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Established prediction models of thermal conductivity of hybrid nanofluids based on artificial neural network (ANN) models in waste heat system
International Communications in Heat and Mass Transfer 110 (2020) 104444
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Established prediction models of thermal conductivity of hybrid nanofluids based on artificial neural network (ANN) models in waste heat system
T
⁎
Jiang Wanga,b, Yuling Zhaia,b, , Peitao Yaoa,b, Mingyan Maa,b, Hua Wanga,b a b
State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Yunnan 650093, China Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Yunnan 650093, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Hybrid nanofluids Thermal conductivity Artificial neural network Genetic algorithm Mind evolutionary algorithm
The properties of water (W)/ethylene glycol (EG) mixtures vary significantly with the proportion of EG and temperature, so it is suitable to use such fluids as exchange heat mediums in a waste heat system with temperature fluctuations. The experiments were conducted with 1.0 wt% Cu/Al2O3- EG/W hybrid nanofluids at temperatures ranging from 20 to 50 °C, where the base fluid (EG/W) mixture ratio was varied from 20:80 to 80:20. To search individuals which contain optimal weights and thresholds, a genetic algorithm (GA) and a mind evolutionary algorithm (MEA) coupled with a back-propagation neural network (GA-BPNN and MEA-BPNN, respectively) were used to improve the accuracy in the predicted thermal conductivity. The results show that the thermal conductivity increases nonlinearly with the ratio of water to ethylene glycol and temperature, due to the higher thermal conductivity of water and stronger collision frequency between molecular and nanoparticles. Binary Polynomial Regression (BPR) was fit with (coefficient of determination) R2 = 0.9984 as functions of temperature and mixture ratio. Comparisons of the prediction performance and capability of BPR, the performance of R2 increases by 0.11% and 0.13% for GA-BPNN and MEA-BPNN. It indicates that the combined BPNNs both predicate more accurately, particularly MEA-BPNN has the highest prediction accuracy.
1. Introduction Given the global energy crisis, more researchers are paying attention to improve overall energy efficiency in a working system [1]. Waste gas or liquid are often produced at high pressure in industrial processes, which contain a large amount of heat or combustible components. For years, many techniques and methods were used to increase utilization of waste heat to maximize energy efficiency and reduce operating cost. In some production processes, most waste heat is released to the environment. For example, in a typical cement plant, approximately 40% of the total energy consumed during cement production is transferred to the environment as waste heat [2]. Le et al. [3] noted that 27.9% of total global final consumption comes from the energy consumption of industrial sectors. Consider an acid production system for example. A large amount of low-temperature waste gas or liquid (nearly 100 °C) is released into the environment during the SO3 and acid cooling processes. In order to recover waste heat, the thermal energy contained in waste gas or liquid can be exchanged with working fluids (e.g., water, ethylene glycol, or a mixture of these fluids), and the Organic Rankine Cycle (ORC) can be used to generate electricity.
However, the temperature of waste gas or liquid varies randomly with the initial amount of gas in the washing tower at the beginning. Therefore, the properties of working fluids should vary with temperature to recover such waste heat. The thermal conductivity, viscosity, specific heat, and density of working fluids are important parameters in determining the pumping power and heat transfer coefficient in cooling or heating systems. Among the various thermophysical properties of nanofluids, the thermal conductivity is one of the most important thermophysical parameters that significantly affect heat exchange. Conventional working fluids like water (W), oils, or ethylene glycol (EG) have poor thermal properties compared to metals or metal oxides [4]. Hence, the addition of nanoparticles with high thermal conductivity to a base fluid can increase the thermal conductivity of the fluid. Recently, the use of two or more nanoparticles in a base fluid was investigated, known as hybrid nanofluids. Kumar et al. [5] reported that the thermal conductivity enhancement of hybrid nanofluids is better than that of single nanofluids due to new physical and chemical bonds. Selvakumar et al. [6] and Dalkılıç et al. [7] both reported that mixing nanoparticles with high thermal conductivity and chemically inert nanoparticles in a base
⁎ Corresponding author at: State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Yunnan 650093, China. E-mail address: [email protected] (Y. Zhai).
https://doi.org/10.1016/j.icheatmasstransfer.2019.104444
0735-1933/ © 2019 Elsevier Ltd. All rights reserved.
International Communications in Heat and Mass Transfer 110 (2020) 104444
J. Wang, et al.
fluid forms a hybrid nanofluid with higher effective thermal conductivity. The thermal conductivity can also be increased by mixing different types of base fluids. The thermophysical parameters of EG/W hybrid nanofluids vary due to the composition of the mixture. Such special characteristic is beneficial to recovery waste gas or liquid with temperature fluctuation. Özdemir et al. [8] and Maïga et al. [9] found that the thermal conductivity of EG base fluids can be increased by more than that of water. Chiam et al. [10] found that the properties of mixed EG/W base fluids vary significantly with the percentage of EG and temperature. Eshgarf et al. [11] noted that mixtures of EG and water are used in many industries as antifreeze agents in heat exchangers and radiators. The thermal conductivity of hybrid nanofluids is also affected by temperature, volume fraction, and mixture ratio. It is difficult to present a general and accurate thermal conductivity prediction in various conditions. The heat transfer mechanism of nanofluids is difficult to explain in terms of traditional liquid-particle suspension models. Maxwell's thermal conductivity model is applicable to homogeneously dispersed nanofluids with low nanoparticle concentration [12]. A modified Maxwell model for predicting the thermal conductivity of hybrid nanofluids was presented by Takabi et al. [13]. However, these equations do not reflect the relationship between thermal conductivity and mixture ratio in hybrid nanofluids and the aspect of the high cost and time is barrier for engineering applications. Many researchers have proposed empirical models for predicting the thermal conductivity of nanofluids. An artificial neural network (ANN) is a mathematical model that simulates the structure and function of biological neural networks, and it can be used for prediction based on limited experimental data. Due to its huge nonlinear mapping ability, many researchers have used ANNs for modeling and predicting the thermal conductivity of nanofluids [14]. ANN models contain many training algorithms like genetic algorithms, back propagation (BP), evolutionary techniques, and conjugate gradients. Among those, a back propagation neural network (BPNN) is a popular model. Xiang et al. [15] used a BPNN model to predict and optimize the thermophysical properties of liquid Galny in microchannel heat sinks. However, due to its serial search, the BP algorithm can get stuck in a local extremum and it converges slowly in the training stage. The other drawback is that it may exhibit overfitting when a small amount of training data is available [16]. To avoid local minima while achieving global convergence, many other algorithms combined with ANN have been used for better estimation. Selimefendigil et al. [17] combined the ANN with fuzzy logic to accurately predicate the average Nusselt numbers for CNT-water nanofluid filled branching channel with an annulus. Ahmadi et al. [18] first presented least square support vector machine-genetic algorithm (LSSVM-GA) to predict thermal conductivity of Al2O3/EG nanofluids with input variables of size, concentration and temperature. The coefficient of determination (R2) and mean squared error are 0.9902 and 8.64 × 10−4 for the model. Recently, a genetic algorithm (GA) or mind evolutionary algorithm (MEA) combined with a BPNN can also be widely use to minimize the total error between experimental data and predictions. Wang et al. [19] used an MEA-BPNN to improve the generalization ability and predictability of BPNN for predicting the height of ocean waves. Karimi et al. [20] used a GA-BPNN to increase the accuracy of proposed density in nanofluids with absolution deviation 0.13% and high correlation coefficient. More researches can be done to establish accurate model to predict thermophysical parameters of nanofluids for engineering application. Esfe et al. [21] conducted ANN optimization combined with NSGA-II algorithm to predict and optimum viscosity and thermal conductivity of Al2O3/ water-EG hybrid nanofluids at maximum temperature. As mentioned above, relevant researches on the thermal conductivity of EG/W hybrid nanofluids are limited. Babu et al. [22] pointed out that base fluids mixed with metallic nanoparticles (high
thermal conductivity but chemically reactive) with metal oxides nanoparticles (good stability but relatively low thermal conductivity) exhibit superior thermophysical and rheological performance. The advantages of Al2O3 nanoparticles are access to production, cheap, stable chemistry and better heat transfer against pumping power [23]. Metal nanoparticles Cu have remarkably high thermal conductivity with 401 W/(m.K) [24]. Hence, a combination of both can achieve excellent performance in hybrid nanofluids. The aim of this paper is to investigate the effect of mixture ratio and temperature on the thermal conductivity of Cu/Al2O3- EG/W hybrid nanofluids. Then, GA-BPNN and MEA-BPNN models are used to increase the accuracy of predicted thermal conductivity values. Finally, comparisons between the empirical correlations and various optimized ANN models are used to predict the thermal conductivity. 2. Materials and methods 2.1. Preparation of hybrid nanofluids In the present study, 20 nm Al2O3 nanoparticles and 50 nm Cu nanoparticles (Beijing DK nano technology Co. LTD, China) were used in the present experiment. 50 wt% Al2O3 and 50 wt% Cu were mixed into base fluids. Hybrid nanofluids were prepared with 1.0 vol% Cu/ Al2O3 nanoparticles with five mixture ratios of base fluids (EG:W): 20:80, 40:60, 50:50, 60:40, and 20:80, where the volume fraction φ can be calculated as follows:
⎡ φ=⎢ ⎢ ⎢ ⎣
() + +( )
w ρ Al O 2 3
()
w ρ Al O 2 3
w ρ Cu
() + +( ) +
w ρ Cu w ρ W
++
() w ρ
⎤ ⎥ ⎥ ⎥ EG ⎦
(1)
where ρ and w are the density (kg/m ) and mass (kg), respectively. 50 g of nanofluids was required to measure the thermal conductivity, so the masses of Al2O3 nanoparticles, Cu nanoparticles, and base fluids were 0.25, 0.25, and 49.5 g by Eq. (1), respectively. Fig. 1. shows the process for preparing Cu/Al2O3 - EG/W hybrid nanofluids by a two-step method. A sensitive electronic balance (ML304T, 0.1 mg, Switzerland) was used to weigh the nanoparticles and base fluids. To obtain stable hybrid nanofluids, the hybrid nanofluids were mixed with a magnetic stirrer for 0.5 h (JK-MSH-HS, China) and the nanofluids were sonicated (CP-3010GTS, China) with power of 400 W at 40 kHz for 0.5 h. 3
2.2. Measurement of thermal conductivity The thermal conductivity of Cu/Al2O3- EG/W hybrid nanofluids with different mixture ratios was measured in the range from 20 to 50 °C using a thermal constant analyzer (Hotdisk TPS2500S, Sweden) in a constant temperature bath. Fig. 2. shows the setup for gathering these measurements using the transient plane source method. Measurements were repeated at least three times and the average value from three measurements was calculated. To reduce the effect of free convection caused by the temperature variations along the sensor, a minimum of 15 min interval time for each data set were selected here [25]. The experimental thermal conductivity data (3% error bar) was compared against Hamid et al.'s data [25] and standard data from ASHRAE [26], as shown in Fig. 3. One can see that the experimental data are consistent with the data obtained from Ref. [25] and ASHRAE [26]. 3. Optimized ANN models 3.1. Standard BPNN A typical BPNN structure consists of input, hidden, and output layers. Of the 49 sets of experimental data, 70% of the data were used for training and the rest were used for testing the model. Input data 2
International Communications in Heat and Mass Transfer 110 (2020) 104444
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Fig. 1. Preparation of hybrid nanofluids.
included mixture ratio of the base fluids R and temperature T. The ANN was designed using the multilayer perceptron algorithm. The prediction is affected by the number of hidden layers and neurons. During each training iteration, a new determined weight and bias were conducted to obtain the minimum error. Thus, the optimum number of hidden layers and neurons was verified in terms of absolute error (AE), coefficient of determination (R2), mean square error (MSE), root mean squared error (RMSE), mean relative percentage error (MRPE), and sum of squared errors (SSE) [27]. These parameters are calculated, respectively, as follows:
MSE =
RMSE =
MRPE =
∑ abs (Pj − Qj
SSE =
)2
(4)
j=1
⎛1 ⎜N ⎝
1/2
N
⎞
∑ (|Pj − Qj |)2⎟ j=1
100% N
⎠
N
Pj − Qj ⎞ ⎟ Pj ⎝ ⎠
∑ ⎛⎜ j=1
(5)
(6)
)2
j=1 N
∑ (Pj )2 j=1
(7)
where N, P, and Q are the number of data, an experimental measurement, and a value predicted with the ANN model. The R2 value closer to 1, and MSE, RMSE, MRPE, and SSE values closer to 0, indicate better consistency between an ANN prediction and an experimental observation [28]. Table 1 shows MSE values for various numbers of hidden layers and
N
∑ (Pj − Qj
∑ (Pj − Qj )2 j=1
(2)
j=1
R2 = 1 −
N
∑ (|Pj − Qj |)2
N
N
AE =
1 N
(3)
Fig. 2. Measurement of thermal conductivity by using Hotdisk TPS2500s. 3
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Fig. 3. Thermal conductivity measurements from base fluids compared with data from the literature (W:EG = 60:40).
Table 1 MSE values for various numbers of neurons and hidden layers with different transfer functions. Number of hidden layers
Number of neurons
Transfer functions
MSE
1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
[3] [3] [3 3] [3 3] [4] [4] [4 4] [4 4] [5] [5] [5 5] [5 5] [6] [6] [6 6] [6 6] [7] [7] [7 7] [7 7]
[tansig] [logsig] [tansig logsig] [logsig tansig] [tansig] [logsig] [tansig logsig] [logsig tansig] [tansig] [logsig] [tansig logsig] [logsig tansig] [tansig] [logsig] [tansig logsig] [logsig tansig] [tansig] [logsig] [tansig logsig] [logsig tansig]
6.6904e-05 8.9818e-05 5.5339e-05 1.0938e-05 1.7569e-05 2.5443e-05 2.4161e-05 1.1368e-05 2.2638e-05 2.604e-05 1.7056e-05 2.3370e-05 3.7594e-05 3.0611e-05 8.5969e-05 1.2192e-05 3.1102e-05 2.6618e-05 3.5957e-05 5.1415e-05
Fig. 4. MSE values for various neurons number in two hidden layers.
layer could produce better results. However, the error of two hidden layers with 4 and 8 neurons number is already extremely low. 3.2. Optimization of BPNN models 3.2.1. Hybrid model 1: GA-BPNN This model was improved using a new genetic algorithm based on BPNN. The training starts with a genetic algorithm, which aim to globally search on the weights range and refine an initial random set of weights to obtain a better estimate. So, the progress of training and refining the solution in BPNN can be improved by GA to approach the optimum outputs. GA-BPNN can be located global optima in a hybrid nanofluid system. The elements of a GA-BPNN include population initialization, selecting a fitness function, population selection, crossover, and mutation. The individual fitness is determined by the absolute error (AE) between the predicted thermal conductivity and the experimental thermal conductivity. Selection is based on the fitness ratio. Crossover operations are interleaved by real number encoding. Mutation operations occur with a certain low probability. Selection, crossover, and mutation operators are used to construct solutions with better fit to the experimental data. More details regarding selection, crossover, and mutation can be found in Ref. [30]. The training stage starts with a genetic algorithm in the GA-BPNN as follows. First, the GA-BPNN is designed to determine the length of the genetic algorithm, and an initial population is chosen randomly. Each individual contains all weights and thresholds from the two-hidden-layer neural network, which determines the neural network structure. Second, the genetic algorithm is used to optimize the weight and bias of the BPNN. Third, the optimized weights and bias are passed to the BPNN to predict thermal conductivity. The GA-BPNN optimization algorithm is represented in Fig. 6. The layer structure of the BPNN was designed to be 2–4–8-1 with 48 weights and 13 thresholds, so the individual coding length of the genetic algorithm is designed to be 61. The population size was initialized to 30, the number of selections was initialized to 40, the crossover probability was initialized to 0.4, and the mutation probability was initialized to 0.1.
the neurons number in each hidden layer. With increasing the neurons number, values of MSE decrease up to an optimum neurons number both for a single hidden layer and two hidden layers, then increase again. The MSE values for models with two hidden layers are always smaller than for a single hidden layer. Therefore, the optimum result is two hidden layers. The tansig, logsig, and purelin functions were used as transfer functions in various layers. Next, the neurons number was determined based on the results in Table 1. Fig. 4 shows MSE values for various neurons number used in two hidden layers. Moya-Rico et al. [29] presented training algorithm using Bayesian regulation, where it was found that 20 training iterations produced the best results. A similar method was used here to determine the neurons number in each hidden layer. As can be seen in Fig. 4, the neurons number in the first and second layer is 4 and 8, respectively. Therefore, the optimum BPNN configuration with the lowest MSE error is a 2–4–8-1 configuration. Therefore, the optimal ANN configuration of thermal conductivity consists of an input layer, two hidden layers, and an output layer, as shown in Fig. 5. This can be used to predict the thermal conductivity of Cu/Al2O3- EG/W hybrid nanofluids. From Fig. 5, the temperature T and the mixture ratio R are used as the input layer, and the thermal conductivity knf is used as the output layer. More hidden layers and different neurons number in each
3.2.2. Hybrid model 2: MEA-BPNN Because an MEA is inspired by genetic algorithms, some of its terms and inherent definitions are basically the same as those used in genetic 4
International Communications in Heat and Mass Transfer 110 (2020) 104444
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Fig. 5. Schematic of a BP-ANN model for predicting the thermal conductivity of Cu/Al2O3-W/EG hybrid nanofluids.
process is recorded in the temporary subgroup. Here, five members were contained in the superior and temporary subpopulations. If all subgroups of the superior subgroup are mature (i.e., their scores stop increasing) and there are no better individuals near each subgroup, the convergence operation will not be needed. However, if the highest scores of the temporary subgroups are lower than those of any subgroups, dissimilation is not required and the system reaches a global optimal value [26]. The MEA-BPNN optimization algorithm is shown in Fig. 7.
algorithms. The MEA-BPNN can improve the generalization ability and predictability of a BPNN and GA-BPNN while avoiding premature convergence. In this experiment, an MEA-BPNN was used to optimize the weight and thresholds of the BPNN in each hidden layer. All individuals in each generation of a group used an iterative algorithm for training. Subgroups can be divided into superior groups and temporary groups. In the process of global competition, data for the superior individual is recorded in the superior subgroup, and data from the competitive
Fig. 6. Flow chart showing the GA-BPNN. 5
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Fig. 7. Flow chart showing the MEA-BPNN.
Fig. 9. Experimental thermal conductivity data fit to Eq. (8).
Fig. 8. Thermal conductivity versus mixture ratio at different temperatures.
4.1. Analysis of experimental thermal conductivity
4. Results and discussion
Fig. 8 shows variations in thermal conductivity of Cu/Al2O3- EG/W hybrid nanofluids with different mixture ratios at different temperatures. One can see that at a certain temperature, the thermal conductivity increases nonlinearly as the ratio of water to ethylene glycol increases. From mixture ratios of 20:80 to 80:20, the thermal conductivity is decreased from 0.5423 to 0.3267 W/(m.K) at the temperature of 30 °C. This is because the thermal conductivity of water is higher than that of ethylene glycol. These results are consistent with data from SiO2-EG/W hybrid nanofluids and CuO/SiO2-EG/W hybrid nanofluids [31,32]. Fig. 8 also shows that the thermal conductivity also increases
In this section, the variation of thermal conductivity was experimentally investigated as functions of temperature and mixture. Based on the experimental data and change rule, Binary Polynomial Regression (BPR) was fit first. Then, two optimized models (GA-BPNN and MEA-BPNN) adopt 2–4–8-1 BPNN configuration. Although the strategy of MEA-BPNN is similar to GA-BPNN, the main aim is to compare the predicted accuracy of the results. Finally, compared with predicted thermal conductivity obtained from BPR and various ANNs, the BPNN with evolutionary algorithm shows better accuracy.
6
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Polynomial regression was used to analyze the experimental data for the thermal conductivity of the Cu/Al2O3- EG/W hybrid nanofluids. The mixture ratio of the base fluid R and temperature T were used as independent variables, and the dependent variable was thermal conductivity knf. Therefore, the experimental thermal conductivity of the Cu/Al2O3- EG/W hybrid nanofluids can be fit to the following polynomial model using Binary Polynomial Regression (BPR):
k nf = 0.2753 + 0.1528R + 3.32687 × 10−4T + 0.1631 R2 + 1.63 × 10−3RT + 6.2389 × 10‐7T 2
(8)
Conditions: Volume fraction of 1.0%, mixture ratios range from 20:80 to 80:20 and at temperature of 20–50 °C. Fig. 9 shows the thermal conductivity modeled as a function of mixture ratio and temperature. Circular scatter points and the threedimensional surface indicate experimental and predicted data, respectively. As seen, most of the experimental data is distributed on the three-dimensional surface obtained from BPR, while others are outside. The values of RMSE, MRPE, SSE and R2 are 0.0107, 2.6213%, 0.001 and 0.9984, showing agreement with the predicted data.
Fig. 10. Fitness value of the genetic algorithm versus iteration number.
nonlinearly as temperature increases. For example, the thermal conductivity rises markedly from 7% to 11.81% when the temperature and mixture ratios ranging from 20 to 50 °C and 80:20 to 20:80, respectively. Moreover, at higher temperature, the thermal conductivity increases significantly because the collision frequency between liquid molecules and solid nanoparticles intensifies. Thus, thermal conductivity increases with the increase in temperature. Satti et al. [33] pointed out that such a phenomenon in nanofluids is more beneficial at higher temperature, especially in a waste heat recovery system.
4.2. Optimization results of GA-BPNN During the process of the genetic algorithm, using 45 generations to evolve and optimized the individual fitness. Fig. 10. shows the fitness value of the results from the genetic algorithm (the sum of the absolute values of the error between the predicted output and the expected
Fig. 11. Thermal conductivity predicted with the GA-BPNN. 7
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J. Wang, et al.
Fig. 12. Similartaxis and dissimilation operations. (a) Similartaxis process for the initial superior subgroups, (b) initial temporary subgroups, (c) superior subgroups after dissimilation, and (d) temporary subgroups after dissimilation.
output) as a function of iteration number. As shown, the fitness value gradually converges to its minimum (0.3623) value after the 21st generation and finally stops. This is because the fitness value has no change after 21st generation. Therefore, 0.3623 is considered as the best fitness value. The BPNN was trained by the optimal results of the initial weights and thresholds, and the result shows the prediction is greatly consistent after repeated training. Fig. 11 shows the thermal conductivity predicted using the GABPNN compared to data obtained from experiments. One can clearly see that the data follows a straight line with slope equal to line Y = T, which indicates that GA-BPNN can be used to predict knf with high precision. From Fig. 11, after GA optimizes the weight and thresholds of BPNN, the R2 can reach 0.99953, which indicates the prediction accuracy significantly improves.
is the same as that used in the GA. The population size of the MEA was set to 200. The similartaxis and dissimilation processes for the initial and subpopulations of the MEA-BPNN are shown in Fig. 12. Fig. 12 (a) shows that each subpopulation has matured (i.e., scores no longer increase) after several similartaxis repetitions. Similartaxis was not applied to subgroup 4 as there was no optimal individual in this subgroup, so its score does not change. By comparing Fig. 12 (a) and (b), one can see that temporary subgroups 1, 2, and 3 have higher scores than superior subgroup 3, subgroup 4, and subgroup 5, so dissimilation should be performed three times and three new subgroups should be added to the temporary subgroups. Fig. 12 (c) and (d) depict the similartaxis process of initial superior and temporary subgroups after dissimilation operation. As shown in Fig. 12 (c), each subgroup has already mature with no better individuals around it. So, the dissimilation operation is no need to perform. By comparing Fig. 12 (c) and (d), each superior subgroup has a higher scores than the temporary subgroup, which indicates that they are in the global billboard. The scores of the subgroups with the highest
4.3. Optimization of MEA-BPNN The MEA was used to optimize the weights and thresholds of the BPNN before training. The code length of the MEA was set to 61, which 8
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Fig. 13. Thermal conductivity predicted with the MEA-BPNN. Table 2 Performance indicators for the various prediction models. Prediction model
RMSE
MRPE(%)
SSE
R2
BPR BPNN GA-BPNN MEA-BPNN
0.0107 0.0035 0.0034 0.0031
2.6213 0.7998 0.772 0.6293
0.0010 1.0869e-04 1.0121e-04 8.8078e-05
0.9984 0.9990 0.9995 0.9997
optimal initial weight and threshold of the BPNN. Fig. 13 shows the thermal conductivity predicted using MEA-BPNN versus compared with the experimental data at the three stages of training, verification and testing. Weights and thresholds were optimized using MEA, and these were used to train the BPNN. The predicted and experimental values are correlated with R2 = 0.99953. When the R2 results in Figs. 11 and 13 are compared, one can see that the outcomes can be also to predicate in suitable range of the inputs if BPNN is developed and optimized. Moreover, the accuracy of the MEA-BPNN is better than that of the GA-BPNN. Fig. 14. Comparison of thermal conductivity predicted with different ANNs.
4.4. Comparison of predictions from the ANN models
score among the temporary subgroups are lower than the scores of any subgroups in the superior subgroup, and the system reaches the global optimal value without performing dissimilation operation. Finally, the optimal individual is decoded according to the coding rule, yielding the
Fig. 14 shows a comparison of the experimental and predicted thermal conductivity, where predictions were generated using Eq. (8) and the ANNs. As shown in Figs. 14, 7 sets of data were used to validate 9
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focused on the preparation of stable nanofluids. The fifth author: Hua Wang. Prof. Wang is another tutor. He directed some parts of the experiments.
the predicted thermal conductivity with different prediction models. The predicted results of BPR show a significant deviation with experimental data. After optimizing BPNN with evolutionary algorithm, these optimal ANNs yield accurate predictions, but data from the MEA-BPNN is closer to the experimental data. This reason is that similartaxis and dissimilation operations can find a better individual than before. Table 2 shows various evaluation indicators for the different models. The predicted results were evaluated using RMSE, MRPE, SSE, and R2 values, the sequence of prediction accuracy of thermal conductivity follows by MEA-BPNN, GA-BPNN, BPNN and BPR. As seen, the predicted values obtained from ANN are more accurate than that from BPR. This indicates that ANN is a useful tool to predicate thermal properties for thermal engineering applications. The margin of deviation between ANN and BPR is calculated as below,
MOD (%) =
Declaration of Competing Interest None. Acknowledgments This project is supported by the National Natural Science Foundation of China (No. 51806090, 51666006). References
PANN ‐PBPR × 100 PANN
(9)
[1] H.W. Xian, N.A.C. Sidik, R. Saidur, Impact of different surfactants and ultrasonication time on the stability and thermophysical properties of hybrid nanofluids, Int. Commun. Heat Mass Transf. 110 (2020) 104389. [2] Z. Fergani, D. Touil, T. Morosuk, Multi-criteria exergy based optimization of an organic Rankine cycle for waste heat recovery in the cement industry, Energy Convers. Manag. 112 (2016) 81–90. [3] V.L. Le, M. Feidt, A. Kheiri, et al., Performance optimization of low-temperature power generation by supercritical ORCs (organic Rankine cycles) using low GWP (global warming potential) working fluids, Energy 67 (2014) 513–526. [4] M. Gupta, V. Singh, R. Kumar, et al., A review on thermophysical properties of nanofluids and heat transfer applications, Renew. Sust. Energ. Rev. 74 (2017) 638–670. [5] D.D. Kumar, A.V. Arasu, A comprehensive review of preparation, characterization, properties and stability of hybrid nanofluids, Renew. Sust. Energ. Rev. 81 (2018) 1669–1689. [6] P. Selvakumar, S. Suresh, Use of Al2O3-Cu/water hybrid nanofluid in an electronic heat sink, IEEE Trans. Compon. Pack. Manuf. Technol. 2 (2012) 1600–1607. [7] A.S. Dalkılıç, G. Yalçın, B.O. Küçükyıldırım, et al., Experimental study on the thermal conductivity of water-based CNT-SiO2 hybrid nanofluids, Int. Commun. Heat Mass Transf. 99 (2018) 18–25. [8] K. Özdemir, E. Ögüt, Hydro-thermal behavior determination and optimization of fully developed turbulent flow in horizontal concentric annulus with ethylene glycol and water mixture based Al2O3 nanofluids, Int. Commun. Heat Mass Transf. 109 (2019) 104346. [9] E.B.M. Sidi, C.T. Nguyen, N. Galanis, et al., Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension, Int.J. Numer. Meth. Heat Fluid Flow 16 (2006) 275–292. [10] H.W. Chiam, W.H. Azmi, N.A. Usri, et al., Thermal conductivity and viscosity of Al2O3 nanofluids for different based ratio of water and ethylene glycol mixture, Exp. Thermal Fluid Sci. 81 (2017) 420–429. [11] H. Eshgarf, N. Sina, M.H. Esfe, et al., Prediction of rheological behavior of MWCNTs-SiO2/EG-water non-Newtonian hybrid nanofluid by desighning new corrlations and optimial artificial neural networks, J. Therm. Anal. Calorim. 132 (2018) 1029–1038. [12] D. Lee, J.W. Kim, B.G. Kim, A new parameter to control heat transport in nanofluids: surface charge state of the particle in suspension, J. Phys. Chem. B 110 (2006) 4323–4328. [13] B. Takabi, S. Salehi, Augmentation of the heat transfer performance of a sinusoidal corrugated enclosure by employing hybrid nanofluid, Adv. Mech. Eng. (2014) 147059. [14] J.D. Moya-Rico, A.E. Molina, J.F. Belmonte, et al., Almendros-Ibáñez, characterization of a triple concentric-tube heat exchanger with corrugated tubes using Artificial Neural Networks (ANN), Appl. Therm. Eng. 147 (2019) 1036–1046. [15] X. Xiang, Y. Fan, A. Fan, et al., Cooling performance optimization of liquid alloys GaIny in microchannel heat sinks based on back-propagation article neural network, Appl. Therm. Eng. 127 (2017) 1143–1151. [16] H. Maddah, M. Ghazvini, M.H. Ahmadi, Predicting the efficiency of CuO/Water nanofluid in heat pipe heat exchanger using neural network, Int. Commun. Heat Mass Transf. 104 (2019) 33–40. [17] F. Selimefendigil, H.F. Öztop, Numerical analysis and ANFIS modeling for mixed convection of CNT-water nanofluid filled branching channel with an annulus and a rotating inner surface at the junction, Int. J. Heat Mass Transf. 127 (2018) 583–599. [18] M.H. Ahmadi, M.A. Ahmadi, M.A. Nazari, et al., A proposed model to predict thermal conductivity ratio of Al2O3/EG nanofluid by applying least squares support vector machine (LSSVM) and genetic algorithm as a connectionist approach, J. Therm. Anal. Calorim. 135 (2019) 271–281. [19] W.X. Wang, R.C. Tang, C. Li, et al., A BP neural network model optimized by mind evolutionary algorithm for prediction the ocean wave heights, Ocean Eng. 162 (2018) 98–107. [20] H. Karimi, F. Yousefi, Application of artificial neural network-genetic algorithm (ANN-GA) to correlation of density in nanofluids, Fluid Phase Equilib. 226 (2012) 79–83. [21] M.H. Esfe, P. Razi, M.H. Hajmohammad, et al., Optimization, modeling and accurate prediction of thermal conductivity and dynamic viscosity of stabilized ethylene glycol and water mixture, Int. Commun. Heat Mass Transf. 82 (2017) 154–160.
2
Calculated by Eq. (9), the margin of deviation of R among various ANNs, such as BPNN and BPR, GA-BPNN and BPR, MEA-BPNN and BPR, decreases by 0.06%, 0.11% and 0.13%, respectively. Thus, this table clearly shows the MEA-BPNN provides the most accurate estimate of thermal conductivity for Cu/Al2O3- EG/W hybrid nanofluids in the relevant experimental conditions. 5. Conclusions Due to the characteristic of EG/W hybrid nanofluids vary with the composition of the mixture, Cu/Al2O3-EG/W hybrid nanofluids with different mixture ratio of base fluid were prepared by using a two-step method. Experiments were conducted with 1.0 wt% Cu/Al2O3- EG/W hybrid nanofluids at temperatures ranging from 20 to 50 °C and base fluid mixture ratio varying from 20:80 to 80:20. A GA-BPNN and MEABPNN were developed based on BPNN to improve the generalization and the accuracy of proposed models. The temperature and mixing ratio of base fluid were used as the input layer, and the thermal conductivity was the output layer. Those proposed models can be used to calculate thermal conductivity as a function of temperature and the mixture ratio of base fluid. Some main conclusions have been drawn as follows. (1) The thermal conductivity increases nonlinearly as temperature and the mixture ratio of base fluid increases. Moreover, the increment of thermal conductivity increases more significantly at higher temperature due to the stronger collision frequency between liquid molecules and nanoparticles. Based on the experimental data and change rule, the BPR was fit and R2 is equal to 0.9984. (2) Compared with BPR, the margin of deviation of R2 for BPNN, GABPNN and MEA-BPNN increases by 0.06%, 0.11% and 0.13%. This indicates that the BPNN combined with GA or MEA are presented to obtain more accurate results than single BPNN. Moreover, the MEABPNN is found to provide the best performance for prediction, with R2, RMSE, MRPE (%), and SSE equal to 0.9997, 0.0031, 0.6293, and 8.8078 e-05, respectively. Author contributions section There are five authors in this paper. The contributions of each other are listed as below. The first author: Jiang Wang. Dr. Wang provided the original idea of this paper, established the ANN model and wrote parts of manuscript. The second and corresponding author: Yuling Zhai. Prof. Zhai is the tutor of Jiang Wang, Peitao Yao and Mingyan Ma. She supervised them to write and revise the manuscript. The third and fourth authors: Peitao Yao and Mingyan Ma. Both of them prepared and conducted the experiments. Dr. Yao focused on the measurement of thermal conductivity, and Dr. Ma 10
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[22] J.A.R. Babu, K.K. Kumar, S.S. Rao, State-of- art review on hybrid nanofluids, Renew. Sust. Energ. Rev. 77 (2017) 551–565. [23] V. Kumar, J. Sarkar, Experimental hydrothermal behavior of hybrid nanofluid for various particles ratio and compassion with other fluids in minichannel heat sink, Int. Commun. Heat Mass Transf. 110 (2020) 104397. [24] K.Y. Leong, I. Razali, K.Z.K. Ahmad, et al., Thermal conductivity of an ethylene glycol/water-based nanofluid with copper-titanium dioxide nanoparticles: an experimental approach, Int. Commun. Heat Mass Transf. 90 (2018) 23–28. [25] K.A. Hamid, W.H. Azmi, M.F. Nabil, et al., Experimental investigation of thermal conductivity and dynamic viscosity on nanoparticle mixture ratios of TiO2-SiO2 nanofluids, Int. J. Heat Mass Transf. 116 (2018) 1143–1152. [26] W.E. Library, American society of heating, refrigerating and air-conditioning engineers, Int. J. Refrig. 2 (2012) 56–57. [27] M.H. Esfe, A.A.A. Arani, An experimental determination and accurate prediction of dynamic viscosity of MWCNT (%40)-SiO2 (%60)/5W50 nano-lubricant, J. Mol. Liq. 59 (2018) 227–237. [28] H. Rostamian, M.N. Lotfollahi, New fuctionlity for energy parameter of Redlich-
[29]
[30] [31]
[32]
[33]
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Kwong equation of state for density calculation of pure carbon dioxide and ethane in liquid, vapor and supercritical phases, period, Polytech. Chem. Eng. 60 (2016) 93. J.D. Moya-Rico, A.E. Molina, J.F. Belmonte, et al., Characterization of a triple concentric-tube heat exchanger with corrugated tubes using Artificial Neural Network (ANN), Appl. Therm, Eng. 49 (2019) 1036–1046. S.A. Kalogirou, Applications of artificial neural-networks for energy systems, Appl. Energy 67 (2000) 17–35. Y.F. Guo, T.T. Zhang, D.G. Zhang, et al., Experimental investigation of thermal and electrical conductivity of silicon oxide nanofluids in ethylene glycol water mixture, Int. J. Heat Mass Transf. 117 (2018) 280–286. K.Y. Leong, I. Razali, K.Z.K. Ahmad, et al., Thermal conductivity of an ethylene glycol water-based nanofluid with copper-titanium dioxide nanoparticles: an experimental approach, Int. J. Heat Mass Transf. 90 (2018) 23–28. A. Akhgar, D. Toghraie, An experimental study on the stability and thermal conductivity of water-ethylene glycol/TiO2-MWCNTs hybrid nanofluid: developing a new correlation, Powder Technol. 338 (2018) 806–818.
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Established prediction models of thermal conductivity of hybrid nanofluids based on artificial neural network (ANN) models in waste heat system
T
⁎
Jiang Wanga,b, Yuling Zhaia,b, , Peitao Yaoa,b, Mingyan Maa,b, Hua Wanga,b a b
State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Yunnan 650093, China Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Yunnan 650093, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Hybrid nanofluids Thermal conductivity Artificial neural network Genetic algorithm Mind evolutionary algorithm
The properties of water (W)/ethylene glycol (EG) mixtures vary significantly with the proportion of EG and temperature, so it is suitable to use such fluids as exchange heat mediums in a waste heat system with temperature fluctuations. The experiments were conducted with 1.0 wt% Cu/Al2O3- EG/W hybrid nanofluids at temperatures ranging from 20 to 50 °C, where the base fluid (EG/W) mixture ratio was varied from 20:80 to 80:20. To search individuals which contain optimal weights and thresholds, a genetic algorithm (GA) and a mind evolutionary algorithm (MEA) coupled with a back-propagation neural network (GA-BPNN and MEA-BPNN, respectively) were used to improve the accuracy in the predicted thermal conductivity. The results show that the thermal conductivity increases nonlinearly with the ratio of water to ethylene glycol and temperature, due to the higher thermal conductivity of water and stronger collision frequency between molecular and nanoparticles. Binary Polynomial Regression (BPR) was fit with (coefficient of determination) R2 = 0.9984 as functions of temperature and mixture ratio. Comparisons of the prediction performance and capability of BPR, the performance of R2 increases by 0.11% and 0.13% for GA-BPNN and MEA-BPNN. It indicates that the combined BPNNs both predicate more accurately, particularly MEA-BPNN has the highest prediction accuracy.
1. Introduction Given the global energy crisis, more researchers are paying attention to improve overall energy efficiency in a working system [1]. Waste gas or liquid are often produced at high pressure in industrial processes, which contain a large amount of heat or combustible components. For years, many techniques and methods were used to increase utilization of waste heat to maximize energy efficiency and reduce operating cost. In some production processes, most waste heat is released to the environment. For example, in a typical cement plant, approximately 40% of the total energy consumed during cement production is transferred to the environment as waste heat [2]. Le et al. [3] noted that 27.9% of total global final consumption comes from the energy consumption of industrial sectors. Consider an acid production system for example. A large amount of low-temperature waste gas or liquid (nearly 100 °C) is released into the environment during the SO3 and acid cooling processes. In order to recover waste heat, the thermal energy contained in waste gas or liquid can be exchanged with working fluids (e.g., water, ethylene glycol, or a mixture of these fluids), and the Organic Rankine Cycle (ORC) can be used to generate electricity.
However, the temperature of waste gas or liquid varies randomly with the initial amount of gas in the washing tower at the beginning. Therefore, the properties of working fluids should vary with temperature to recover such waste heat. The thermal conductivity, viscosity, specific heat, and density of working fluids are important parameters in determining the pumping power and heat transfer coefficient in cooling or heating systems. Among the various thermophysical properties of nanofluids, the thermal conductivity is one of the most important thermophysical parameters that significantly affect heat exchange. Conventional working fluids like water (W), oils, or ethylene glycol (EG) have poor thermal properties compared to metals or metal oxides [4]. Hence, the addition of nanoparticles with high thermal conductivity to a base fluid can increase the thermal conductivity of the fluid. Recently, the use of two or more nanoparticles in a base fluid was investigated, known as hybrid nanofluids. Kumar et al. [5] reported that the thermal conductivity enhancement of hybrid nanofluids is better than that of single nanofluids due to new physical and chemical bonds. Selvakumar et al. [6] and Dalkılıç et al. [7] both reported that mixing nanoparticles with high thermal conductivity and chemically inert nanoparticles in a base
⁎ Corresponding author at: State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Yunnan 650093, China. E-mail address: [email protected] (Y. Zhai).
https://doi.org/10.1016/j.icheatmasstransfer.2019.104444
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fluid forms a hybrid nanofluid with higher effective thermal conductivity. The thermal conductivity can also be increased by mixing different types of base fluids. The thermophysical parameters of EG/W hybrid nanofluids vary due to the composition of the mixture. Such special characteristic is beneficial to recovery waste gas or liquid with temperature fluctuation. Özdemir et al. [8] and Maïga et al. [9] found that the thermal conductivity of EG base fluids can be increased by more than that of water. Chiam et al. [10] found that the properties of mixed EG/W base fluids vary significantly with the percentage of EG and temperature. Eshgarf et al. [11] noted that mixtures of EG and water are used in many industries as antifreeze agents in heat exchangers and radiators. The thermal conductivity of hybrid nanofluids is also affected by temperature, volume fraction, and mixture ratio. It is difficult to present a general and accurate thermal conductivity prediction in various conditions. The heat transfer mechanism of nanofluids is difficult to explain in terms of traditional liquid-particle suspension models. Maxwell's thermal conductivity model is applicable to homogeneously dispersed nanofluids with low nanoparticle concentration [12]. A modified Maxwell model for predicting the thermal conductivity of hybrid nanofluids was presented by Takabi et al. [13]. However, these equations do not reflect the relationship between thermal conductivity and mixture ratio in hybrid nanofluids and the aspect of the high cost and time is barrier for engineering applications. Many researchers have proposed empirical models for predicting the thermal conductivity of nanofluids. An artificial neural network (ANN) is a mathematical model that simulates the structure and function of biological neural networks, and it can be used for prediction based on limited experimental data. Due to its huge nonlinear mapping ability, many researchers have used ANNs for modeling and predicting the thermal conductivity of nanofluids [14]. ANN models contain many training algorithms like genetic algorithms, back propagation (BP), evolutionary techniques, and conjugate gradients. Among those, a back propagation neural network (BPNN) is a popular model. Xiang et al. [15] used a BPNN model to predict and optimize the thermophysical properties of liquid Galny in microchannel heat sinks. However, due to its serial search, the BP algorithm can get stuck in a local extremum and it converges slowly in the training stage. The other drawback is that it may exhibit overfitting when a small amount of training data is available [16]. To avoid local minima while achieving global convergence, many other algorithms combined with ANN have been used for better estimation. Selimefendigil et al. [17] combined the ANN with fuzzy logic to accurately predicate the average Nusselt numbers for CNT-water nanofluid filled branching channel with an annulus. Ahmadi et al. [18] first presented least square support vector machine-genetic algorithm (LSSVM-GA) to predict thermal conductivity of Al2O3/EG nanofluids with input variables of size, concentration and temperature. The coefficient of determination (R2) and mean squared error are 0.9902 and 8.64 × 10−4 for the model. Recently, a genetic algorithm (GA) or mind evolutionary algorithm (MEA) combined with a BPNN can also be widely use to minimize the total error between experimental data and predictions. Wang et al. [19] used an MEA-BPNN to improve the generalization ability and predictability of BPNN for predicting the height of ocean waves. Karimi et al. [20] used a GA-BPNN to increase the accuracy of proposed density in nanofluids with absolution deviation 0.13% and high correlation coefficient. More researches can be done to establish accurate model to predict thermophysical parameters of nanofluids for engineering application. Esfe et al. [21] conducted ANN optimization combined with NSGA-II algorithm to predict and optimum viscosity and thermal conductivity of Al2O3/ water-EG hybrid nanofluids at maximum temperature. As mentioned above, relevant researches on the thermal conductivity of EG/W hybrid nanofluids are limited. Babu et al. [22] pointed out that base fluids mixed with metallic nanoparticles (high
thermal conductivity but chemically reactive) with metal oxides nanoparticles (good stability but relatively low thermal conductivity) exhibit superior thermophysical and rheological performance. The advantages of Al2O3 nanoparticles are access to production, cheap, stable chemistry and better heat transfer against pumping power [23]. Metal nanoparticles Cu have remarkably high thermal conductivity with 401 W/(m.K) [24]. Hence, a combination of both can achieve excellent performance in hybrid nanofluids. The aim of this paper is to investigate the effect of mixture ratio and temperature on the thermal conductivity of Cu/Al2O3- EG/W hybrid nanofluids. Then, GA-BPNN and MEA-BPNN models are used to increase the accuracy of predicted thermal conductivity values. Finally, comparisons between the empirical correlations and various optimized ANN models are used to predict the thermal conductivity. 2. Materials and methods 2.1. Preparation of hybrid nanofluids In the present study, 20 nm Al2O3 nanoparticles and 50 nm Cu nanoparticles (Beijing DK nano technology Co. LTD, China) were used in the present experiment. 50 wt% Al2O3 and 50 wt% Cu were mixed into base fluids. Hybrid nanofluids were prepared with 1.0 vol% Cu/ Al2O3 nanoparticles with five mixture ratios of base fluids (EG:W): 20:80, 40:60, 50:50, 60:40, and 20:80, where the volume fraction φ can be calculated as follows:
⎡ φ=⎢ ⎢ ⎢ ⎣
() + +( )
w ρ Al O 2 3
()
w ρ Al O 2 3
w ρ Cu
() + +( ) +
w ρ Cu w ρ W
++
() w ρ
⎤ ⎥ ⎥ ⎥ EG ⎦
(1)
where ρ and w are the density (kg/m ) and mass (kg), respectively. 50 g of nanofluids was required to measure the thermal conductivity, so the masses of Al2O3 nanoparticles, Cu nanoparticles, and base fluids were 0.25, 0.25, and 49.5 g by Eq. (1), respectively. Fig. 1. shows the process for preparing Cu/Al2O3 - EG/W hybrid nanofluids by a two-step method. A sensitive electronic balance (ML304T, 0.1 mg, Switzerland) was used to weigh the nanoparticles and base fluids. To obtain stable hybrid nanofluids, the hybrid nanofluids were mixed with a magnetic stirrer for 0.5 h (JK-MSH-HS, China) and the nanofluids were sonicated (CP-3010GTS, China) with power of 400 W at 40 kHz for 0.5 h. 3
2.2. Measurement of thermal conductivity The thermal conductivity of Cu/Al2O3- EG/W hybrid nanofluids with different mixture ratios was measured in the range from 20 to 50 °C using a thermal constant analyzer (Hotdisk TPS2500S, Sweden) in a constant temperature bath. Fig. 2. shows the setup for gathering these measurements using the transient plane source method. Measurements were repeated at least three times and the average value from three measurements was calculated. To reduce the effect of free convection caused by the temperature variations along the sensor, a minimum of 15 min interval time for each data set were selected here [25]. The experimental thermal conductivity data (3% error bar) was compared against Hamid et al.'s data [25] and standard data from ASHRAE [26], as shown in Fig. 3. One can see that the experimental data are consistent with the data obtained from Ref. [25] and ASHRAE [26]. 3. Optimized ANN models 3.1. Standard BPNN A typical BPNN structure consists of input, hidden, and output layers. Of the 49 sets of experimental data, 70% of the data were used for training and the rest were used for testing the model. Input data 2
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Fig. 1. Preparation of hybrid nanofluids.
included mixture ratio of the base fluids R and temperature T. The ANN was designed using the multilayer perceptron algorithm. The prediction is affected by the number of hidden layers and neurons. During each training iteration, a new determined weight and bias were conducted to obtain the minimum error. Thus, the optimum number of hidden layers and neurons was verified in terms of absolute error (AE), coefficient of determination (R2), mean square error (MSE), root mean squared error (RMSE), mean relative percentage error (MRPE), and sum of squared errors (SSE) [27]. These parameters are calculated, respectively, as follows:
MSE =
RMSE =
MRPE =
∑ abs (Pj − Qj
SSE =
)2
(4)
j=1
⎛1 ⎜N ⎝
1/2
N
⎞
∑ (|Pj − Qj |)2⎟ j=1
100% N
⎠
N
Pj − Qj ⎞ ⎟ Pj ⎝ ⎠
∑ ⎛⎜ j=1
(5)
(6)
)2
j=1 N
∑ (Pj )2 j=1
(7)
where N, P, and Q are the number of data, an experimental measurement, and a value predicted with the ANN model. The R2 value closer to 1, and MSE, RMSE, MRPE, and SSE values closer to 0, indicate better consistency between an ANN prediction and an experimental observation [28]. Table 1 shows MSE values for various numbers of hidden layers and
N
∑ (Pj − Qj
∑ (Pj − Qj )2 j=1
(2)
j=1
R2 = 1 −
N
∑ (|Pj − Qj |)2
N
N
AE =
1 N
(3)
Fig. 2. Measurement of thermal conductivity by using Hotdisk TPS2500s. 3
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Fig. 3. Thermal conductivity measurements from base fluids compared with data from the literature (W:EG = 60:40).
Table 1 MSE values for various numbers of neurons and hidden layers with different transfer functions. Number of hidden layers
Number of neurons
Transfer functions
MSE
1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
[3] [3] [3 3] [3 3] [4] [4] [4 4] [4 4] [5] [5] [5 5] [5 5] [6] [6] [6 6] [6 6] [7] [7] [7 7] [7 7]
[tansig] [logsig] [tansig logsig] [logsig tansig] [tansig] [logsig] [tansig logsig] [logsig tansig] [tansig] [logsig] [tansig logsig] [logsig tansig] [tansig] [logsig] [tansig logsig] [logsig tansig] [tansig] [logsig] [tansig logsig] [logsig tansig]
6.6904e-05 8.9818e-05 5.5339e-05 1.0938e-05 1.7569e-05 2.5443e-05 2.4161e-05 1.1368e-05 2.2638e-05 2.604e-05 1.7056e-05 2.3370e-05 3.7594e-05 3.0611e-05 8.5969e-05 1.2192e-05 3.1102e-05 2.6618e-05 3.5957e-05 5.1415e-05
Fig. 4. MSE values for various neurons number in two hidden layers.
layer could produce better results. However, the error of two hidden layers with 4 and 8 neurons number is already extremely low. 3.2. Optimization of BPNN models 3.2.1. Hybrid model 1: GA-BPNN This model was improved using a new genetic algorithm based on BPNN. The training starts with a genetic algorithm, which aim to globally search on the weights range and refine an initial random set of weights to obtain a better estimate. So, the progress of training and refining the solution in BPNN can be improved by GA to approach the optimum outputs. GA-BPNN can be located global optima in a hybrid nanofluid system. The elements of a GA-BPNN include population initialization, selecting a fitness function, population selection, crossover, and mutation. The individual fitness is determined by the absolute error (AE) between the predicted thermal conductivity and the experimental thermal conductivity. Selection is based on the fitness ratio. Crossover operations are interleaved by real number encoding. Mutation operations occur with a certain low probability. Selection, crossover, and mutation operators are used to construct solutions with better fit to the experimental data. More details regarding selection, crossover, and mutation can be found in Ref. [30]. The training stage starts with a genetic algorithm in the GA-BPNN as follows. First, the GA-BPNN is designed to determine the length of the genetic algorithm, and an initial population is chosen randomly. Each individual contains all weights and thresholds from the two-hidden-layer neural network, which determines the neural network structure. Second, the genetic algorithm is used to optimize the weight and bias of the BPNN. Third, the optimized weights and bias are passed to the BPNN to predict thermal conductivity. The GA-BPNN optimization algorithm is represented in Fig. 6. The layer structure of the BPNN was designed to be 2–4–8-1 with 48 weights and 13 thresholds, so the individual coding length of the genetic algorithm is designed to be 61. The population size was initialized to 30, the number of selections was initialized to 40, the crossover probability was initialized to 0.4, and the mutation probability was initialized to 0.1.
the neurons number in each hidden layer. With increasing the neurons number, values of MSE decrease up to an optimum neurons number both for a single hidden layer and two hidden layers, then increase again. The MSE values for models with two hidden layers are always smaller than for a single hidden layer. Therefore, the optimum result is two hidden layers. The tansig, logsig, and purelin functions were used as transfer functions in various layers. Next, the neurons number was determined based on the results in Table 1. Fig. 4 shows MSE values for various neurons number used in two hidden layers. Moya-Rico et al. [29] presented training algorithm using Bayesian regulation, where it was found that 20 training iterations produced the best results. A similar method was used here to determine the neurons number in each hidden layer. As can be seen in Fig. 4, the neurons number in the first and second layer is 4 and 8, respectively. Therefore, the optimum BPNN configuration with the lowest MSE error is a 2–4–8-1 configuration. Therefore, the optimal ANN configuration of thermal conductivity consists of an input layer, two hidden layers, and an output layer, as shown in Fig. 5. This can be used to predict the thermal conductivity of Cu/Al2O3- EG/W hybrid nanofluids. From Fig. 5, the temperature T and the mixture ratio R are used as the input layer, and the thermal conductivity knf is used as the output layer. More hidden layers and different neurons number in each
3.2.2. Hybrid model 2: MEA-BPNN Because an MEA is inspired by genetic algorithms, some of its terms and inherent definitions are basically the same as those used in genetic 4
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Fig. 5. Schematic of a BP-ANN model for predicting the thermal conductivity of Cu/Al2O3-W/EG hybrid nanofluids.
process is recorded in the temporary subgroup. Here, five members were contained in the superior and temporary subpopulations. If all subgroups of the superior subgroup are mature (i.e., their scores stop increasing) and there are no better individuals near each subgroup, the convergence operation will not be needed. However, if the highest scores of the temporary subgroups are lower than those of any subgroups, dissimilation is not required and the system reaches a global optimal value [26]. The MEA-BPNN optimization algorithm is shown in Fig. 7.
algorithms. The MEA-BPNN can improve the generalization ability and predictability of a BPNN and GA-BPNN while avoiding premature convergence. In this experiment, an MEA-BPNN was used to optimize the weight and thresholds of the BPNN in each hidden layer. All individuals in each generation of a group used an iterative algorithm for training. Subgroups can be divided into superior groups and temporary groups. In the process of global competition, data for the superior individual is recorded in the superior subgroup, and data from the competitive
Fig. 6. Flow chart showing the GA-BPNN. 5
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Fig. 7. Flow chart showing the MEA-BPNN.
Fig. 9. Experimental thermal conductivity data fit to Eq. (8).
Fig. 8. Thermal conductivity versus mixture ratio at different temperatures.
4.1. Analysis of experimental thermal conductivity
4. Results and discussion
Fig. 8 shows variations in thermal conductivity of Cu/Al2O3- EG/W hybrid nanofluids with different mixture ratios at different temperatures. One can see that at a certain temperature, the thermal conductivity increases nonlinearly as the ratio of water to ethylene glycol increases. From mixture ratios of 20:80 to 80:20, the thermal conductivity is decreased from 0.5423 to 0.3267 W/(m.K) at the temperature of 30 °C. This is because the thermal conductivity of water is higher than that of ethylene glycol. These results are consistent with data from SiO2-EG/W hybrid nanofluids and CuO/SiO2-EG/W hybrid nanofluids [31,32]. Fig. 8 also shows that the thermal conductivity also increases
In this section, the variation of thermal conductivity was experimentally investigated as functions of temperature and mixture. Based on the experimental data and change rule, Binary Polynomial Regression (BPR) was fit first. Then, two optimized models (GA-BPNN and MEA-BPNN) adopt 2–4–8-1 BPNN configuration. Although the strategy of MEA-BPNN is similar to GA-BPNN, the main aim is to compare the predicted accuracy of the results. Finally, compared with predicted thermal conductivity obtained from BPR and various ANNs, the BPNN with evolutionary algorithm shows better accuracy.
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Polynomial regression was used to analyze the experimental data for the thermal conductivity of the Cu/Al2O3- EG/W hybrid nanofluids. The mixture ratio of the base fluid R and temperature T were used as independent variables, and the dependent variable was thermal conductivity knf. Therefore, the experimental thermal conductivity of the Cu/Al2O3- EG/W hybrid nanofluids can be fit to the following polynomial model using Binary Polynomial Regression (BPR):
k nf = 0.2753 + 0.1528R + 3.32687 × 10−4T + 0.1631 R2 + 1.63 × 10−3RT + 6.2389 × 10‐7T 2
(8)
Conditions: Volume fraction of 1.0%, mixture ratios range from 20:80 to 80:20 and at temperature of 20–50 °C. Fig. 9 shows the thermal conductivity modeled as a function of mixture ratio and temperature. Circular scatter points and the threedimensional surface indicate experimental and predicted data, respectively. As seen, most of the experimental data is distributed on the three-dimensional surface obtained from BPR, while others are outside. The values of RMSE, MRPE, SSE and R2 are 0.0107, 2.6213%, 0.001 and 0.9984, showing agreement with the predicted data.
Fig. 10. Fitness value of the genetic algorithm versus iteration number.
nonlinearly as temperature increases. For example, the thermal conductivity rises markedly from 7% to 11.81% when the temperature and mixture ratios ranging from 20 to 50 °C and 80:20 to 20:80, respectively. Moreover, at higher temperature, the thermal conductivity increases significantly because the collision frequency between liquid molecules and solid nanoparticles intensifies. Thus, thermal conductivity increases with the increase in temperature. Satti et al. [33] pointed out that such a phenomenon in nanofluids is more beneficial at higher temperature, especially in a waste heat recovery system.
4.2. Optimization results of GA-BPNN During the process of the genetic algorithm, using 45 generations to evolve and optimized the individual fitness. Fig. 10. shows the fitness value of the results from the genetic algorithm (the sum of the absolute values of the error between the predicted output and the expected
Fig. 11. Thermal conductivity predicted with the GA-BPNN. 7
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Fig. 12. Similartaxis and dissimilation operations. (a) Similartaxis process for the initial superior subgroups, (b) initial temporary subgroups, (c) superior subgroups after dissimilation, and (d) temporary subgroups after dissimilation.
output) as a function of iteration number. As shown, the fitness value gradually converges to its minimum (0.3623) value after the 21st generation and finally stops. This is because the fitness value has no change after 21st generation. Therefore, 0.3623 is considered as the best fitness value. The BPNN was trained by the optimal results of the initial weights and thresholds, and the result shows the prediction is greatly consistent after repeated training. Fig. 11 shows the thermal conductivity predicted using the GABPNN compared to data obtained from experiments. One can clearly see that the data follows a straight line with slope equal to line Y = T, which indicates that GA-BPNN can be used to predict knf with high precision. From Fig. 11, after GA optimizes the weight and thresholds of BPNN, the R2 can reach 0.99953, which indicates the prediction accuracy significantly improves.
is the same as that used in the GA. The population size of the MEA was set to 200. The similartaxis and dissimilation processes for the initial and subpopulations of the MEA-BPNN are shown in Fig. 12. Fig. 12 (a) shows that each subpopulation has matured (i.e., scores no longer increase) after several similartaxis repetitions. Similartaxis was not applied to subgroup 4 as there was no optimal individual in this subgroup, so its score does not change. By comparing Fig. 12 (a) and (b), one can see that temporary subgroups 1, 2, and 3 have higher scores than superior subgroup 3, subgroup 4, and subgroup 5, so dissimilation should be performed three times and three new subgroups should be added to the temporary subgroups. Fig. 12 (c) and (d) depict the similartaxis process of initial superior and temporary subgroups after dissimilation operation. As shown in Fig. 12 (c), each subgroup has already mature with no better individuals around it. So, the dissimilation operation is no need to perform. By comparing Fig. 12 (c) and (d), each superior subgroup has a higher scores than the temporary subgroup, which indicates that they are in the global billboard. The scores of the subgroups with the highest
4.3. Optimization of MEA-BPNN The MEA was used to optimize the weights and thresholds of the BPNN before training. The code length of the MEA was set to 61, which 8
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Fig. 13. Thermal conductivity predicted with the MEA-BPNN. Table 2 Performance indicators for the various prediction models. Prediction model
RMSE
MRPE(%)
SSE
R2
BPR BPNN GA-BPNN MEA-BPNN
0.0107 0.0035 0.0034 0.0031
2.6213 0.7998 0.772 0.6293
0.0010 1.0869e-04 1.0121e-04 8.8078e-05
0.9984 0.9990 0.9995 0.9997
optimal initial weight and threshold of the BPNN. Fig. 13 shows the thermal conductivity predicted using MEA-BPNN versus compared with the experimental data at the three stages of training, verification and testing. Weights and thresholds were optimized using MEA, and these were used to train the BPNN. The predicted and experimental values are correlated with R2 = 0.99953. When the R2 results in Figs. 11 and 13 are compared, one can see that the outcomes can be also to predicate in suitable range of the inputs if BPNN is developed and optimized. Moreover, the accuracy of the MEA-BPNN is better than that of the GA-BPNN. Fig. 14. Comparison of thermal conductivity predicted with different ANNs.
4.4. Comparison of predictions from the ANN models
score among the temporary subgroups are lower than the scores of any subgroups in the superior subgroup, and the system reaches the global optimal value without performing dissimilation operation. Finally, the optimal individual is decoded according to the coding rule, yielding the
Fig. 14 shows a comparison of the experimental and predicted thermal conductivity, where predictions were generated using Eq. (8) and the ANNs. As shown in Figs. 14, 7 sets of data were used to validate 9
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focused on the preparation of stable nanofluids. The fifth author: Hua Wang. Prof. Wang is another tutor. He directed some parts of the experiments.
the predicted thermal conductivity with different prediction models. The predicted results of BPR show a significant deviation with experimental data. After optimizing BPNN with evolutionary algorithm, these optimal ANNs yield accurate predictions, but data from the MEA-BPNN is closer to the experimental data. This reason is that similartaxis and dissimilation operations can find a better individual than before. Table 2 shows various evaluation indicators for the different models. The predicted results were evaluated using RMSE, MRPE, SSE, and R2 values, the sequence of prediction accuracy of thermal conductivity follows by MEA-BPNN, GA-BPNN, BPNN and BPR. As seen, the predicted values obtained from ANN are more accurate than that from BPR. This indicates that ANN is a useful tool to predicate thermal properties for thermal engineering applications. The margin of deviation between ANN and BPR is calculated as below,
MOD (%) =
Declaration of Competing Interest None. Acknowledgments This project is supported by the National Natural Science Foundation of China (No. 51806090, 51666006). References
PANN ‐PBPR × 100 PANN
(9)
[1] H.W. Xian, N.A.C. Sidik, R. Saidur, Impact of different surfactants and ultrasonication time on the stability and thermophysical properties of hybrid nanofluids, Int. Commun. Heat Mass Transf. 110 (2020) 104389. [2] Z. Fergani, D. Touil, T. Morosuk, Multi-criteria exergy based optimization of an organic Rankine cycle for waste heat recovery in the cement industry, Energy Convers. Manag. 112 (2016) 81–90. [3] V.L. Le, M. Feidt, A. Kheiri, et al., Performance optimization of low-temperature power generation by supercritical ORCs (organic Rankine cycles) using low GWP (global warming potential) working fluids, Energy 67 (2014) 513–526. [4] M. Gupta, V. Singh, R. Kumar, et al., A review on thermophysical properties of nanofluids and heat transfer applications, Renew. Sust. Energ. Rev. 74 (2017) 638–670. [5] D.D. Kumar, A.V. Arasu, A comprehensive review of preparation, characterization, properties and stability of hybrid nanofluids, Renew. Sust. Energ. Rev. 81 (2018) 1669–1689. [6] P. Selvakumar, S. Suresh, Use of Al2O3-Cu/water hybrid nanofluid in an electronic heat sink, IEEE Trans. Compon. Pack. Manuf. Technol. 2 (2012) 1600–1607. [7] A.S. Dalkılıç, G. Yalçın, B.O. Küçükyıldırım, et al., Experimental study on the thermal conductivity of water-based CNT-SiO2 hybrid nanofluids, Int. Commun. Heat Mass Transf. 99 (2018) 18–25. [8] K. Özdemir, E. Ögüt, Hydro-thermal behavior determination and optimization of fully developed turbulent flow in horizontal concentric annulus with ethylene glycol and water mixture based Al2O3 nanofluids, Int. Commun. Heat Mass Transf. 109 (2019) 104346. [9] E.B.M. Sidi, C.T. Nguyen, N. Galanis, et al., Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension, Int.J. Numer. Meth. Heat Fluid Flow 16 (2006) 275–292. [10] H.W. Chiam, W.H. Azmi, N.A. Usri, et al., Thermal conductivity and viscosity of Al2O3 nanofluids for different based ratio of water and ethylene glycol mixture, Exp. Thermal Fluid Sci. 81 (2017) 420–429. [11] H. Eshgarf, N. Sina, M.H. Esfe, et al., Prediction of rheological behavior of MWCNTs-SiO2/EG-water non-Newtonian hybrid nanofluid by desighning new corrlations and optimial artificial neural networks, J. Therm. Anal. Calorim. 132 (2018) 1029–1038. [12] D. Lee, J.W. Kim, B.G. Kim, A new parameter to control heat transport in nanofluids: surface charge state of the particle in suspension, J. Phys. Chem. B 110 (2006) 4323–4328. [13] B. Takabi, S. Salehi, Augmentation of the heat transfer performance of a sinusoidal corrugated enclosure by employing hybrid nanofluid, Adv. Mech. Eng. (2014) 147059. [14] J.D. Moya-Rico, A.E. Molina, J.F. Belmonte, et al., Almendros-Ibáñez, characterization of a triple concentric-tube heat exchanger with corrugated tubes using Artificial Neural Networks (ANN), Appl. Therm. Eng. 147 (2019) 1036–1046. [15] X. Xiang, Y. Fan, A. Fan, et al., Cooling performance optimization of liquid alloys GaIny in microchannel heat sinks based on back-propagation article neural network, Appl. Therm. Eng. 127 (2017) 1143–1151. [16] H. Maddah, M. Ghazvini, M.H. Ahmadi, Predicting the efficiency of CuO/Water nanofluid in heat pipe heat exchanger using neural network, Int. Commun. Heat Mass Transf. 104 (2019) 33–40. [17] F. Selimefendigil, H.F. Öztop, Numerical analysis and ANFIS modeling for mixed convection of CNT-water nanofluid filled branching channel with an annulus and a rotating inner surface at the junction, Int. J. Heat Mass Transf. 127 (2018) 583–599. [18] M.H. Ahmadi, M.A. Ahmadi, M.A. Nazari, et al., A proposed model to predict thermal conductivity ratio of Al2O3/EG nanofluid by applying least squares support vector machine (LSSVM) and genetic algorithm as a connectionist approach, J. Therm. Anal. Calorim. 135 (2019) 271–281. [19] W.X. Wang, R.C. Tang, C. Li, et al., A BP neural network model optimized by mind evolutionary algorithm for prediction the ocean wave heights, Ocean Eng. 162 (2018) 98–107. [20] H. Karimi, F. Yousefi, Application of artificial neural network-genetic algorithm (ANN-GA) to correlation of density in nanofluids, Fluid Phase Equilib. 226 (2012) 79–83. [21] M.H. Esfe, P. Razi, M.H. Hajmohammad, et al., Optimization, modeling and accurate prediction of thermal conductivity and dynamic viscosity of stabilized ethylene glycol and water mixture, Int. Commun. Heat Mass Transf. 82 (2017) 154–160.
2
Calculated by Eq. (9), the margin of deviation of R among various ANNs, such as BPNN and BPR, GA-BPNN and BPR, MEA-BPNN and BPR, decreases by 0.06%, 0.11% and 0.13%, respectively. Thus, this table clearly shows the MEA-BPNN provides the most accurate estimate of thermal conductivity for Cu/Al2O3- EG/W hybrid nanofluids in the relevant experimental conditions. 5. Conclusions Due to the characteristic of EG/W hybrid nanofluids vary with the composition of the mixture, Cu/Al2O3-EG/W hybrid nanofluids with different mixture ratio of base fluid were prepared by using a two-step method. Experiments were conducted with 1.0 wt% Cu/Al2O3- EG/W hybrid nanofluids at temperatures ranging from 20 to 50 °C and base fluid mixture ratio varying from 20:80 to 80:20. A GA-BPNN and MEABPNN were developed based on BPNN to improve the generalization and the accuracy of proposed models. The temperature and mixing ratio of base fluid were used as the input layer, and the thermal conductivity was the output layer. Those proposed models can be used to calculate thermal conductivity as a function of temperature and the mixture ratio of base fluid. Some main conclusions have been drawn as follows. (1) The thermal conductivity increases nonlinearly as temperature and the mixture ratio of base fluid increases. Moreover, the increment of thermal conductivity increases more significantly at higher temperature due to the stronger collision frequency between liquid molecules and nanoparticles. Based on the experimental data and change rule, the BPR was fit and R2 is equal to 0.9984. (2) Compared with BPR, the margin of deviation of R2 for BPNN, GABPNN and MEA-BPNN increases by 0.06%, 0.11% and 0.13%. This indicates that the BPNN combined with GA or MEA are presented to obtain more accurate results than single BPNN. Moreover, the MEABPNN is found to provide the best performance for prediction, with R2, RMSE, MRPE (%), and SSE equal to 0.9997, 0.0031, 0.6293, and 8.8078 e-05, respectively. Author contributions section There are five authors in this paper. The contributions of each other are listed as below. The first author: Jiang Wang. Dr. Wang provided the original idea of this paper, established the ANN model and wrote parts of manuscript. The second and corresponding author: Yuling Zhai. Prof. Zhai is the tutor of Jiang Wang, Peitao Yao and Mingyan Ma. She supervised them to write and revise the manuscript. The third and fourth authors: Peitao Yao and Mingyan Ma. Both of them prepared and conducted the experiments. Dr. Yao focused on the measurement of thermal conductivity, and Dr. Ma 10
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