranging from 30 to50°C. Investigation on the proposed models from ANN method indicates that ANN and correlation outputs are in good agreement with the experimental data. Therefore, TCR values of the FSWCNTs- EG nanofluid can be appropriately predicted by the ANN and correlation models.

4. Conclusion In this work, we have shown that by adding 0.75% SWCNTs to ethylene glycol thermal conductivity can be increased to 45%. We have also showed that the artificial neural network (ANN) technique can be used as one of the approaches to present an accurate model in prediction of 11

thermal conductivity of nanofluids. In addition a new correlation based on artificial neural network (ANN) technique as a function of two parameters as nanoparticles volume fraction and temperature has been provided. For that purpose, seven different nanoparticles volume fractions from 0.02% to 0.75%, each of which at five various temperatures, have been used. The MSE of the ANN technique and the proposed correlation were up to 6.70E-6 and 1.953E-4, respectively.

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Tables Table 1 Physicochemical specification of SWCNTTs Value

Parameter Color Purity SSA Outer diameter Inner diameter Length True density

black Carbon nanotubes > 96 wt% > 580 m2/g 1-2 nm 0.8-1.6 nm 15-50 um ~2.1g/cm3

Table 2 Performance of ANN with different structure

Number layers 1 1 1 1 1 1 1 2 2 2 2 2 2 2

of

hidden Number of neurons in MSE each hidden layers 2 5.50E-5 3 5.65E-5 4 6.70E-6 5 2.96E-5 6 7.28E-5 7 4.45E-5 8 1.42E-4 2 4.89E-5 3 6.37E-5 4 2.16E-5 5 8.45E-5 6 1.02E-5 7 1.11E-4 8 3.27E-5

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MAE 0.0175 0.0124 9.90E-03 0.0139 0.0102 0.0231 0.026 0.0215 8.30E-03 0.0129 0.0222 0.0068 0.0579 0.0112

Figures

200 SWCNT(OD=0.8-1.6 nm, ID= 1-2nm)

Lin (counts)

150

100

50

0

20

40

60

80

2 Theta- scale

Fig. 1. XRD and TEM image of the SWCNTs

Fig. 2. TCR with respect to nanoparticles volume fraction and temperature

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Fig. 3. TCE of nanofluid with respect to nanoparticles volume fraction at different temperatures

1.2

Experimental correlation

1

Std. Dev.= 0.034 0.8

R-Squared= 0.9867 TCR

0.6

0.4

0.2

0

-0.2 -5

0

5

10

15

20

25

30

35

40

Num. of data Fig. 4. Comparison between correlation outputs and experimental data

18

Fig. 5 Sensitivity analyze at various solid volume fractions and temperatures

19

Fig. 6. ANN process Flowchart

20

Dependent Variable

Hidden Neurons

Independent Variables Temperature

Thermal Conductivity Ratio

Nanoparticles Volume Fraction

Fig. 7. One layer neural network with four hidden layers and one output layer

Fig. 8. A network regression diagram after training and for all data

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Fig. 9. Margin of deviation of the proposed ANN topology versus data number

Fig. 10. Comparison between ANN outputs and experimental TCR

22

Highlights 

Functionalized Single Walled Carbon Nanotubes were suspended in Ethylene Glycol (EG).



By adding 0.75% SWCNTs to ethylene glycol thermal conductivity can be increased to 45%.



ANN technique is a suitable approach to predict the thermal conductivity of nanofluids.



A new correlation based on ANN technique has been provided as a function T and φ.

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