water nanofluid utilizing ANN methods

Sustainable Energy Technologies and Assessments 37 (2020) 100578

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Energy and exergy evaluation of the evacuated tube solar collector using Cu2O/water nanofluid utilizing ANN methods

T

Gholamabbas Sadeghia, , Saeed Nazaria, Mehran Amerib, Farzin Shamac ⁎

a

Department of Mechanical Engineering, Faculty of Engineering, Razi University, Kermanshah, Iran Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran c Department of Electrical Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran b

ARTICLE INFO

ABSTRACT

Keywords: Evacuated tube solar collector (ETSC) Cu2O/W nanofluid Energy efficiency MLP and RBF models

In this paper, the improvement of the thermal characteristics of an evacuated tube solar collector for different volumetric flow rates of the fluid (10, 30 and 50 L/h) was experimentally enhanced by using copper oxide/water (Cu2O/W) nanofluid, and a parabolic concentrator. Moreover, the effect of different volume fractions of the utilized nanofluid on the energy and exergy efficiencies, convective heat transfer coefficient, Nusselt number, and useful heat gain of the solar collector was experimented. Finally, the accuracy of the experimentations was verified via Artificial Neural Networks (ANNs). The Multi-layer Perceptron (MLP) and Radial Basis Function (RBF) models were investigated to predict the performance of the constructed tubular collector, and their results were compared to one another. The results demonstrated that the MLP method can make a more accurate prediction of the collector performance than the RBF one. The highest error rate for the MLP model was less than that of the RBF model. It was also concluded that the increase in both the flow rate and concentration of the nanofluid leads to an increase in the thermal performance of the solar collector.

Introduction “Nano” and “Energy” are two internationally compelling keywords in the modern world. Renewable energy also attained great significance due to a considerable plunge in fossil fuels consumption. In other words, environmentalists would like to see fossil fuel resources replaced by renewable sources [1]. Solar energy is one of these renewable energy resources, which can substitute for fossil fuels in many thermodynamic industrial applications, such as solar collectors and batteries [2,3]. On the other hand, although there exist some limitations in terms of stability and cost of using nanofluids, they are extensively applied to a large number of heating and cooling solar systems, such as combined cooling, heating and power (CCHP) stations, water heating systems, heat pumps, and desalination systems, to improve the efficiency of solar systems [4,5]. Nowadays, using nanofluids, such as aluminum oxide (Al2O3), copper oxide (Cu2O), and silver-based nanofluids in thermal systems has become a reassuring approach to improving the thermo-physical properties of the working fluid inside the thermodynamic systems [6–8]. Moreover, the modeling of the solar systems has often been carried out conventionally [9]; however, there exist some alternative approaches which predict the efficiency of the system even more

⁎

accurately than the best conventional modeling approaches of solar systems, such as artificial neural network, genetic algorithm, genetic programming, and other promising machine learning based approaches. Sadeghi et al. [10] improved the thermal efficiency of an ETSC using Cu2O/distilled water nanofluid and parabolic concentrator up to 11%. Moreover, the impact of different concentrations of nanoparticles on the thermo-physical properties of the working fluid was also investigated. Milanese et al. [11] conducted a molecular-based simulation on the thermal conductivity of CuO, and Cu nanoparticles. In contrast to the CuO nanoparticles, a layering phenomenon was observed when Cu nanoparticles of different sizes were surrounded by water. Potenze et al. [12] fabricated a parabolic trough collector. They could reach the thermal efficiency of 65% for the solar system by use of a mixture of CuO nano powder and air. Colangelo et al. [13] utilized Al2O3 nanofluid to enhance the energy efficiency of a heat exchanger for cooling electronic devices. Colangelo et al. [14] assessed the stability factors of Al2O3 nanofluid and impact of surfactant on its thermal conductivity. The results demonstrated that the temperature while the nanofluid is being prepared, denotes to what extent its stability is, and the temperature during mixing with magnetic stirrer determines the sedimentation behavior. Lacobazzi et al. [15] found that the difference of mass dispersion reduces the thermal conductivity of Al2O3 nanofluid

Corresponding author. E-mail address: [email protected] (G. Sadeghi).

https://doi.org/10.1016/j.seta.2019.100578 Received 29 June 2019; Received in revised form 28 September 2019; Accepted 7 November 2019 2213-1388/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

Ac Acoil b Cp Cp, np Cp, nf Cp, bf Cj Da Ex i Ex o Ex d FR fn G H h0 hi ho I Knf m Nu n N Qu s0 si so Tsun Ta Tini Tfi Th

Tf , i Tf , o T UL wi Xi (Ex ) Xi (Pr ) Yi y

The collector area (m2) The coil area (m2) Each neuron bias term Specific heat (J kg−1 K−1) Specific heat of nanoparticle (J kg−1 K−1) Specific heat of nanofluid (J kg−1 K−1) Specific heat of base fluid (J kg−1 K−1) Center vector for the jth hidden node Average diameter of the coil The input Exergy rate (W) The output Exergy rate (W) The destructed Exergy rate (W) Removal factor Hidden layers activation functions Intensity of solar radiation (W m−2) Convective heat transfer coefficient (J m−2 K−1) The dead state enthalpy (J kg−1) Enthalpy of the inlet water (J kg−1) Enthalpy of the outlet water (J kg−1) Unit matrix Conductivity of the nanofluid (J m−1 K−1) Fluid flow rate (Lit hr−1) Nusselt number Hidden layers number Number of experiments Useful heat transfer (J) The dead state entropy (J kg−1 K−1) Entropy of the inlet water (J kg−1 K−1) Entropy of the outlet water (J kg−1 K−1) The temperature of the sun surface (K) The ambient temperature (K) Initial temperature of the fluid (K) Final temperature of the fluid (K) Shell side temperature of the fluid (K)

Temperature of the inlet water (K) Temperature of the outlet water (K) Temperature difference in an hour (K) Overall heat loss coefficient Weighting factors Experimental data Predicted data The ith output The output variable

Subscripts ANN ETSC LM Lit/hr MLP MRE MAE MSE NF RBF vol

Artificial Neural Network Evacuated tube solar collector Generalized cross-validation Liter per hour Multi-layer Perceptron Mean relative error Mean absolute error Mean square error Nanofluid Radial basis function Volume fraction of nanoparticles

Greek letters

I II bf nf

np

more than other factors, such as Brownian motion, thermal boundary resistance, layering, and clustering. Colangelo et al. [16] investigated the thermal performance of an innovatively designed solar collector using different volume fractions of the Al2O3 nanofluid through RadThem ThermoAnalytics rel. 10.5 software. The results indicated thet the thermal performance of the collector was enhanced up to 8% by applying nanofluid. Sadeghi et al. [17] experimentally investigated the effect of argan and air gases between cover and absorber coil in a tubular solar collector at different mass flow rates. The results indicated

Thermal diffusivity of fluid (m2 s−1) Energy efficiency Exergy efficiency Density of the base fluid (kg m−3) Density of nanofluid (kg m−3) Density of nanoparticles (kg m−3) Transmittance coefficient Volume concentration of nanofluid

that the optimum mass flow rate is 3.5 kg/h and argon gas presents better efficiency due to less Prandtl number Fischer et al. [18] drew a comparison among various ways of modeling solar collectors. The results showed that for complicated-structure solar collectors, predictive approaches can contribute to forecasting the efficiency of the solar system even more accurately than conventional methods of modeling. Mensour et al. [19] developed a model by the use of Multi-layer perceptron modeling to predict total monthly solar irradiation using meteorological data. Boukelia et al. [20] carried out a novel investigation

Fig. 1. a) The Cu2O/W nanofluid used in the experimentations, b) and c) Confirmation of stability of the synthesized Cu2O/W nanofluid after six months. 2

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Fig. 2. a) XRD analysis of Cu2O nanoparticles, b) The absorption of light through the proposed nanofluid over the period of time, c) SEM image of the Cu2O nanoparticles.

on the prediction and optimization of the levelized electricity cost of two different thermal power plants with two various working fluids with artificial neural network. Kalogirou [21] used Artificial Neural Networks (ANN) to forecast the performance parameters of flat plate solar collectors. The results demonstrated that ANN method could predict the substantial thermal parameters of the solar system more precisely than the conventional methods of modeling solar systems. Burrati et al. [22] verified the accuracy of certificates related to energy consumption of buildings in Italy through Artificial Neural Network modeling. A novel index was defined in the work in order to achieve certainty as to which energy certificate needs to be under control. Vakili et al. [23] estimated the global daily solar insolation by means of ANN using environmental data, such as air temperature and particles suspended in the air. The results indicated that the prediction of the solar radiation was more accurate in comparison with the previous studies using other methods. Tomy et al. [24] forecasted the efficiency of flat plate solar collector with silver/water nanofluid using Artificial Neural Network (ANN). The Reynolds number was between 5000 and 25,000. The results were in exact agreement with the experimental investigation. In 2014, Mahian et al. [25] mathematically analyzed the effect of volume fraction of nanoparticles in the base fluid and the shape of nano materials on the second law efficiency of thermal solar systems. Goudarzi et al. [26] investigated the impact of nanofluids pH on the performance of solar collectors. It was found that changing the pH of nanofluids can tangibly influence thermo-physical properties of the fluid, and could report the 52% efficiency. In the present study, the thermal characteristics of a constructed ETSC with parabolic concentrator and the use of copper oxide/water nanofluid are investigated. Afterwards, the accuracy of the experiments is verified by the ANN method, namely MLP and RBF. The input data are adopted from experimental investigations, and the results derived from the experimental data are compared to those of the predicted results to ensure the accuracy of the Artificial Neural Network prediction modeling. Furthermore, the accuracy of the two proposed Artificial Intelligence algorithms (MLP and RBF) are compared with one another. Moreover, the effect of parabolic concentrator on the diffuse irradiance is examined. Lastly, the thermal characteristics of the optimum ETSC at various mass flow rates are investigated.

concentrations, the two-step method is more efficient than the one-step method for decreasing sedimentation and increasing the dispersal behavior [27,28]. In this procedure, polyvidone (PVP-K90) was added to the prepared solution which was used as the surfactant, and the nanoparticles were scattered by the magnetic stirrer. In the next step, the nanofluid was set under an Ultra-Sonicator device, the frequency of which was 60 KHz over half an hour period of time, in order to appropriately blend the nanofluid. Subsequently, ascorbic acid (C6H8O6) was added, and then the prepared stabilized solution was kept under the frequency of the ultrasonic vibration once again for better stabilization purposes for the same duration. The nanofluid was used in this experimental investigation two days after preparation. The stability confirmations of the nanofluid have been shown in Fig. 1((a)–(c)), respectively. Stabilization analyses In this paper, XRD, FT-IR, UV–Vis, SEM and FESEM analyses were undertaken to validate the utilized nanofluid. X-Ray Diffraction (XRD) is an effective approach in examining the qualifications of the crystals. In order to examine this analysis, 0.9 g of Cu2O was placed in the Inlet model XRD machine, and was investigated by a particular wavenumber 1.53 Angstrom. The XRD image of the nanoparticles is shown in Fig. 2(a). As shown in Fig. 2(b), the dispersal of the nanoparticles and the absorption of light through UV–Vis analysis have been conducted, and the concentration of all samples is 0.08 vol fraction. It can be concluded that the more the aggregation, the more light transmits through the nanofluid. Moreover, sample 1 is the Cu2O/W nanofluid used in the experiments, sample 2 is the nanofluid after one week, and sample 3 is the proposed nanofluid after four weeks. The SEM image of the nanoparticles is illustrated in Fig. 2(c) which displays small sizes of the nanoparticles (15–20 nm) that can lead to the better performance of the solar system. So as to denote the size of nanoparticles by FESEM image, the electronic microscope Model (Vace = 25kv) HITACHI S4160 has been used (see Fig. 3). Experimentation procedure description A schematic of the adopted experimental procedures with a concise explanation of each part is presented in Fig. 4. The experimentations were carried out in Kermanshah at longitude 34.3 °E and latitude 46.7 °N in August in 2018. The nanofluids were prepared for different volume concentrations (0.4 and 0.08 vol). As illustrated in Fig. 5, the

Synthesis and stability of the Cu2O/W nanofluid For the preparation of the Cu2O/W nanofluid with 0.04 and 0.08 vol 3

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Fig. 2. (continued)

ETSC setup contains three WGETSC evacuated tubes, seven storage tanks with volumes of 10, 20, 25, 30, 40, 50, and 60 L, a curved mirror as the parabolic concentrator used in the bottom of the tubes, a steel frame with holes inside to lessen the weight of the collector for more convenient maintenance, and the sheet elastomeric material insulation of the tanks. Inasmuch as the experiments were undertaken in summer and the azimuth angle is high, the collector ought to be positioned at angles less than the latitude of the studied region. The collector was positioned at 35° tilt angle. According to a similar work [10], the range of the working fluid inside the tank is between 75 °C and 85 °C. Hence, the thermal storage tank can be utilized to supply the required hot water for mainly domestic utilizations. To reach this aim, an aluminum coil with inner and outer diameters of 4 mm and 6 mm was placed inside the storage tank to obtain the heat from the fluid inside the tank. Aluminum coil was selected instead of prevalent copper coils to avoid the reaction between the Cu2O/W nanofluid and the copper coil. The fluid flow passed through the coil at different flow rates. The stream inside the coil is based on forced convection using a pump. The flow meter RAGK model Rota meter manufactured by Yokogava Corporation was utilized to

adjust the flow rate of the fluid. Ten K-type thermocouples were used in the experimentations. The thermocouples were installed in the inlet outlet of the tube, storage tank, and inlet outlet of the coil to measure the temperature at different places of the collector for the thermal analysis of the ETSC. One thermocouple was used to measure the average ambient temperature. The thermocouples were connected to the data logger BTM4208 model, which is produced by Lutron Cooperation. The characteristics of the constructed setup are displayed in Table 1. At the end of each day of the experiment, the entire working fluid inside the ETSC was evacuated and a fresh supply was substituted in the following morning so that the previous leftover would not influence the ongoing experiment. The data was recorded from half an hour before starting the thermal investigations (from 8:30 a.m.) in order to eliminate temperature fluctuations from performance estimation. The solar insolation was measured every minute through TES132 solar meter. The experiments were conducted from 9 a.m. to 6 p.m.

4

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via Eqs. (1) and (2) [29].

=

I

mCp (Tf , o Tf , i ) Qu = Ac G Ac G

= FR (

)eff

Tf , i

FR UL

(1)

Ta (2)

G

where ( )eff is the multiplication of collector effective transmittanceabsorptance. The specific heat capacity of the nanofluid at different volume fractions was obtained from [30]:

Cp, nf =

[

np Cp, np

+ (1

)

bf

Cp, bf ] (3)

nf

where nf

=

nf

is the nanofluid density derived from [30]:

np

+ (1

)

(4)

bf

In addition, Table 2 presents the thermodynamic characteristics of the utilized materials. Second law efficiency Exergy is utilized for qualifying and denoting the availability of energy. To balance the exergy equation of a control volume the following equation is derived [33]:

Exi

Ex o =

Ex d

(5)

Furthermore, the exergy rate is obtained from [34]:

Ex = mf [(h

h 0)

Ta (s

s0)]

(6)

In the present study, the second law efficiency of the ETSC was obtained from: Fig. 3. FESEM image of Cu2O nanofluid for scales of; (a) 100 nm, (b) 500 nm.

II

Thermal concepts

=

mf [(h o A cG 1

hi)

4 3

To (so

s i )] Ta 4 Tsun

( )+ ( ) Ta Tsun

1 3

(7)

The thermal efficiencies were carried out at hourly intervals.

First law efficiency

Fluid properties

The first law efficiency of the proposed collector could be obtained

To estimate the convective heat transfer coefficient in the heat

Fig. 4. Schematic of the constructed ETSC and nanoscopic phenomena occurring in the system affecting the thermal performance of the ETSC. 5

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Fig. 5. (a) Image of the constructed optimum ETSC water heater, (b) Side view. Table 1 Characteristics of the experimental setup. Characteristics

Dimension

Area of the collector Diameter of the 10 lit tank Height of the 10 lit tank Diameter of the 20 lit tank Height of the 20 lit tank Diameter of the 25 lit tank Height of the 25 lit tank Diameter of the 30 lit tank Height of the 30 lit tank Diameter of the 40 lit tank Height of the 40 lit tank Diameter of the 50 lit tank Height of the 50 lit tank Diameter of the 60 lit tank Height of the 60 lit tank Interior diameter of the tube The distance between evacuated tubes Texture of glass Exterior diameter of the tube Inner diameter of the coil Outer diameter of the coil Length of the coil Type of thermocouples Number of thermocouples Insulation material Insulation sheet thickness Sealing material Frame material

m m m m m m m m m m m m m m m m m – m m m m – – – m – –

2

TLMTD =

Value

(Th

Tf , i ) ln

0.85 0.07 0.65 0.01 0.635 0.01 0.955 0.15 0.425 0.15 0.565 0.15 0.71 0.2 0.48 0.0049 0.12 Borosilicate 0.0059 0.004 0.006 4 K-type 10 Elastomeric sheet 0.009 Adhesive Steel

(

(Th

Th

Tf , i

Th

Tf , o

)

Tf , o) (8)

Hence, according to Eqs. (1) and (8), useful heat transfer can be obtained from:

Qu = mCp (Tf , o

(9)

Tf , i ) = HA coil TLMTD

The convective heat transfer coefficient (H) can be calculated based on Eq. (6),

H=

mCp (Tf , o

Tf , i ) (10)

Acoil TLMTD

The Nusselt number (Nu) for the tube side can be acquired based on Eq. (7),

Nu =

HDa Knf

(11)

where Knf is the conductivity of the nanofluid measured by a KD2 Pro thermal analyzer manufactured by Decagon Company, and Da is the average diameter of the coil. Artificial neural networks (ANN) methodology Artificial Neural Networks (ANNs) have been classified as precise tools of modeling for recognizing the characteristics of the systems with high complexity and nonlinearity, such as solar water heating systems. There exist many different types of neural networks that can be chosen for use in accordance with the type of problem to be solved. For problems that require prediction, Multi-layer Perceptron (MLP) and Radial Basis Function (RBF) are the most common options. In the present research, these two networks will be applied to predict the efficiency and the suitability of performance parameters. MATLAB R2014b software is used to train the ANN networks.

exchanger (set of coil integrated with the storage tank that can be regarded as a shell and tube heat exchanger), Logarithm Mean Temperature Difference (LMTD) is necessary which is defined as:

Table 2 Thermodynamic properties of water and Cu2O [31,32]. Substance

Density (kg m−3)

Thermal conductivity (W m−1 k−1)

Specific heat capacity (J kg−1 k−1)

Thermal diffusivity (m2 s−1)

1. Water 2. Cu2O

907 6080

0.603 42

4178 474

0.143 × 10−6 1.11 × 10−4

6

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b

a

Tempreture X Presure

Ij

Wi1

f1

Wi2

Win

f2

fn

Y

Y

Volume Input layer

bi1

bi2

bin

1st hidden layer

nth hidden layer

1st hidden layer 2nd hidden layer

2nd hidden layer

Output layer

Fig. 6. a) The general architectures of an MLP, b) Architecture of the designed MLP network. Table 3 The organization of the designed MLP.

Table 4 The organization of the designed RBF.

ANN type

MLP

ANN type

RBF

No. of neurons in the input layer No. of neurons in the 1st hidden layer No. of neurons in the 2nd hidden layer No. of neurons in the output layer Number of chosen epochs Activation function

3 5 3 2 2000 tansig

No. of neurons in the input layer No. of neurons in the hidden layer No. of neurons in the output layer Spread Target Error Activation function

3 30 2 2 0 Gaussian

MLP network

Table 5 Correction functions of the utilized thermocouples.

What is considered as the input of the MLP network is the constant number of past data that allows the time series to perform a prediction. Therefore, the output in this case is the predicted future data in this case [35]. A Multi-layer Perceptron is a feed forward type of neural networks with more than one hidden layer. Neurons are nodes of an ANN. Total activation for each neuron is calculated by the sum of the weight and output of the prior layer plus a constant bias [36]. This function is often a non-linear function that produces the output of a neuron. In the training action, calculating the number of hidden layers and the number of neurons per hidden layers create balance model accuracy during model training and testing [36]. A general MLP network architecture with j number of inputs (I) and an output of Y can be seen in Fig. 6(a). The output can be calculated through the following formulas:

Y (n ) =

fn (y (n

1). Win )+bin

Y (1) =

f1 ((I j ). Wi1)+bi1

(12) (13)

f2

Anemometer Flow meter Conductivity meter Viscosity meter Thermocouples Pyranometer Energy efficiency Exergy efficiency

±1.2% ±3.2% ±0.9% ±1.3% ±0.8% ±1.5% ±2.3% ±3.4%

W1

f1

I2

Uncertainty analysis

respectively. For the purpose of training the MLP networks, some learning algorithms in the case of Levenberg-Marquardt (LM) have been used for training the designed MLP architecture. What makes this algorithm a good candidate for MLP learning, is the fast and stable convergence [37]. LM algorithm is an approximation of the Hessian matrix typically found in Newton’s optimization procedure. This allows the algorithm to greatly reduce intricacy, which is an important advantage [38]. The architecture of the designed MLP can be seen in Fig. 6(b). This architecture includes three inputs and two outputs. The inputs are three

where n, b,Wi and fn are the hidden layers number, each neuron's bias term, the weighing factors, and hidden layers activation functions, I1

Variation name

W2

Tempreture Y1 Y2

WL

X Presure

fL

Ij

Y

Volume

a

input layer

hidden layer

output layer

b

Input layer

Fig. 7. a) General structure of an RBF, b) Architecture of the designed RBF model. 7

Output layer

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Fig. 8. a) The regression diagram of MLP training procedure for the first output (inlet outlet temperature difference), b) The regression diagram of MLP testing procedure for the first output (inlet outlet temperature difference), c) The regression diagram of MLP training procedure for the second output (energy efficiency of the ETSC), d) The regression diagram of MLP testing procedure for the second output (energy efficiency of the ETSC).

network has two hidden layers. The first and the second layers contain five and three neurons, respectively. As seen in Table A1, the required training data-sets gathered from experimental investigations are separated into two sets; 70% of the data was considered as training data and 30% was regarded testing data. Table 3 demonstrates the organization of the designed MLP network. RBF network The Radial Basis Function (RBF) networks are feed forward type networks with only three layers usually with a Gaussian activation function for each neuron in the hidden layer, and a linear transfer function in the output layer [39]. The number of neurons is equal to the number of input and output data, respectively. Some advantages of the RBF networks include simple structure, fast training process, strong ability to control input noises, good generalization, and the ability to learn online compared to other feed forward ANNs [40]. The general structure of an RBF is shown in Fig. 7(a) with two outputs considered. The distances between the input vectors and the weight vectors is calculated and taken to a Gaussian function. Therefore, the output of an RBF network is given as follows [41]:

Fig. 9. The MSE (mean square error) per epoch.

L

Table 6 The achieved defined errors of the designed MLP.

Yi = j=1

Defined Error

Train 1

Test 1

Train 2

Test 2

MAE MRE RMSE

0.0027 0.2370 0.0025

0.0080 1.5747 0.0104

0.0025 0.2058 0.0027

0.0078 0.9933 0.0090

L

Wj f j =

Wj exp j=1

1 I Cj 2 2

2

th

(14)

where Cj is the center vector for the j hidden node specified by the Kmeans clustering method. I Cj is the Euclidean norm, and 2 is the variance of the Gaussian function. These utilized inputs and outputs data sets are extracted from Table A.1; similar to the MLP model the required data set is divided into two sets; 70% of these data were considered as training data, and 30% were considered as testing data. The architecture has been designed and is displayed in Fig. 7(b). In order to achieve minimum error rate, the designed network contains sixteen neurons in the hidden layer.

extracted features from performance parameters of the proposed ETSC. The outputs of the architecture contain the temperature difference of the inlet and outlet fluid flow passing through the coil. The designed 8

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Fig. 10. a) The regression diagram of RBF training process for the first output (inlet outlet temperature difference), b) The regression diagram of RBF testing process for the first output (inlet outlet temperature difference), c) The regression diagram of MLP training process for the second output (energy efficiency of the ETSC), d) The regression diagram of MLP testing procedure for the second output (energy efficiency of the ETSC).

Table 7 The achieved defined errors of the designed RBF. Defined Error

Train 1

Test 1

Train 2

Test 2

MAE MRE RMSE

0.004114489126588 0.073876077254289 0.005223892351061

0.004235140259985 0.521031288106272 0.004860905074814

0.014153195185058 0.214128840198804 0.017643440463424

0.020349043038239 1.949727449259427 0.024920250283668

The organization of the designed RBF network has been shown in Table 4.

Error analysis The defined errors contain mean relative error percentage (MRE %), root mean square error (RMSE), and mean absolute error percentage (MAE %) which have been calculated as below [42,43]:

Uncertainty analysis and error investigation Since many errors occur while conducting experiments such as data mining, the uncertainty investigation of all parameters should be carried out to verify the applicability of the experimentations. The uncertainty equations related to the validation of thermal characteristics (energy and exergy analyses) of the constructed ETSC are represented as follows: 2 I

II

=

I f

=

II

Ta

f

+

2

Ta

+

2

I

Tini

II

Tini

Tini

+

2

Tini

+

2

I

Tfi

Tfi

II

Tfi

+

RMSE = 100 ×

1 2 2

I

G

G

MAE % =

(15) 1

2

Tfi

MRE % = 100 ×

+

II

G

G

1 N

1 N

N

Xi (Ex ) Xi (Pr ) Xi (Ex )

i=1 N i=1

(Xi (Ex )

Xi (Pr ))2

N

(17) 0.5

(18)

Z

|Xi (Ex ) i=1

Xi (Pr )|

(19)

Results and discussion

2 2

The experiments have been conducted for different fractions of nanoparticles, but the results are presented for only the 0.04 and 0.08 concentrations of the nanofluid in order to summarize the findings, and extract trend. The results have been divided into two parts; experimental and numerical investigations. In this section, in the first place the effects of nanofluid on the thermal characteristics of the fluid have been investigated, then the ANN optimization models are compared and eventually the experimental thermal investigations of the optimum

(16) In Eq. (15), f is the working fluid density. In this work, solar radiation, mass flow rate, measurement of temperatures, and wind velocity caused the probable errors. The thermocouples were calibrated by a Platinum thermometer with 0.1 °C measurement accuracy. The maximum uncertainties of the investigated solar water heater are illustrated in Table. 5. 9

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Fig. 12. Energy efficiency of the ETSC with parabolic concentrator at different flow rates using Cu2O/W.

Fig. 11. a) Heat transfer coefficient of the fluid flow inside the heat exchanger for different volume concentrations of nanofluids at different volume flow rate, b) Variation of Nusselt number for different volume concentrations of nanofluids at different volume flow rate of the working fluid, c) Useful heat transfer for various volume fractions of the nanofluid at various volume flow rates of the water inside the heat exchanger.

compared to the empirical results can be found as regression diagrams for training and testing actions for the first and second outputs. In Fig. 9, the mean square error is displayed during the training period process. The best training performance is 6.0572e-05 at epoch 1092. The errors defined for the mentioned MLP model have been illustrated in Table. 6. As can be seen from this table, which is highly desirable, the errors obtained for the test data are very low.

constructed ETSC is conducted. ANN-based prediction of the ETSC performance

RBF results As can be seen in Fig. 10((a)–(d)), the obtained results using designed RBF compared to the experimental results can be found as regression diagrams for training and testing actions for the first and

MLP results As can be seen in Fig. 8((a)–(d)), new MLP has been designed and the obtained results using the aforementioned designed MLP network 10

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with an acceptable accuracy is the designed MLP model. Variation of fluid properties Convective heat transfer coefficient is one of the most important thermal performance parameters of the solar systems; hence, it has to be taken into account for evaluating the feasibility of the constructed ETSC. In this study, the heat transfer coefficient of the fluid flow inside the heat exchanger has been estimated under the assumption that the temperature of the fluid inside the tank is considered uniform. Eq. (10) was employed to acquire the heat transfer coefficient of the fluid flow. Fig. 11(a) reveals that at 10 L/h volume flow rate the convective heat transfer coefficient increases with the increase in the volume concentration of the nanofluid due to the increase in the temperature difference of the tube side. This trend becomes steep at higher volume flow rates of the fluid inside the coil (30 and 50 L/h) due to the increase in the velocity of the fluid. On the other hand, Nusselt number of the fluid flow for different volume concentrations of the working fluid at different volume flow rates of the fluid is shown in Fig. 11(b). As illustrated in Fig. 11(b), at 10 L/h volume flow rate, increasing the volume concentration of the nanofluid leads to the reduction of Nusselt number; in that the increase in conductivity of nanofluid is completely predominant over increase in convective heat transfer coefficient. This trend weakens as the volume flow rate of the fluid rises because at higher flow rates, increase in convective heat transfer coefficient becomes more predominant over rise in conductivity of the fluid. Hence, based on Eq. (11), as the concentration of nanoparticles in the base fluid rises, the Nusselt number also increases. Moreover, change of convective heat transfer coefficient and Nusselt number for different volume fractions of the nanofluid at various volume flow rates of water might not a practical option for estimating the feasibility of the solar collector. Therefore, the impact of different concentrations and flow rates on useful heat transfer to the fluid inside the heat exchanger through Eq. (9). Fig. 11(c) reveals that the major effect of using nanofluid in the enhancement of the efficiency of the heat exchanger is up to the 0.04 vol concentration. Afterwards, useful heat transfer enhances gradually and can be considered negligible. Empirical investigation of the thermal characteristics Energy efficiency Energy efficiency of the optimum ETSC for flow rates of 10, 30, and 50 L/h was calculated based on Eq. (1). According to Fig. 12, the energy efficiency of the ETSC increases by raising the flow rate and the volume fraction of the nanoparticles, which displays one of great points of this research. As illustrated in Fig. 12, while water is used inside the ETSC with parabolic concentrator as the working fluid, for volumetric flow rates of 10, 30, and 50 L/h, the maximum energy efficiencies were 22, 26 and 32%, respectively. When Cu2O/W nanofluid for 0.04 vol fraction was utilized for the same flow rates of the fluid, the maximum energy efficiencies were 38, 46, and 48%, respectively. Ultimately, by using Cu2O/W nanofluid for 0.08 vol fraction for the examined flow rates, these figures (maximum energy efficiency of the ETSC) were reported 47, 55, and 60%, respectively. Therefore, the effect of increasing Cu2O nanoparticles on the thermal efficiency of the collector within 0.00–0.04 vol fractions was more tangible than 0.04–0.08 vol fractions of the nanofluid. The energy efficiencies are plotted against the reduced temperature considering the ambient temperature (Ta ) and the instantaneous fluid temperature (Tf ) defined as:

Fig. 13. Exergy efficiency of the ETSC with parabolic concentrator at different flow rates using Cu2O/W.

second outputs. After training, the obtained mean square error (MSE) is MSE = 0.000177188 for sixteen neurons in the hidden layer. Table 7 shows the obtained defined errors for the designed RBF model. Therefore, it can be deduced that the MLP model more efficiently predicts the performance parameters of the ETSC water heater in comparison with the RBF model because it yields less errors; however, the proposed RBF model has advantages over the MLP model, namely its simplicity, fast processing, and miniaturization. In brief, a good way to predict the thermal efficiency of the evacuated tube solar collector

RT =

(Tf

Ta ) G

(21)

With 0.08 vol concentration of Cu2O nanofluid at volumetric flow rates of 10, 30, and 50 L/h, the thermal solar characteristic values of FR ( )eff were 0.47, 0.55 and 0.6, respectively. 11

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Exergy efficiency Additionally, the exergy efficiency of the optimum ETSC at three different flow rates of water was estimated by Eq. (7). As illustrated in Fig. 13, increasing the flow rate does not considerably enhance the second law efficiency of the solar collector. However, using nanofluid is effective, and enhances the second law efficiency of the ETSCs tangibly. On average, when Cu2O/W nanofluid for 0.04 vol fraction, and Cu2O/W nanofluid for 0.08 vol fraction are utilized as the working fluid inside the storage tank, exergy efficiencies of the ETSC increase by 2.1% and 3.7%, respectively.

difference of the fluid passing through the coil, and energy efficiency). The results demonstrated that the designed ETSC with 25 Lit capacity of the thermal storage tank, 0.08 vol concentration of the Cu2O/W nanofluid at 50 L/h volumetric flow rate of the fluid presents the highest efficiency for the solar water heater. Furthermore, the MLP method presents better prediction of the performance parameters of the system than the RBF method with giving less MAE, MRE, and RMSE errors. The results indicated that increase in volume fraction of the nanoparticles, and volumetric flow rate of the fluid lead to increase in the energy efficiency of the system. In the present work, the maximum energy efficiency of 60% and maximum exergy efficiency of 6% for 50 L/h flow rate and 0.08 vol concentration of the nanofluid were reported for the constructed optimum ETSC. Future studies can be centered on denoting the optimum performance parameters of the proposed ETSC through optimization procedures, such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and similar cases.

Conclusion This paper presents some findings about the effect of using Cu2O/W nanofluid on improving the thermodynamic efficiency of the ETSCs. The experimentations were carried out for three flow rates of the fluid. The thermal characteristics (first law and second law efficiencies) of the constructed evacuated tubular collector (ETSC) were also investigated at different flow rates of the fluid by applying various volume fractions of the Cu2O/W nanofluid. As for verification, two evolutionary algorithms (MLP and RBF models) were employed to verify the findings. The prediction procedure consisted of three inputs (Tank volume, nanofluid concentration, and flow rate) and two outputs (temperature

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

Appendix A The data used in the ANN models are tabulated in Table A.1. Table A1 The gathered training data-set. OUTPUTS

INPUTS

Temperature Difference (Inlet outlet of the coil)

Energy Efficiency

Volume of tank

Concentration of nanofluid (vol)

Mass flow rate of fluid (L/h)

24 7.2 5 30.1 10 9 35.8 11.8 11 25 8 5.9 31 10.8 9.7 36.9 12.1 12 27 8.7 6.9 32.4 12 10.5 38.1 13 12.7 24 7.5 5.2 30 10.1 8.9 36

0.17 0.21 0.28 0.32 0.42 0.44 0.39 0.47 0.53 0.2 0.23 0.32 0.35 0.44 0.45 0.41 0.49 0.57 0.22 0.26 0.34 0.38 0.46 0.48 0.45 0.55 0.58 0.19 0.21 0.31 0.33 0.43 0.44 0.4

10 10 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 25 25 25 25 25 25 25 25 25 30 30 30 30 30 30 30

0 0 0 0.04 0.04 0.04 0.08 0.08 0.08 0 0 0 0.04 0.04 0.04 0.08 0.08 0.08 0 0 0 0.04 0.04 0.04 0.08 0.08 0.08 0 0 0 0.04 0.04 0.04 0.08

10 30 50 10 30 50 10 30 50 10 30 50 10 30 50 10 30 50 10 30 50 10 30 50 10 30 50 10 30 50 10 30 50 10

(continued on next page) 12

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Table A1 (continued) OUTPUTS

INPUTS

Temperature Difference (Inlet outlet of the coil)

Energy Efficiency

Volume of tank

Concentration of nanofluid (vol)

Mass flow rate of fluid (L/h)

11.9 11.5 23 7 4.9 29.1 9.5 8 34.9 11.1 10.4 22 6.2 5.1 28.7 8.7 7.2 33.8 10.5 9.8 21 5.3 4.5 27.2 7.8 6.5 32.1 9.7 8.7

0.47 0.56 0.18 0.2 0.3 0.31 0.42 0.41 0.38 0.46 0.53 0.17 0.19 0.28 0.29 0.4 0.39 0.36 0.45 0.5 0.16 0.17 0.27 0.28 0.38 0.36 0.35 0.43 0.48

30 30 40 40 40 40 40 40 40 40 40 50 50 50 50 50 50 50 50 50 60 60 60 60 60 60 60 60 60

0.08 0.08 0 0 0 0.04 0.04 0.04 0.08 0.08 0.08 0 0 0 0.04 0.04 0.04 0.08 0.08 0.08 0 0 0 0.04 0.04 0.04 0.08 0.08 0.08

30 50 10 30 50 10 30 50 10 30 50 10 30 50 10 30 50 10 30 50 10 30 50 10 30 50 10 30 50

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