Effects on thermophysical properties of carbon based

International Journal of Heat and Mass Transfer 125 (2018) 920–932

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Effects on thermophysical properties of carbon based nanofluids: Experimental data, modelling using regression, ANFIS and ANN Abdullah A.A.A. Alrashed a, Maryam Soltanpour Gharibdousti b, Marjan Goodarzi c,⇑, Letícia Raquel de Oliveira d, Mohammad Reza Safaei e, Enio Pedone Bandarra Filho d a

Department of Automotive and Marine Engineering Technology, College of Technological Studies, The Public Authority for Applied Education and Training, Kuwait Industrial and System Engineering Department, State University of New York at Binghamton, Binghamton, USA Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam d School of Mechanical Engineering, Federal University of Uberlandia (UFU), Av. Joao Naves de Avila, 2121, Santa Monica, Uberlandia, MG 38408-514, Brazil e Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran b c

a r t i c l e

i n f o

Article history: Received 28 February 2018 Received in revised form 23 April 2018 Accepted 26 April 2018

Keywords: ANFIS ANN Non-linear regression Carbon based nanofluid Experimental measurement

a b s t r a c t Viscosity, density and thermal conductivity of Diamond-COOH and MWCNT-COOH nanoparticles dispersed in water was studied without adding any surfactants or additives for a range of 20 °C < T < 50 °C and 0.0 < u < 0.2 vol%. Accordingly, based on the experimental data, a new correlation was introduced that predicts the nanofluids’ relative thermophysical properties. Besides the non-linear regression for minimum prediction error, an adaptive neuro-fuzzy inference system (ANFIS) and optimal artificial neural network (ANN) were developed. The model was fed by 120 experimental data. 70% of data points were included in the dataset training set and 30% were used as test set. The results of different theoretical models, predicted results and experimental data were compared together. The root-mean-square error (RMSE) and mean absolute percentage error (MAPE) were used to evaluate the results. The models explored the influence of material type, nanoparticle concentration and temperature on the thermophysical properties of nanofluids. As the results show the majority of theoretical models define the thermophysical properties accurately, if correct values of base fluid properties are fed to them. Yet, the current soft-computing methods show less error in comparison to the existing correlations. The ANN is recommended for future studies, as it provides the best fits to the experimental data. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Three strategies can be used to make a more compact and efficient heat transfer system, including passive, active and the compound techniques. Many studies have adopted the passive technique, because it does not need an external power to function [1]. Generally, this method adds an additive to the working fluid [2,3] or uses geometrical or surface modifications to the flow channel [4,5]. Several past studies have attempted to develop new passive methods to increase the convection heat transfer coefficient or improve the effective thermal conductivity of the fluid. In one of the methods, high thermal conductive solid particles such as metal

⇑ Corresponding author at: Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam. E-mail address: [email protected] (M. Goodarzi). https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.142 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.

or metal oxides are added to the base liquid. To do so, suspensions of micrometer or millimeter-sized particles were used. Even though, some improvement was achieved, the thermal system showed issues, such channel abrasion and clogging as a result of the poor stability of the suspension, particularly in micro- and/or mini-channels. Choi and Eastman [6] developed a new passive method, i.e., ‘‘nanofluids” that solved some problems of the large-particle suspensions [7]. Nanofluids comprise of nanoparticles suspensions with high thermally-conductive materials, such as metals [8], metal oxides [9] and carbon [10] into heat transfer fluids to enhance the total thermal conductivity. Usually, these nanoparticles are of order 100 nm or lower. The shape of nanoparticles can be cylindrical [11], spherical [12], or plate [13]. Compared to a low-pressure drop, the suspensions of nanoparticles may enhance the fluid’s effective thermal conductivity [14]. Yet, these materials exhibit less erosion in comparison with micrometer or millimeter particles [15].

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A.A.A.A. Alrashed et al. / International Journal of Heat and Mass Transfer 125 (2018) 920–932

The chemical and physical specifications of the base fluid and nanoparticles can control the thermo-physical properties of nanofluids. Thus, it is very important to use an appropriate type of nanofluids to gain a high rate of heat transfer. Viscosity and thermal conductivity have been the majority of the studies done in this area, due to influence on heat transfer enhancement [16,17] as well as the pressure drop and consequently pumping power increment factor [18,19]. Nevertheless, other researchers have studied other important parameters of nanofluids such as temperature [20], specific heat capacity [21], density [22], particle type and size [23], type of surfactant [24], weight percentage/volume fraction of dispersed nanoparticles in working fluid [25], particle shape [26] and type of base fluid [27]. There is evidence that nanofluids should be studied excessively as they are advantageous coolants [28,29]. However, there is still a gap in research on stability and preparation of carbon-based nanofluids without the use of additives or surfactants. The current research studied thermal conductivity, viscosity, and density of distilled water as base fluid as well as carboxylic multi-walled carbon nanotubes and carboxylic diamond as nanoparticles. The nanofluids with different temperatures (20 °C < T95% 3–6 – – – Grey

>95% 8–15 3–5 10–50 230 Black

Odor Morphology Melting point (°C) Boiling point (°C)

Odorless Spherical 3727 Not determined 1000

Odorless Multiple wall 3652–3697 Not determined 1500

99% – – – – Almost colorless Odorless – 0.00 100

3520 500 –

2100 710 –

Thermal conductivity (W/m K) Density (kg/m3) Cp (J/kg K) Viscosity (Pa s)

provides not only the addition of the carbonyl groups (sbndCOOH) but also to remove impurities from the carbon nanotubes surface. The acid functionalization of the MWCNTs was done with nitric and sulfuric acids (Synth) in proportion (1:3) respectively. The mixture of acids was added at the carbon nanotubes and stirred for 10 min. Then 100 mL of distilled water at 100 °C was slowly added to the mixture kept under magnetic stirring for about 16 h. Afterwards, the MWCNTs were separated by centrifugation of acid solution and washed with deionized water until the pH level of MWCNTs reaches a value of 7. The described method was an adaptation of Esumi, Ishigami [31] which provided the covalent attachment of sbndCOOH groups on the surface of MWCNTs.

0.6 (20 °C) 998.21 (20 °C) 4186 (20 °C) 0.1 Pa s (20 °C)

Volumetric concentration (%)

Water volume (mL) (±0.1 mL)

Nanoparticles mass (g) (±0.001 g)

u = 0.020 u = 0.080 u = 0.100 u = 0.200

1000.0 1000.0 1000.0 1000.0

0.210042 0.840673 1.051051 2.104208

Table 3 Di-COOH nanoparticles and water mass used for the synthesis of the stable nanofluids. Volumetric concentration (%)

Water volume (mL) (±0.1 mL)

Nanoparticles mass (g) (±0.001 g)

u = 0.020 u = 0.080 u = 0.100 u = 0.200

300.0 300.0 300.0 300.0

0.14928 0.59747 0.74699 1.49547

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functionalization. The FTIR measurements were accomplished in a Vertex 70 (Platinum ATR Bruker) spectrometer. All characterizations were made at room temperature. The nanoparticles structure and surface morphological characterization were determined by SEM (ZEISS, EV MA10) and TEM (JEOL, JEM-2100). 3. Methodology 3.1. Measurements 3.1.1. Thermal conductivity Thermal conductivity was evaluated by using a LINSEIS, THB -1 thermal conductivity meter. This device has been manufactured based on the transient hot bridge (THB) method, which allows the measurement of thermal conductivity, thermal diffusivity and specific heat of various materials, as solids to liquids. The conductivity meter provides fully automatic measurements and is controlled by THB Measurement software. In addition, it offers advantages such as higher accuracy, non-destructive measurement, no reference sample or calibration required, being absolute measurement, besides having a wide measurement range of thermal conductivity (0.01–1 W/m K) and temperature (50 to 200 °C). The measurement uncertainty of the device is ±2%, as determined by the LINSEIS company and the difference between two consecutive evaluation was 2.4% [32]. The experimental apparatus was shown in Ref. [32], consisted of a thermal bath used to guarantee the constant temperature, a stainless steel container, in which the nanofluid sample was placed, the conductivity meter and a computer with the program of data acquisition. The probe was inserted into the nanofluid sample contained in the stainless steel vessel connected to a thermal bath. The measurement was automatic, and performed through software on a coupled computer, with 10 measurements per cycle for each sample. 3.1.2. Dynamic viscosity and density Dynamic viscosity and density of the working fluids were measured by using an Anton Paar viscometer, model SVM 3000. The measuring uncertainty of the apparatus is ±0.35%, as defined by the Anton Paar company. The viscosity measurement is based on a torque of 50 pico-N m, requiring small sample volumes, approximately 2.5 mL. For measurement of the specific mass, the equipment contains a measuring cell, which operates according to the ‘‘U” tube oscillation principle, the two measuring cells of viscosity/density and specific mass being filled by the sample, simultaneously operating [33]. The temperature was controlled by the equipment itself. Measurements were carried out at temperatures of 20, 30, 40 and 50 °C. After injection of samples into the equipment, the value of viscosity was calculated through rotor speed. To reduce error, at each constant rotational speed, four experiments were repeated and the average value was reported. The density and viscosity measurements in the SVM 3000 comply with ASTM D7042 standard. 3.2. Soft computing Three different prediction models applied on the six available datasets to forecast thermal conductivity, viscosity or density of two nanofluids. Then, the model with the smallest number of errors will be favored for the task of prediction. Indeed, a variety of errors exist for the comparison of the prediction models. At first, assume that yt represents the actual data, yt indicates the estimated value of yt , and n shows the sample size. In this way, the mean squared error (MSE) will be the first measured error through

which the average value of the squares of the errors or deviations is calculated. In the other words, it refers to the difference between the estimator and what has already been estimated: i¼n X 2 MSE ¼ 1=n ðyî yi Þ

ð1Þ

i¼1

The MSE is considered as a measure of an estimator’s quality which, indeed, is the risk function that matches the predicted value of the squared error loss or quadratic loss. If the square root of MSE yields, the root-mean-square error or root-mean-square deviation (RMSE or RMS), is considered as the estimated quantity, the RMSE will be tantamount to the square root of the variance, aka the standard deviation for an unbiased estimator. This study seeks to opt for the most appropriate model with the minimum error for the conduct of prediction via the comparison of the values of MSE, RMSE and MAPE among all the various models. MAPE, which is also known as mean absolute percentage deviation (MAPD), is the second measure that reflects the prediction accuracy of a forecasting method in statistics:

i¼n X yty^t MAPE ¼ 1=n yt i¼1

ð2Þ

It is noteworthy that only the mean absolute percentage error (MAPE) does not have any scaled output, while all error estimation approaches contain the scaled output. Since the input data that have been exerted for the model estimation hold differing scales, the MAPE method is considered as the favored method for the estimation of the relative errors. 3.2.1. Data preparation Here, 70% of the dataset is employed to train models and the remains, i.e. 30% is used for the purpose of testing the models. It is very important to go for the pertinent sample for training and testing towards the decrease of prediction error. In this regard, the temperature values from 20 °C to 50 °C and the fraction volumes from 0.0% to 0.2% should be included in the training set should include; otherwise, a statistically significant increase in errors will come out. 3.2.2. Non-linear regression Regression in statistics refers to an approach for modeling the relation between a dependent (y) and one or more explanatory (or independent) (X) variables. This kind of linear relationship may not exist in all the situations. The polynomial regression model is possible to be put in the form of a matrix, made up of a design matrix, a response vector, a parameter vector, and a vector of random errors. In fact, the polynomial regression aims at modeling a nonlinear relation between the independent and dependent variables or, to say more technically, between the independent variable and the dependent variable’s conditional mean. In the same way, the main objective of nonparametric regression is to reach a non-linear regression relationship. 3.2.3. Artificial neural network An artificial neural network (ANN) is an information processing paradigm which gets inspired by biological nervous systems, which includes the brain processing the information. A lot of interconnected processing elements (neurons) operating in harmony with each other are the main constituting parts of this system toward the resolution of unique problems. Generally, neural networks are the mathematical methods constructed to have different functions. Taking different configurations in order to carry out various tasks, neural networks can carry out data mining, pattern recognition, classification, prediction and process modeling [34].


Like individuals, ANNs learn by process of exemplification. As mentioned above, an ANN can be arranged for a particular purpose and usage, such as forecasting or data classification through a learning process. Being actively involved in learning, biological systems should be adjusted to the synaptic connections between neurons. ANNs also go through the same procedure. Topologically, ANNs are classified into two groups: (1) feed-forward networks and (2) feedback networks. Multilayer perceptron (MLP) is a famous feed-forward network. Each of the architectures is useful regarding its criteria, with MLP having the most useful application in the field of engineering. MLP networks are able to adjust networks to the model if put together with Backpropagation learning algorithm. Backpropagation learning that is categorized under supervised learning methods was proposed by Werbos [35] after that was extended Rumelhart and McClelland [36]. This algorithm provides the appropriate output for the set of the input. Resolution of a neural network problem includes three steps as follows: the first step is training, the second step is generalization, and the last one is implementation. During the training process, the network learns to distinguish the current pattern from the input dataset. The process of presenting the training examples to the network includes a pattern of activities for the input units together with an optimal design of actions for the output. Thus, each neural network follows a series of training rules used to define and formulate the training method. The network capability for the derivation of a probable solution will be assessed through generalization or testing if the inputs are not known and not trained to the network. Regarding this, the specification of how real network’s real output is close in line with the optimal output in new settings is required. The interconnection weights within the learning process are adjusted so that the network can generate a more appropriate approximation of the favored output. Learning in neural networks happens by exemplification for these networks cannot be pre-programmed to execute a particular task. The examples must be chosen with care and causation; otherwise, it may lead to the waste of optimal time or the network may malfunction. The main weakness here is that the network finds out the solution to the problem alone and, thereby, it may have an unpredictable operation [37]. Prior to the training of an ANN with the data, it is necessary to normalize the data between zero and one. For two reasons, it is required to conduct this normalization. Initially, all the entries should be guaranteed to hold the same weight. Second, it is required for transferring neurons’ functions because either a

Fig. 1. X-ray diffraction patterns of pristine and carboxylic multi-walled carbon nanotubes.

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hyperbolic tangent or a sigmoid function is measured while these can only be fulfilled within a restricted series of values. When the unscaled to a suitable range is utilized with an ANN, no network convergence take place on training, or else meaningless results could be produced. The data scaling is done automatically during the sampling process. 3.2.4. Adaptive Neuro-fuzzy inference system How different learning techniques available in the neural network literature are applied to fuzzy modeling or a fuzzy inference system (FIS) refers to Neuro-fuzzy modeling [38]. Neuro-fuzzy system is responsible for the integration of neural networks and fuzzy logic and it has recently attracted the high attention of researchers in terms of application. In this connection, the Neuro-fuzzy approach has the benefit of decreased training time because of its smaller dimensions as well as the initialization of the network with the parameters related to the scope of the problem. It can be said that the advantages of fusing fuzzy and neural network technologies which are shown by these results, lead to the facilitation of a precise initialization of the network regarding the fuzzy reasoning system parameters [39]. Adaptive neuro-fuzzy inference system (ANFIS) is a unique method in neuro-fuzzy development, especially in the modeling of nonlinear functions; it has led to statistically noteworthy results. In ANFIS, in order to search for fuzzy decision rules that carry out a specific task properly, a feed-forward network is used. By usage a dataset with an input–output, ANFIS produces a FIS whose membership function parameters are adjusted only via a back-propagation algorithm or via the integration of a backpropagation algorithm with a least-squares method. This way the fuzzy systems learn from the data which are getting modeled. For more information on ANFIS, interested readers are referred to Jang et al. [40] comprehensive text. For optimizing the adaptive parameters’ values, he designed a hybrid learning algorithm for ANFIS, which takes advantage of the feature of quickness compared to the classical back-propagation method in terms of approximating the precise value of the model parameters. There are two alternating phases in the hybrid learning algorithm of ANFIS. First is the gradient descend: the initial phase that calculates the error signals from the output layer backward to the input nodes. Second is the least squares method which provides a possible series of consequent parameters. As to the specific fixed values of elements of premise parameters, the overall output can be stated in the form

Fig. 2. The FTIR spectra of pristine and carboxylic MWCNT.

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(b) Functionalized

(a) Pristine Fig. 3. TEM images of MWCNT samples.

of a linear combination of the consequent parameters. The ANFIS architecture is not unique for some layers can be mixed together so as to generate the same output. The framework which combines both neural networks and fuzzy inference systems is called ANFIS. Therefore, ANFIS contains both the structured knowledge representation used in fuzzy inference systems and the learning ability of neural networks. So, ANFIS suitable for nonlinear modeling is a fuzzy inference system integrating the gradient descent with a hybrid learning strategy [40,41]. 3.2.5. FIS generation approach and parameter adjustment A network-type version can be used in order to explain the input/output map. In fact, this version is like that of a neural network and maps inputs via input membership functions and the relevant parameters, and then via output membership functions and the relevant parameters to outputs. A gradient vector specifies the way the fuzzy inference system models the input/output data for a specific series of parameters. After the gradient vector is obtained, each of the optimization routines can be used so that the parameters can be adjusted to decrease the error value. ANFIS employs either a backpropagation or an integration of the least squares estimation and backpropagation to estimate membership function parameter. 1. Grid part (Number of MFs 5, Input MF Type gaussmf, output MF type linear) 2. Sub-clustering (Influence Radius 0.2, Maximum Number of Epochs 100, Initial Step size 0.01, Step size decrease rate 0.8, Step size increase rate 1.1) 3. FCM (Number of clusters 10, Partition Matrix exponent 2, Maximum number of iterations 100, Minimum improvement 1 105)

4. Results and discussion 4.1. Analysis methods and characterization 4.1.1. MWCNT-COOH The XRD technique utilized for obtaining information on the impurities, the interlayer spacing and the structural strain. However, compared to the X-ray incident beam, the CNTs have several orientations [42]. Chiralities and diameters distribution as well as several layers for the MWCNTs are also observed which result in the statistical characterization of CNTs. The MWCNTs’ XRD pattern

Fig. 4. SEM image of MWCNT.


is shown in Fig. 1. The sharp peaks for pristine MWCNT attributes to (1 1 2), (1 0 1), (0 0 2) Miller indices, located at 2h equal to 64.1, 44.2, and 26.1 degrees, respectively. As can be seen from the X-ray diffraction, with well-aligned straight CNTs on the substrate surface, no (0 0 2) peak can be measured. When the tube axis of CNTs is perpendicular to the substrate surface, the incident beam is not collected but is scattered inside the sample. As a result, the intensity of (0 0 2) drops because of better alignment of CNTs [43]. Overall, the size of CNTs causes broad peaks for all of them. Moreover, there are no impurities such as heavy metals or arsenic within the CNTs’ structures. This is significant as impurities may cause significant variations in thermo-physical properties of nanofluids. Similarly, size calculation through the Scherrer shows that the resultant size complies well with the sizes claimed by the manufacturer as well as the size obtained visually from the SEM/TEM images. Fig. 2 shows the FTIR spectra of the carboxylic and pristine MWCNT. As it can be seen, as compared to the pristine MWCNT, the carboxylic samples have identifiable cues. The MWCNTCOOH spectrum exhibited an ordered ACAOAH stretch about 3000 cm1, where the CNT surface coordinates the hydroxyl [44]. At 1128 cm1, the CAO stretch was seen, which shows well functionalization of MWCNTs with ACOOH groups [45]. Yet, broader

Fig. 5. Typical XRD spectra of pristine and carboxylic diamond.

Fig. 7. TEM images of nano-sized diamond crystals.

Fig. 6. FTIR spectrum of pristine and carboxylic diamond.

Fig. 8. Scanning electron microscopy (SEM) of diamond nanoparticles.

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peaks were observed with the FTIR spectra of MWCNT-COOH in comparison with the pristine MWCNT. TEM (transmission electron microscopy) image of the MWCNTs is seen in Fig. 3. All the nanotubes have a tubular and hollow shape. Pristine nanotubes are entangled and in the absence of treatment, form agglomerates. But no agglomerate is seen after functionalization, as the nanotubes have no noticeable cluster structures and are uniformly dispersed. The scanning electron microscope (SEM) micrograph is used to study the surface morphology of the prepared nanomaterials and their morphological features. The SEM image of the MWCNT is

(a) MWCNT-COOH: After synthesis

(b) MWCNT-COOH: After 2 months

shown in Fig. 4. As shown, the pristine MWCNTs are very tangled as a result of high the specific surface area, porous structures and strong van der Waals forces. 4.1.2. Di-COOH The typical XRD spectra of diamond-COOH and pristine diamond are shown in Fig. 5. Four sharp peaks are identified in this figure. The first one at 43.91° is a characteristic reflection of the plane (1 1 1) and the 2nd peak at 75.27° indicates the plane (2 2 0). The diamond peak of (1 1 1) is more intensive, compared to the peak of (2 2 0), which shows that the growing process happens

(d) Di-COOH: After 2 days

(e) Di-COOH: After 10 days

(c) Di-COOH: After synthesis Fig. 9. Stability of the prepared suspensions.

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especially at the plane (1 1 1), otherwise the orientation of the diamond films must be in the transversal plane to (1 1 1), i.e., plane (1 1 0). Moreover, as there is no peak between 20° < 2h < 30°, it can be inferred that there is no amorphous carbon material in the samples [46]. Furthermore, the XRD peaks for the carboxylic diamond are similar to the peaks for samples made from pristine diamond. Yet, the carboxylic diamond peaks have smaller intensity. However, the intensity of carboxylic diamond peaks are smaller. Fig. 6 depicts Fourier-transform infrared spectrometer (FTIR) of the carboxylic and pristine diamond. Bands situated at 896 cm1 and 1450 cm1 are assigned to the bending and stretching of CAC sp3 hybridization, respectively. Also, a band at 1210 cm1 is allotted to the sp3 bond of carbon hybridization [47]. The peak at 1624 cm1 (weak peak) is to allocated carbon double hybridization bond. The bands at 1192 cm1 and 905 cm1 are assigned to the CAC bonds [48]. A very broad peak at 3300 is seen for Di-COOH, showing the likelihood of OAH stretching in the carboxylic group. As shown in Fig. 7, the size and shape of diamond nanoparticles were characterized by TEM. After preparation process, the nanoparticle dimensions are close to those claimed by the manufacturer. Moreover, according to TEM images, it is interesting to mention that several diamond nanoparticles exhibit wellfeatured crystal faces in the form of twinned hexagonal plates, truncated octahedra. A SEM was used to define the grain size and the morphology of the diamond powder (Fig. 8). To do so, before the collection on carbon-coated copper grids, the samples were provided by ultrasonic dispersing of the material in ethanol [32]. The agglomerated particles of powders are observed in the SEM images, which by appropriate disperse in the base fluid may be broken to the particles with nanometer size [49,50]. Fig. 9(a–e) depicts stability of the prepared suspensions and the dispersibility of the nanoparticles in the base fluid. As shown, the studied nanoparticles can easily disperse in the solvent with high stability. Also, the MWCNT-COOH samples did not show any clear sedimentation even after two months. The fluid prepared for carboxylic diamond/water nanofluid was stable after two days and even after 10 days. Only after 10 days at / = 0.2% of this nanofluid, an insignificant sedimentation was seen. As the findings reveal, using a correct method for preparation of low concentration nanofluids results in highly stable suspensions, without the need of chemical additives or surfactants. This seems to be desirable,

Table 4 Thermal conductivity of nanofluids.

because the surfactants may change the suspensions’ thermal conductivity [51]. 4.2. Thermophysical properties analysis Mean values of measured thermal conductivity of nanofluids are shown in Table 4. The results reveal that temperature and volume fraction have considerable effects on thermal conductivity enhancement. The enhancement is achieved because the ratio of particles’ surface area to volume increases, as the diameter is reduced. Moreover, increasing the temperatures cause an increment in the mixing effects in the nanoparticles suspensions which results in further the thermal conductivity augmentation. This can be attributed to thermal dispersion effects introduced by Li, Xuan [52]. Also, the results show that the nanofluids with Diamond-COOH nanoparticles exhibited greater improvement in the thermal conductivity compared to MWCNT-COOH (up to 3.81%) in the same nanoparticle temperature and volume concentration. Table 5 Viscosity of nanofluids. Temperature

20 °C 20 °C 20 °C 20 °C 20 °C 30 °C 30 °C 30 °C 30 °C 30 °C 40 °C 40 °C 40 °C 40 °C 40 °C 50 °C 50 °C 50 °C 50 °C 50 °C

Volume

0.00% 0.02% 0.08% 0.10% 0.20% 0.00% 0.02% 0.08% 0.10% 0.20% 0.00% 0.02% 0.08% 0.10% 0.20% 0.00% 0.02% 0.08% 0.10% 0.20%

Viscosity (Pa s) MWCNT-COOH/water

Diamond-COOH/water

0.0010751 0.0010755 0.0010981 0.0011479 0.0016328 0.0008913 0.0008938 0.0009054 0.0009346 0.0014169 0.0007556 0.0007598 0.0007835 0.0007918 0.0010273 0.0006236 0.0006352 0.0006598 0.0006968 0.0008243

0.001075 0.001076 0.001081 0.001082 0.001099 0.000891 0.000893 0.000899 0.000904 0.000923 0.000756 0.000757 0.000764 0.000769 0.000783 0.000624 0.000757 0.000764 0.000769 0.000783

Table 6 Density of nanofluids.

Thermal conductivity (W/m K) Temperature

Volume

Diamond-COOH/water

MWCNT-COOH/water


0.00% 0.02% 0.08% 0.10% 0.20% 0.00% 0.02% 0.08% 0.10% 0.20% 0.00% 0.02% 0.08% 0.10% 0.20% 0.00% 0.02% 0.08% 0.10% 0.20%

0.6230 0.6312 0.6338 0.6358 0.6387 0.6321 0.6538 0.6543 0.6585 0.6641 0.6434 0.6649 0.6665 0.6676 0.6738 0.6657 0.6916 0.6965 0.7040 0.7178

0.6230 0.6275 0.6316 0.6360 0.6381 0.6321 0.6355 0.6360 0.6436 0.6452 0.6434 0.6464 0.6499 0.6541 0.6585 0.6657 0.6662 0.6728 0.6872 0.6941

Temperature

Volume


0.00% 0.02% 0.08% 0.10% 0.20% 0.00% 0.02% 0.08% 0.10% 0.20% 0.00% 0.02% 0.08% 0.10% 0.20% 0.00% 0.02% 0.08% 0.10% 0.20%

Density (kg/m3) MWCNT-COOH/water

Diamond-COOH/water

998.10 998.38 998.65 999.08 999.88 995.38 995.84 996.00 996.48 997.53 992.10 992.38 992.48 992.78 993.05 987.41 987.84 988.43 989.13 990.78

998.10 999.35 999.78 999.95 1000.55 995.38 996.77 997.13 997.75 998.45 992.10 993.33 993.48 994.03 995.15 987.41 992.45 992.58 993.25 994.63

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Table 5 lists the viscosities of nanofluids based on temperature and volume concentration. As can be seen, the viscosity increases with nanoparticle concentration increment. This rise was over 58% when 0.2 vol% carboxylic MWCNT was used at 30 °C, in comparison with the distilled water at similar temperature. Moreover, the nanofluid with MWCNT-COOH nanoparticles exhibit higher viscosity than H2O/Di-COOH nanofluids for the same volumetric concentration of nanoparticles. This outcome is perhaps because of the size of carboxylic MWCNT nanoparticles (8–15 nm outside diameter, 3–5 nm inside diameter) versus 3–6 nm for the

carboxylic diamond nanoparticles. However, it should be noted that although increasing temperature, decreases the viscosity of the fluids. This decrement is more considerable for carboxylic MWCNT/ water nanofluids, compared to nanofluids containing carboxylic diamond. For studied range, the average viscosity decrease was 13.94% and 1.49% for these two materials, respectively. Another important thermophysical property is the density of nanofluid, which has a considerable role in heat transfer rate [28]. The findings show that reasonable volume fractions of nanoparticles have an insignificant effect on the density, while

(a) Density of MWCNT-COOH/water

(b) Density of Diamond-COOH/water

(c) Thermal conductivity of MWCNT-COOH/water Fig. 10. Comparison of soft computing methods with experimental data and exist formulations.


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(d) Thermal conductivity of Diamond-COOH/water

(e) Viscosity of MWCNT-COOH/water

(f) Viscosity of Diamond-COOH/water Fig. 10 (continued)

considerably affects the viscosity (Table 6). Compared to distilled water, the average density increment for both nanofluids was below 0.3%. However, the effects of temperature on density of fluids are same as their influences on viscosity.

structures (three experiments for different outputs for two nanofluids) were created and compared with the results of other researchers [53–58]. Results of soft computing methods and their comparison with experimental data and existing formulations for two studied nanofluids are shown in Fig. 10(a–f).

4.3. Modelling For studied nanofluids, three outputs are considered as thermal conductivity, viscosity and density. Therefore, six independent

4.3.1. Model evaluation To define the accuracy of proposed developed models, the values of statistical indices including root mean square error (RMSE)

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Table 7 RMSE and MAPE for thermophysical properties of studied nanofluids. MWCNT-COOH/water

Diamond-COOH/water

Method

RMSE

MAPE

RMSE

MAPE

(a) Thermal conductivity Non-linear regression ANN ANFIS Timofeeva et al. [53] model Pak and Cho [54] model Singh et al. [56] model

0.00858 0.00624 1.355 104 0.00936 0.00672 0.04626

0.011956 0.00842 0.16294 0.01281 0.00848 0.00936

0.02871 0.02915 0.02734 0.02238 0.01975 0.03403

0.04236 0.01636 0.02744 0.02706 0.02361 0.04471

(b) Density Non-linear regression ANN ANFIS Formula

0.87415 0.46618 0.49062 0.45848

0.00070 0.00023 0.00047 0.00029

1.52600 1.31298 1.703093 1.78797

0.00096 0.00054 0.09998 0.00124

(c) Viscosity Non-linear regression ANN ANFIS Singh et al. [56] model Brinkman [57] model Maiga et al. [58] model

0.00017 0.01349 0.00015 0.00019 0.00018 0.00018

0.10662 0.04617 0.09275 0.08833 0.08009 0.07692

0.000061 0.000060 0.00018 7.05601 105 6.47292 105 6.28308 105

0.06340 0.02877 0.09894 0.05292 0.04355 0.04010

and coefficient of determination (R2) were computed. For n data, the observed output values are given by y1:yn and the predicted values are noted by f1:fn, and the average of observed data are calculated through Eq. (3):

y¼

n 1X y n i¼1 i

ð3Þ

Dataset variation is defined by means of two summations: first, the total sum of squares:

SStot ¼

n X ðyi yÞ2

ð4Þ

i¼1

Second, the sum of squared residuals:

SSres ¼

n X 2 ðyi f i Þ

ð5Þ

i¼1

Then, the coefficient of determination is calculated using Eq. (6).

R2 ¼ 1

SSres SStot

ð6Þ

Root mean square error is given as:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðyi f i Þ RMSE ¼ n

ð7Þ

In this paper, thermophysical properties of nanofluids have been forecasted using ANN, ANFIS and non-linear regression. Results are also compared with former experimental studies, based on the two measures that were mentioned earlier; mean absolute percentage error and root mean square error. Comparison based on the MAPE and RMSE for each method is shown in Table 7(a–c). As

Table 8 Coefficients of model fitting. Parameter

Nanofluid

X

Y

Density

MWCNT-COOH/water Diamond-COOH/water MWCNT-COOH/water Diamond-COOH/water MWCNT-COOH/water Diamond-COOH/water

1.00000 1.00000 0.64272 0.63235 0.00215 0.00124

0.13288 0.10645 0.00144 0.00552 0.00020 0.00006

Thermal conductivity Viscosity

mentioned before, lower the MAPE value, the model can predict the system’s behavior better. As it is shown through Table 7, ANN has the least MAPE in forecasting of density, viscosity, and thermal conductivity of both nanofluids, compared to other models and this makes it a reliable model for prediction purposes. Moreover, ANN has either lower or almost equal RMSE, in comparison with other models. As mentioned earlier, the main performance measure in the present study is MAPE, therefore ANN is selected as the best predictor for both nanofluids. Beside from ANN, ANFIS and non-linear regression are also used to predict thermophysical properties, but as ANN outperformed them as well in this case, bringing the results of ANN has found to be more efficient. Fig. 10(a–f) compares the performance of prediction done by former scientists’ formulations and present results obtained using soft computing methods as ANN, ANFIS and non-linear regression. As can be seen in the figure, ANN has the best fit to predict thermophysical properties of studied nanofluids, with the closest results to experimental. This claim is supported by the calculation in Table 7. ANFIS gives excellent fit for viscosity, reasonable result for density but most far results for thermal conductivity of studied nanofluids. It should be noted that using present experimental data for base fluid cause very good results for existing formulations like Timofeeva et al. [53] and Pak and Cho [54] formula for thermal conductivity or Brinkman [57] and Maiga et al. [58] formula for viscosity. However, Singh et al. [56] predictions for viscosity and thermal conductivity were different with experimental data. For density, the result of existing formula had a different trend, compared to experimental data. 4.3.2. Mathematical modeling An exponential function is used to fit some curves on thermal conductivity, density and viscosity. To this end, a unique equation is extracted to predict the behavior of studied nanofluids’ thermophysical properties, as shown in Eq. (8). The corresponding coefficients are presented in Table 8.

ljkjq ¼ X ðY ½lnðTemperature 1Þ lnðVolumeÞÞ

ð8Þ

5. Conclusions Carboxylic diamond and multi-walled carbon nanotubes nanoparticles were dispersed in water with utilization of


any additives or surfactants. After that, viscosity, thermal conductivity and density of the mentioned nanofluids were measured at a temperature range of 20 °C–50 °C and maximum volume fraction of 0.2 vol%. The results showed that using nanoparticles in a reasonable volume of fractions has insignificant influence on density, but a great influence on thermal conductivity and viscosity of working fluids. Increasing the temperature causes an enhancement on thermal conductivity values but density and viscosity reduction. After that, utilizing these experimental data, a non-linear regression as well as ANN and ANFIS models are employed to forecast the thermophysical properties of nanofluids. Prediction was based on three input variables consisting of volume fraction, temperature and particles type and three outputs, dynamic viscosity, density and thermal conductivity. The aim of soft computing methods was to obtain the least error in prediction of thermophysical properties of carbon-based nanofluids. As mentioned before, two error rates as the performance measure of the work of former researchers and the results from soft computing approaches are used as an indicator to compare the methods. MAPE and RMSE are both common measurements to evaluate the performance of predictors and since the raw input data holds different scales, MAPE is a better measurement for this aim. Results show that soft computing methods have the least MAPE and RMSE in all cases, in forecasting of thermal conductivity, density and viscosity of both nanofluids. Among soft computing methods, ANN always has the least MAPE which leads it to be the best predictor of the mentioned features for both nanofluids. Based on the ANN outputs, a comprehensive correlation was obtained to forecast thermophysical properties of the nanofluids. The correlation was compared against experimental data and an excellent agreement was found between correlation and experimental results. Acknowledgements The fourth and sixth authors gratefully acknowledge CAPES, CNPq and FAPEMIG for support in conducting this research work. Author contributions Experimental part has been done by L.R.O. and E.P.B.F. Nonlinear regression, ANN and ANFIS parts as well as their related texts have been developed by M.S.G. Conceptualization, formal analysis, investigation, methodology, project administration, resources, supervision, visualization, writing the original draft, and editing are provided by A.A.A.A.A., M.G., M.R.S and E.P.B.F. All authors have read and approved the final manuscript. Conflict of interests The authors declare that there are no conflicts of interest. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijheatmasstransfer. 2018.04.142. References [1] M.N.A.W.M. Yazid, N.A.C. Sidik, W.J. Yahya, Heat and mass transfer characteristics of carbon nanotube nanofluids: A review, Renew. Sustain. Energy Rev. 80 (2017) 914–941. [2] M.H. Esfe et al., Multi-objective optimization of nanofluid flow in double tube heat exchangers for applications in energy systems, Energy 137 (2017) 160– 171.

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