Simulation of turbulent convective heat transfer of γ-al2o3water nanofluid in a tube by ann and anfi

Abstract

Keywords: Nanofluids; Heat transfer coefficient; ANN; ANFIS; Prediction

Introduction

Today, since rising energy cost and environmental pollution, reduction and optimization of energy consumption in the various industrial process become important; using renewable resource energy[1] and alternative green fuel is necessary[2]. Heat transfer phenomena are one of the extensive areas of industrial processes. In general, at each

industrial process, energy add to (or remove from) the process, and it has become the main task of industrial needs. Heat transfer enhancement leads to reduce process timing, operating and fixed costs due to reducing equipment size. There are several ways to encourage heat transfer performance in the process. Increasing the thermal conductivity

*Corresponding author. *E-mail address: m.esfandyari@ub.ac.ir This paper was recommended for publication in revised form by Regional Editor Mustafa Kilic Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

of the working fluid, is one of the efficient methods to increase heat transfer performance. Almost in three last decades, nanofluids, which are superior heat transfer liquids[3], have been considered to apply for improving heat transfer in process. Nanofluids are homogenous suspensions containing colloidal particles in the nanoscale. These fluids noticeable because of their promoted thermo-physical properties such as thermal conductivity compared to prevalent liquids[3]; and modified heat and mass transfer process [4]. One of the most important limitations of usual heat transfer fluids is their low thermal conductivity. Fotukian and Nasr Esfahany[4] measured heat transfer coefficient of γ-AL2O3/ H2O nanofluid in the circular cooper tube with the inner diameter of 5 mm and 0.5 mm thickness. Their results showed that addition of small amount of nanoparticles to pure water could be improved the heat transfer performance significantly. Hojjat et al.[5] investigated γ-Al2O3, CuO and TiO2/carboxymethyl cellulose non-Newtonian nanofluids inside the stainless steel tube. They observed that heat transfer coefficient increased with Reynolds and Peclet number. At volume concentration of 0.5%, enhancement of heat transfer coefficient for suspension contain Al2O3 nanoparticle is more than two other nanofluids. Using a multichannel flat aluminum tube heat transfer of Al2O3– water nanofluids was investigated, showing that heat transfer enhancement was about 5.9% for Re=1732 and volume concentration 0.5% [6]. Alrashed et al.[7] had modeled the heat transfer and flow of CNT/water nanofluids in backwared-facing contracting channel. According to their results, surface temperature was reduced by enhancement of weight percentage of nanotubes and Reynolds numbers. Computational intelligence which includes neeural network and fuzzy systems has become universal tools for many applications. Because of proximity and ability to learn, artificial neural networks widely used for simulation of dynamic processes, identification, prediction and control. Vast investigations were done on intelligence modeling and simulation of heat transfer phenomena through other media expect nanofluids [8–10]. While little modeling studied was existed on heat transfer of nanofluids [11,12]. In this study, experimental data that have reported in [4] were used to simulate turbulent convective heat transfer of nanofluids γ-Al2O3 in a tube by ANFIS and ANN.

Theory

Adaptive Neuro-Fuzzy Inference System (ANFIS) Fuzzy Inference System using if-then rules and can model the qualitative part of human knowledge and also predict the processes without employing a careful analysis. Takagi and Sugeno Fuzzy modeling were discovered first by systematically and finds applying application in control, predict and inference.

Neural Network Neural networks is divided into two classification: artificial neural networks (ANNs) and natural neural networks (NNNs). ANNs are data processor system which have the same properties with NNNs. An ANN is a generalized mathematical model of human diagnosis based on neurobiology. The neural network is made from a combination of simple elements operated in parallel. These elements obtain from natural neural systems. The number of pages for the manuscript must be no more than ten, including all the sections. Please make sure that the whole text ends on an even page. Please do not insert page numbers. Please do not use the Headers or the Footers because they are reserved for the technical editing by editors.

Result And Discussion

ANFIS model In this study in order to simulation turbulent convective heat transfer of γ-Al2O3 nanofluids in a circular tube by ANFIS and neural network, experimental data from reference was used. In ANFIS and neural network, data conclude two parts: inputs and outputs. In this investigation, volume fractions and Reynolds number are inputs and heat transfer coefficient are output of networks. In order to use ANFIS and ANN, input and output data should be normalized. After normalization, data randomly should be divided into two parts: train and test data. In this study, 75 percent of all data that means 33 data was chosen as train data and 25 percent of them (11 data) is test data. In the next step, type and number of membership functions specified in the middle layers and the bottom layer. Optimum membership function for both train data and test data are Gaussian membership function, and optimum number of membership function obtained for Gaussian is 5. As can be seen in Figure 1, except for a small number of data, there is a good agreement between train and target data. In investigation agreement between test and target data, complete overlap between the data was observed. Base on Figure 1 and Figure 2 the best number and type of membership function has been chosen. Figure 3 a and b show experimental data versus predicted data for train and test data, respectively. The coefficient of determination values (R2), that shown in Figure 3, which quantifies the degree of agreement between experimental observations and numerically calculated values were found greater than 0.99 for all train output variables and equal one for test output. Changing in heat transfer coefficient based on inputs in three dimensional shown in Figure 4. According to Figure 4 adding small amount of nanoparticles to base fluid, dramatically increasing heat transfer coefficient, and also heat

Figure 3. Predicted data versus experimental data by ANFIS, (a) train data, (b) test data.

transfer coefficient increasing due to increase Reynold number. Table 1 reports average relative error (ARE), Mean square error (MSE) and R2 value for train and test data. R2 value should be near one and ARE and MSE value should be near zero. According Table 1 acceptable they have values. ANN model In the neural network, Parameters such as the number of hidden layers, the percentage of training, test and validation data are determined. By changing the parameters values and comparing the error values and coefficient of determination can be achieved optimal values for them. The number of hidden layers major impact on the accuracy

of prediction by the neural network. After trial and error, hidden layer, percentage of train data, test data and validation data were obtained. The results were summarized in Table 2. Predicted results respect to experimental data are shown in Figure 5. According to this figure, relation between predicted data and experimental data is linear and coefficient of determination value is 0.99. Ideal value for R2 is one, so this prediction is good because the R2 value is close to one. Error value unlike R2 should be zero. In neural network, ARE error equal –0.003. It is very close to zero so prediction has a good result. Where MSE and R2 are 6.38264 × 10–5 and

Conclusions

Heat transfer coefficient is an important issue in industrial, so increasing that is important too. There is several ways to increase this coefficient but newest way is using nanofluids as working fluids. Researchers testing any kind of nanofluids experimentally, but experimental spend many money and time. In this study, in order to reduce cost and time of experimental, heat transfer coefficient of

Anfis

γ-AL2O3 nanofluids in tube was simulated and investigated by ANFIS and ANN. The results of ANFIS and ANN compared with experimental data. Coefficient of determination, average relative error and mean square error were used to investigation agreement between experimental and ANFIS and ANN results. R2, ARE and MSE for train data are 0.99, -0.000089 and 6.5476 × 10–5, respectively. For test data, R2, ARE and MSE are one, zero and zero, respectively. It can conclude ANFIS and ANN models are reliable. When plot experimental data versus predicted data, all data is on straight line and focus on it. Because of these conclusions, ANFIS and ANN can be used to predict arbitrary data. The heat transfer coefficient changes by changing the Reynolds number and volume fraction. According to ANFIS and ANN results, heat transfer coefficient of nanofluids increase with Reynolds number and nanoparticles volume fraction. Increasing the volume fraction also results in an increase in the heat transfer coefficient.

Nomeclature

ANFIS Adaptive Neuro-fuzzy inference system ANN Artificial neural networks ARE Average relative error

Mean square error Nusselt number Coefficient of determination values Reynolds number

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

References

1. Keramati M, Beiki H. The effect of pH adjustment [10] Mehrabi M, Pesteei SM. Modeling of heat transfer together with different substrate to inoculum ratios and fluid flow characteristics of helicoidal double- on biogas production from sugar beet wastes in pipe heat exchangers using adaptive neuro-fuzzy an anaerobic digester. J Energy Manag Technol inference system (ANFIS). Int Commun Heat Mass 2017;1:6–11. Transf 2011;38:525–532. [CrossRef]
2. Beiki H. Pore network model for catalytic dehy- [11] Salehi H, Zeinali-Heris S, Esfandyari M, Koolivand dration of methanol at particle level. AICHE M. Neuro-fuzzy modeling of the convection heat J.2011;57:826. transfer coefficient for the nanofluid. Heat Mass
3. Shahmohammadi P, Beiki H. A numerical investiga- Transfer 2013;49:575-583. [CrossRef] tion of γ-Al2O3-water nano fluids heat transfer and [12] Hussein AM. Adaptive Neuro-Fuzzy Inference pressure drop in a shell and tube heat exchanger. System of friction factor and heat transfer nanofluid Transport Phenomena in Nano and Micro Scales turbulent flow in a heated tube. Case Stud Therm 2016;4:29-35. Eng 2016;8:94–104. [CrossRef]

Share and Cite