sustainability

Article

Application of New Artificial Neural Network to Predict HeatTransfer and Thermal Performance of a Solar Air-Heater Tube

Suvanjan Bhattacharyya 1, Debraj Sarkar 2, Rahul Roy 3, Shramona Chakraborty 3, Varun Goel 4

and Eydhah Almatrafi 5,*

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Citation: Bhattacharyya, S.; Sarkar,

D.; Roy, R.; Chakraborty, S.; Goel, V.;

Almatrafi, E. Application of New

Artificial Neural Network to Predict

Heat Transfer and Thermal

Performance of a Solar Air-Heater

Tube. Sustainability 2021, 13, 7477.

https://doi.org/10.3390/su13137477

Academic Editor: Alessandro Franco

Received: 18 April 2021

Accepted: 30 June 2021

Published: 5 July 2021

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4.0/).

1 Department of Mechanical Engineering, Birla Institute of Technology and Science Pilani, Pilani Campus,Vidya Vihar, Pilani 333031, Rajasthan, India; suvanjan.bhattacharyya@pilani.bits-pilani.ac.in

2 Department of Textile Technology, Government College of Engineering and Textile Technology, Berhampore,Murshidabad 742101, West Bengal, India; suva.raindrops@gmail.com

3 Department of Computer Science and Engineering, Indian Institute of Technology,Kharagpur 721302, West Bengal, India; rahulmckviecse@gmail.com (R.R.); shramo.cse@gmail.com (S.C.)

4 Department of Mechanical Engineering, National Institute of Technology Hamirpur,Hamirpur 177005, HP, India; varun@nith.ac.in

5 Mechanical Engineering Department-Rabigh, Center of Excellence in Renewable Energy and Power Systems,King Abdulaziz University, Jeddah 21589, Saudi Arabia

* Correspondence: Ealmatrafi@kau.edu.sa

Abstract: In the present study, the heat transfer and thermal performance of a helical corrugationwith perforated circular disc solar air-heater tubes are predicted using a machine learning regressiontechnique. This paper describes a statistical analysis of heat transfer by developing an artificialneural network-based machine learning model. The effects of variation in the corrugation angle (θ),perforation ratio (k), corrugation pitch ratio (y), perforated disc pitch ratio (s), and Reynolds numberhave been analyzed. An artificial neural network model is used for regression analysis to predict theheat transfer in terms of Nusselt number and thermohydraulic efficiency, and the results showedhigh prediction accuracies. The artificial neural network model is robust and precise, and can beused by thermal system design engineers for predicting output variables. Two different models aretrained based on the features of experimental data, which provide an estimation of experimentaloutput based on user-defined input parameters. The models are evaluated to have an accuracyof 97.00% on unknown test data. These models will help the researchers working in heat transferenhancement-based experiments to understand and predict the output. As a result, the time and costof the experiments will reduce.

Keywords: machine learning; ANN; prediction; fluid flow; heat transfer; enhancement

1. Introduction

Conservation of energy is one of the main concerns of today’s world. This is pos-sible using energy-efficient equipment which enables us to utilize less available energy,at the same time without a reduction in its working capacity. Every day, our world ismoving one step forward by making new inventions and achievements in the field ofenergy conservation. However, this growth is surpassed by the need for energy utilization.Growing nations require more energy for the running of businesses, which puts pressure onthe power generation units to meet their demands. As of 2019, coal-fired power generationunits contribute to 38%, gas-based plants contribute to 23%, hydropower contributes 19%,nuclear power contributes around 10%, while solar and wind energy together contribute7%. The mentioned figures show that still, we rely mainly on non-renewable energy sourcessuch as coal, gas, and nuclear energy for power generation, however over-exploitationof these resources will vanish soon if we do not find other options. This results in theworld economies switching to renewable sources of energy, such as water, wind, tidal,solar, etc. Although hydropower plants have provided energy to us for many decades,

Sustainability 2021, 13, 7477. https://doi.org/10.3390/su13137477 https://www.mdpi.com/journal/sustainability

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the reservoir for the storage of water in very vast quantities damages the ecosystem aroundthe hydropower plant, which creates problems such as habitat loss to the wild animals.Besides, these plants are accident-prone, which has led to flood-like situations. A safe formof energy that is clean and available to us forever is solar energy. The simplest way ofharnessing solar energy is by using solar collectors. Solar collectors find applications inspace heating, drying industries, process heating, and manufacturing industries, etc.

Solar energy was used for the first time by Greek scientist Archimedes in 212 BC,for burning the Roman fleet with the help of several concave mirrors [1]. In the 19thcentury, Augustin Mouchot first developed solar-powered steam engines [2], but the costassociated with the construction is not feasible. Many scientists have studied solar powersince then but were not able to make any impact and commercialize it. The commercial-ization of solar-powered devices started in the mid-20th century [3,4]. During this time,researchers investigated the solar devices concerning various aspects. The main disad-vantage that researchers come across is the low efficiency of solar-powered equipment.The efficiency of such devices can be increased by employing various passive and activetechniques of heat transfer (HT) enhancement, but these techniques need external powersuch as electric field, magnetic field, etc. [5–8], which is costly as well as risky. For twomass velocities and various heat fluxes, the effects of an applied DC electric field on flowboiling heat transfer in a vertical mini-channel heat sink are examined experimentallyby Feng et al. [5]. Bezaatpour and Goharkhah [6] proposed a new method to improvethe heat transfer coefficient in a heat exchanger by involving magnetic nanofluid alongwith magnetic field. Zhang and Lai [7] carried out a numerical investigation to evaluateheat transfer enhancement in a square channel using corona wind. Cheraghi et al. [8]also incorporate the corona wind for heat transfer enhancement. Passive techniques aresimple and safe in operation and utilize surface and geometrical modification for heattransfer enhancement. Some examples of passive techniques involve corrugation on thesurface of the duct or channel, use of turbulators such as swirl devices, vortex generators,tapes, and inserts, and artificial roughness such as ribs, dimples, protrusions, etc. [9–20].Various researchers made efforts to increase the thermohydraulic efficiency of devicesand decrease the heat losses associated with the operational process. Cheraghi et al. [9]performed a numerical study on the novel geometry of the dimpled tube for thermal andflow performance and reported a 600% enhancement in heat transfer (HT) and a rise inpressure drop (PD). Rainieri et al. [10] experimentally studied the effect of the helicallycoiled, twisted corrugated tube for mixed convective HT. For the experimental test run,high Prandtl number fluid was used as a working fluid with Re varied from 70 to 1200 andDean number varied between 12 and 290. Three twist ratios have been used, while the tubecorrugation remains the same for all configurations. Enhancement of heat transfer of about25 times was observed for helically twisted walls in comparison to plain channel, while thepressure drop ranged between 1.5 to 2.5. Ramadhan et al. [11] numerically studied theeffect of the square, triangular, trapezoidal, and circular groove carved on the surface ofthe tube for HT enhancement and flow behavior for Reynolds number (Re) between 10,000and 20,000. Air is taken as the working fluid. It was revealed that triangular groovesperform best among all other groove geometries for all depths, with a maximum of 64%enhancement in thermal transport. It was also observed that shallow grooves in all casesperform better when compared with smooth channels. Ren et al. [12] experimentally aswell as numerically reported the effect of rectangular and triangular surface roughnesson the jet impingement cooling augmentation. Air is taken as a working fluid with a Reof 900, 1500, 5000, and 11,000. It was revealed that for low Reynolds numbers (Re) of 900and 1500, rectangular and triangular roughness results in a drop in Nu and HT coefficients,while increasing the height of rectangular roughness shows an enhancement in Nu andheat transfer rate. At higher Re, the roughness promotes vorticity and turbulent mixing offluid, which increases heat transfer and Nu. It was also revealed that rectangular roughnessperforms better in comparison to triangular roughness for all cases. An experimental workon HT enhancement of jet impingement using two geometries (circular protrusion and

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V-grooves) of surface roughness was conducted by Nagesha et al. [13]. The study wasfocused on a turbulent region with Re between 10,000 and 27,500 and the application in aheat exchanger (HE). Augmentation in HT was observed in both cases in comparison tothe smooth plate, while the plate with circular protrusion showed maximum heat transferenhancement. Roughness enhances the surface area of the plate as well as helps in theturbulent mixing of fluid, which results in the augmentation of HT. Yadav and Sahu [14]conducted an experimental investigation for analyzing the HT and PD in a double-pipeHE with a smooth inner pipe and corrugated outer pipe, and developed a correlation forpredicting Nu and friction factor (f). The study is concluded with 71% augmentation in Nuand 81% enhancement in f as a result.

Jin et al. [15] reported a numerical work on a six-start spirally corrugated duct forinvestigating the effect of variation in geometric parameters such as pitch, depth of corru-gation, Re, and fluid properties on the HT performance. Eiamsa-ard et al. [16] numericallyexplored a triple-start spirally corrugated tube fitted with twisted tape (TT) inserts withdifferent orientation and width ratio for HT augmentation, and reported enhancement inHT and f with an increase in width ratio, while belly to neck orientation performed betterthan belly to belly orientation. Andrade et al. [17] performed an investigation for analyzingthe thermohydraulic characteristics in the corrugated channel with Re varied between 429and 6212 for both adiabatic and diabatic conditions, and reported that corrugated tubes aremore effective in transitional flow regime (TFR) when compared with the transition in asmoother tube. Wang et al. [18] experimentally studied the novel arrangement of ellipsoidaldimples on tube surface for thermal and flow characteristics and reported enhancementin HT and f. Xie et al. [19] computationally reported the impact of tear-drop dimpleson the surface of the tube and compared the results with the ellipsoidal- and spherical-dimpled tube data. A significant drop in recirculation flow, as well as a pressure drop,is reported when results are compared with that of the ellipsoidal- and spherical-dimpledtube. Li et al. [20] performed experiments to explore the influence of dimple-enhancedtubes on the thermal transport and pressure drop for water and water/glycol solution asthe working fluids. The results of simulations revealed that dimples disrupt the boundarylayers and create secondary flows, which enhance turbulence, resulting in enhanced heattransfer. Bhattacharyya and Chattopadhyay [21] conducted an investigation to study theinfluence of twisted strips on the thermohydraulic performance of fluid in a turbulentflow regime for different pitch ratios. An increase in Nu and a decrease in f were reportedwith increasing Re for all configurations. Moghadam et al. [22] performed a computationalinvestigation on a corrugated tube fitted with a wire coil insert for thermal and flow perfor-mance, and reported an increase in heat transfer and pressure drop with an increase in Re.Yang et al. [23] conducted a numerical investigation to analyze the influence of TT insertsfitted inside an externally corrugated tube for thermal and flow behavior, and the obtainedresults are compared with smooth tube results.

A numerical assessment to investigate the influence of nanofluid flow on the HT andPD inside a corrugated tube has been performed by Ahmed et al. [24]. An increment inHT, as well as a slight increase in PD, was reported with an increase in the volume fractionof nanoparticles and Reynolds number. Navaei et al. [25] numerically investigated theinfluence of different nanofluids flowing inside corrugated tubes of various configurationsfor thermal and flow characteristics and reported augmentation in Nu for the increase involume fraction, while a decrease in Nusselt number (Nu) was reported with an increasein the size of the nanoparticles. Wongcharee and Eiamsa-ard [26] experimentally reveal theinfluence of volume fraction of nanoparticles and twist ratio, an arrangement of twistedtape inserts fitted inside a corrugated tube on thermal and flow behavior, and reportedenhancement in HT, f, and thermal performance.

A new efficient technique is gaining momentum, which is more accurate and consumesless time to predict thermal performance, and the technique is known as machine learning(ML) prediction. The utilization of this system helps in reducing the time, cost, and effortassociated with experimental and numerical work by predicting the results in a permissible

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range and learning from previous tasks. Tang et al. [27] employed the ML method foranalyzing and optimizing the geometric and operation parameters of a phase-changematerials-based hybrid cooling system. Krishnayatra et al. [28] utilized k-nearest neighbor,also known as KNN, for predicting the performance of HE, which resulted in highlyaccurate predictions. Beig et al. [29] investigated T performance in a tube fitted withthree blocks at the bottom, and a triangular bar was used as a vortex generator. The MLmethod of the genetic algorithm was used for prediction of the Nusselt number, and theGaussian process was used for predicting the optimal position of the triangular bar inthe channel for maximum heat transfer. Methods of ML prediction have been utilized topredict the Nu for nanofluid flowing through the coils [30]. The variables considered for theprediction are Prandtl number (Pr), volumetric concentration (φ), and the helical numberof helically coiled corrugated tubes. The model predicted using the least-squares supportvector machine (LSSVM) shows the best performance and approaches the R-square valueof 1. Hobold and Silva [31] presented a neural network-based model to predict the heat fluxduring nucleate boiling and showed that the correlation developed by the model showeda 7% error in the predicted results when compared with the experimentally obtaineddata. Khairul et al. [32] employed fuzzy logic to investigate the influence of CuO/waternanofluid (NF) flowing inside a corrugated tube to predict the thermal performance ofnanofluid. Models have been developed to predict the Nu and f, and the values obtainedfrom such models are fitted well in the acceptable range of 5%. Sotgiu et al. [33] employedML and tensor representation theory to predict the heat flux in a turbulent flow regime.The validation of Poiseuille flow for different values of Re using the given model showsgood agreement between the obtained value and reference values. While an ML modelmakes decisions according to what it has learned from the data, a neural network isa more sophisticated ML approach that arranges various ML algorithms in a fashionwhereby it can make better accurate decisions by itself [34]. An artificial neural network(ANN) works similarly to the human brain’s neural network. It is the foundation of AIand solves problems that would prove impossible or difficult by human or statisticalstandards [35]. Rabbi et al. [36] predicted the magneto hydro-dynamics flow and entropyproduction for heat sinks filled with Copper-water nanofluid using the method of artificialneural networking (ANN). The effect of Hartman number (Ha) and Volume fraction (φ)on the Nu and Bejan number (Be) have been predicted using ANN. Akdag et al. [37]performed experiments to investigate the HT on the flat plate subjected to transversepulsating jets. Constant heat flux is supplied to the plate. The data obtained from theexperimental study were used to process ANN for predicting the solution. The resultsobtained from the ANN were in very good agreement with the experimental data, with lessthan 1% error. The ML prediction method is also used to predict the PD during theevaporation of R407C by Khosravi et al. [38]. Three methods of ML, namely MLFFNN,SVR, and GMDH, are employed to predict the pressure drop, and the results obtainedfrom all the methods are compared. Both MLFFNN and GMDH perform better, witherrors of less than 1%, compared to the SVR method of ML prediction. Song et al. [39]investigated the application of ultrasound in industrial evaporators. They predicted thethermal performance of an ultrasonic evaporator using seven different algorithms of MLand found that SVM and NNet predicted the results most accurately. Park and Lee [40]employed an ML prediction technique for predicting the wall temperature at critical heatflux (CHF). The ML prediction method utilized here helped in reducing the calculation timeby 86%. Kim and Lee [41] utilized convolutional neural networks (CNN) for the predictionof HT in turbulent flow, and the results are associated with the data obtained from directnumerical simulations (DNS). The results obtained from the analysis show great agreementbetween CNN and DNS, with a correlation coefficient of 0.98. Kahrom et al. [42] employeda pareto genetic algorithm to generate the most suitable edge size and position of a quadinsert in a turbulent flow regime to maximize the HT. Kahani et al. [43] predicted the Nuand PD for TiO2-water NF flowing through a coiled channel using the MLPANN andLSSVM models. The predicted results through MLPANN models show more accuracy

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when compared with the data obtained by the LSSVM model. Gerdroodbary [44] predictedthe heat transfer (HT) rate of MHD NF inside an inclined enclosure with a sinusoidalwall using the ML prediction method of the group method of data handling (GMDH).The data obtained from GMDH are compared with data obtained from the control volume-based method (CVFEM) and results show that GMDH is far more accurate in predictingthe heat transfer (HT). ML is also used to predict the thermal conductivity of NFs [45].Karami et al. [46] employed the ML method of adaptive neuro-fuzzy inference system(ANFIS) to predict the thermal performance of an air-cooler fitted with TT inserts. Theresult obtained from the prediction showed a maximum error of 2.37% when compared withexperimental results. Other authors who also investigated the ML prediction for predictingthe heat transfer and pressure drop, thermal performance, and thermal resistance areNasirzadehroshenin et al. [47], Li and Liu [48], and Zhan et al. [49], respectively.

In view of the above literature review, it is clear that a lot of available literatureaddress HT and PD in a helically corrugated tube, but very few studies address helicalcorrugated tubes with turbulator inserts, and no literature are available on the applicationof machine learning (ML) prediction of HT and PD in a corrugated tube with inserts. In fact,only a few studies are available to predict thermal performance of unknown parametersby ML techniques. Hence, the main aim and the novelty of this work is to predict theHT and thermal performance in a helically corrugated tube fitted with perforated circulardisc turbulator inserts by employing the ML. Additionally, these models will help futureinvestigators working in the field of HT enhancement-based experiments to understandand predict the output.

2. Experimentation and Data Reduction

The basic design of the helical corrugation channel with turbulator disc inserts isshown in Figure 1 [50]. The setup used in this investigative work is quite prominent,and the same test rig (Figure 2) was utilized in previous studies [50].

The tests were conducted in an air-conditioned lab, where the average room temper-ature varied from 290 to 295 K. A 7 kW air blower was used to draw fresh air from theatmosphere. A rotameter was fitted in the line to quantify the mass flow rate of the air.A manometer was used to display the pressure difference between pressure taps.

Brass was used for the fabrication of the test section. The test section is circular incross-section, having an internal diameter of 20 mm, while the total length of the test sectionis fixed at 3500 mm. A total of 28 thermocouples were used at 7 locations to measure theouter wall temperatures. In previous research conducted by the authors [51–61], the basicfabrication method is well-represented. Other specifications of different parameters areoutlined in Table 1, and the ideas of choosing the arrangement of the considered solarair-heater followed Bhattacharyya et al. [50,56].

Table 1. Experimental investigated parameters.

Sl. No. Parameters Values

1 Corrugation depth (d) 3 mm

2 Corrugation angle (θ) 30◦ and 60◦

3 Perforation ratio (k) 0.16, 0.25, and 0.33

4 Corrugation pitch ratio (y) 0.7 and 1.0

5 Perforated disc pitch ratio (s) 1.5 and 2.5

6 Reynolds number (Re) 10,000–50,000

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1

Figure 1. Schematic diagram: (a) helical corrugated tube and (b) perforated disc details [50].

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(a)

(b)

Figure 2. (a) Schematic diagram of the experimental setup [50], and (b) photograph of the experimental setup.

Figure 2. (a) Schematic diagram of the experimental setup [50], and (b) photograph of the experimental setup.

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3. ANN-Based Heat Transfer Prediction

ML is an application of artificial intelligence (AI) where systems automatically learn,develop knowledge, and improve the ability to predict with more accuracy with experi-ence [62–68]. Shankar et al. [65] developed an ANN approach to predict interface tempera-ture. Farzaneh-Gord et al. [66] employed machine learning for predicting the temperaturein the throttle process. Jin et al. [67] also employed the same approach for determiningthe auto-ignition temperature. Baghban et al. [68] employed the ML for determining thethermal performance of nanofluid under observation.

In this section, the influence of different architectures and their variants and trainingstrategies are exhaustively described. The numerical operation is computed by usinguser-defined model architecture and is discussed in Section 3.1, the details of the datasetare explained in Section 3.2, and the computational environment is described in Section 3.3.

3.1. Model

The primary step of the ANN-based approach is collecting the experimental datathat is used to train the model. The dataset provides a large number of true values fordifferent sets of parameters. Figure 3a,b demonstrate the architecture of the ANN-basedapproach for the prediction of Nusselt number (Nu) and the thermohydraulic efficiency ofthe solar air-heater.

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3. ANN-Based Heat Transfer Prediction ML is an application of artificial intelligence (AI) where systems automatically learn,

develop knowledge, and improve the ability to predict with more accuracy with experi-ence [62–68]. Shankar et al. [65] developed an ANN approach to predict interface tem-perature. Farzaneh-Gord et al. [66] employed machine learning for predicting the tem-perature in the throttle process. Jin et al. [67] also employed the same approach for de-termining the auto-ignition temperature. Baghban et al. [68] employed the ML for de-termining the thermal performance of nanofluid under observation.

In this section, the influence of different architectures and their variants and training strategies are exhaustively described. The numerical operation is computed by using user-defined model architecture and is discussed in Section 3.1, the details of the dataset are explained in Section 3.2, and the computational environment is described in Section 3.3.

3.1. Model The primary step of the ANN-based approach is collecting the experimental data

that is used to train the model. The dataset provides a large number of true values for different sets of parameters. Figure 3a, b demonstrate the architecture of the ANN-based approach for the prediction of Nusselt number (Nu) and the thermohydraulic efficiency of the solar air-heater.

(a)

Figure 3. Cont.

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(b)

Figure 3. Architecture of the ANN-based approach for prediction of (a) Nusselt number (Nu) and (b) efficiency.

3.1.1. Workflow of ANN At the initial stage, the dataset is divided into three categories: training data, vali-

dation data, and test data. A “neuron” in ANN is a single computing cell, and the model is composed of several neurons. Each neuron has activation functions that are mathe-matical equations of the weighted sum of the outputs of the previous layer with a bias added to it. Different types of activation functions are binary-step functions, linear, and non-linear activation functions, as analyzed by Dabal [62]. A few efficient activation functions were chosen for the particular study and are as follows.

Linear: Linear activation is a straight-line function where the input (that is the weighted sum from the neuron) is proportional to the activation. It can be written as:

A(x) = cx (1)

Rectified linear units (ReLU): The function’s formula is ambiguously simple: max (0, z). Despite its name and appearance, it is not linear and provides the same benefits as Sigmoid but with much better performance. It can be written as:

A(z) = z if z > 0 or

A(z) = 0 if z 0 (2)

Exponential linear unit (ELU): It is a function which tends to more quickly converge cost to zero and produce more accurate results. In contrast to other activation functions, an ELU has an extra positive constant, 𝛼.

A(z) = 𝛼.ez − 1 if z 0 or (3)

Figure 3. Architecture of the ANN-based approach for prediction of (a) Nusselt number (Nu) and (b) efficiency.

3.1.1. Workflow of ANN

At the initial stage, the dataset is divided into three categories: training data, valida-tion data, and test data. A “neuron” in ANN is a single computing cell, and the model iscomposed of several neurons. Each neuron has activation functions that are mathematicalequations of the weighted sum of the outputs of the previous layer with a bias added toit. Different types of activation functions are binary-step functions, linear, and non-linearactivation functions, as analyzed by Dabal [62]. A few efficient activation functions werechosen for the particular study and are as follows.

Linear: Linear activation is a straight-line function where the input (that is theweighted sum from the neuron) is proportional to the activation. It can be written as:

A(x) = cx (1)

Rectified linear units (ReLU): The function’s formula is ambiguously simple: max (0, z).Despite its name and appearance, it is not linear and provides the same benefits as Sigmoidbut with much better performance. It can be written as:

A(z) = z if z > 0 orA(z) = 0 if z ≤ 0

(2)

Exponential linear unit (ELU): It is a function which tends to more quickly convergecost to zero and produce more accurate results. In contrast to other activation functions,an ELU has an extra positive constant, α.

A(z) = α.ez − 1 if z ≤ 0 orA(z) = z otherwise z > 0

(3)

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3.1.2. ANN Model for Nusselt Number

The five-layered neural network-based machine learning model was used to predictthe Nusselt number. Several tests were performed using different models with severalnumbers of neurons and hidden layers [63,64]. Among them, a model with four hid-den layers, with each having 40–50 neurons, was determined to have decent accuracy.The present neural network with four dense hidden layers with 50 neurons in each had thebest accuracy, and hence this configuration was selected for comparison of accuracy andcalculation speed. The linear error function (Equation (1)) was used in the output layerand the ReLU error function (Equation (2)) was used in all the hidden layers. The trainingand validation accuracy are shown in Table 2. The neural network was trained by takingbatch size as 32 and epoch size as 200. The change in training and validation loss with anincrease in epoch numbers is shown in Figure 4.

Table 2. Training accuracy for Nusselt number.

Neural Network Model Training Accuracy Validation Accuracy

40 × 40 × 40 × 40 neurons 99.90% 99.96%

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A(z) = z otherwise z > 0

3.1.2. ANN Model for Nusselt Number The five-layered neural network-based machine learning model was used to predict

the Nusselt number. Several tests were performed using different models with several numbers of neurons and hidden layers [63,64]. Among them, a model with four hidden layers, with each having 40–50 neurons, was determined to have decent accuracy. The present neural network with four dense hidden layers with 50 neurons in each had the best accuracy, and hence this configuration was selected for comparison of accuracy and calculation speed. The linear error function (Equation (1)) was used in the output layer and the ReLU error function (Equation (2)) was used in all the hidden layers. The training and validation accuracy are shown in Table 2. The neural network was trained by taking batch size as 32 and epoch size as 200. The change in training and validation loss with an increase in epoch numbers is shown in Figure 4.

Figure 4. Mean squared error as the function of epochs for Nusselt number.

Table 2. Training accuracy for Nusselt number.

Neural Network Model Training Accuracy Validation Accuracy 40 × 40 × 40 × 40 neurons 99.90% 99.96%

3.1.3. ANN Model for Efficiency The five-layered neural network-based ML model was built to predict thermohy-

draulic efficiency. The main difference of this model is the error function used in the hidden layers. The ELU error function (Equation (3)) was used here as it provides better results in terms of producing negative outputs. The neural network with four dense hidden layers with 50 neurons in each was predicted to have the best validation set ac-curacy, and hence this configuration was considered for comparison of accuracy and calculation speed. The neural network was trained by taking batch size as 10 and epoch size as 200. The change in training and validation loss with an increase in epoch numbers is shown in Figure 5. The training and validation accuracy is shown in Table 3.

Figure 4. Mean squared error as the function of epochs for Nusselt number.

3.1.3. ANN Model for Efficiency

The five-layered neural network-based ML model was built to predict thermohy-draulic efficiency. The main difference of this model is the error function used in the hiddenlayers. The ELU error function (Equation (3)) was used here as it provides better resultsin terms of producing negative outputs. The neural network with four dense hiddenlayers with 50 neurons in each was predicted to have the best validation set accuracy,and hence this configuration was considered for comparison of accuracy and calculationspeed. The neural network was trained by taking batch size as 10 and epoch size as 200.The change in training and validation loss with an increase in epoch numbers is shown inFigure 5. The training and validation accuracy is shown in Table 3.

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Table 3. Training accuracy for efficiency.

Neural Network Model Training Accuracy Validation Accuracy 50 × 50 × 50 × 50 neurons 99.91% 99.98%

Figure 5. Mean squared error as the function of epochs for thermohydraulic efficiency.

3.2. Dataset The experimental data consist of five independent input parameters, namely cor-

rugation angle (θ), corrugation pitch ratio (y = P/D), perforated disc pitch ratio (s = H/D), perforation ratio (k = h/D), and Reynolds number. The experimentation was already ex-plained in Section 2, and detailed experimentation can be found in the authors’ previous work [50–61]. Depending on the experimental analysis, the two main important de-pendent output parameters, such as Nusselt number and thermohydraulic efficiency, are taken into consideration. The detailed analysis of the dataset can be visualized in Table 4. The total count of data points was 1347. The mean and standard deviation of every indi-vidual parameter were calculated, showing the statistical analysis of the experimental data which are used to train and test the models.

Table 4. Analysis of experimental data.

Corrugation Angle

Corrugation Pitch Ratio

Perforation Ratio

Perforated Disc Pitch

Ratio

Reynolds Number

Nusselt Number

Efficiency

Count 1347.000 1347.000 1347.000 1347.000 1347.000 1347.000 1347.00 Mean 44.877 0.848 0.235 2.004 30,636.728 144.2535 1.8309

Standard Deviation 15.005 0.150 0.072 0.500 11,836.229 31.294 0.47

3.3. Computational Environment All the experiments were run on Google Colab Notebook with Nvidia GPU version

1.4.0 enabled, and Keras 2.4.0 was used as an API to train and test the neural network models, as a way to clone hardware configuration. This computational environment was

Figure 5. Mean squared error as the function of epochs for thermohydraulic efficiency.

Table 3. Training accuracy for efficiency.

Neural Network Model Training Accuracy Validation Accuracy

50 × 50 × 50 × 50 neurons 99.91% 99.98%

3.2. Dataset

The experimental data consist of five independent input parameters, namely corru-gation angle (θ), corrugation pitch ratio (y = P/D), perforated disc pitch ratio (s = H/D),perforation ratio (k = h/D), and Reynolds number. The experimentation was alreadyexplained in Section 2, and detailed experimentation can be found in the authors’ previouswork [50–61]. Depending on the experimental analysis, the two main important dependentoutput parameters, such as Nusselt number and thermohydraulic efficiency, are taken intoconsideration. The detailed analysis of the dataset can be visualized in Table 4. The totalcount of data points was 1347. The mean and standard deviation of every individualparameter were calculated, showing the statistical analysis of the experimental data whichare used to train and test the models.

Table 4. Analysis of experimental data.

CorrugationAngle

CorrugationPitch Ratio

PerforationRatio

Perforated DiscPitch Ratio

ReynoldsNumber

NusseltNumber Efficiency

Count 1347.000 1347.000 1347.000 1347.000 1347.000 1347.000 1347.00Mean 44.877 0.848 0.235 2.004 30,636.728 144.2535 1.8309

StandardDeviation 15.005 0.150 0.072 0.500 11,836.229 31.294 0.47

3.3. Computational Environment

All the experiments were run on Google Colab Notebook with Nvidia GPU version1.4.0 enabled, and Keras 2.4.0 was used as an API to train and test the neural networkmodels, as a way to clone hardware configuration. This computational environment wasused to compare and execute the various possible choices of model for the experimentaldata studied in this paper. In total, the results for more than 100 experimental trials weresummed up.

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4. Results and Discussion

The test accuracy is shown in Table 5 and the R-squared values (another statisticalmeasure of how close to the data are to the fitted regression line) of test data are shownin Table 6 for both the trained models. Figures 6 and 7 show the assessment betweenthe predicted and actual experimental value of the test data for Nu and efficiency (η),respectively. From the figures, one can understand that the ANN model fits the datasetacceptably. The performance of both the models reported an accuracy of more than 97.00%on the test dataset.

Table 5. Test accuracy for Nu and thermohydraulic efficiency.

Test accuracy for Nusselt number 98.19%

Test accuracy for thermohydraulic efficiency 97.15%

Table 6. R-squared value for Nu and thermohydraulic efficiency.

Test accuracy for Nusselt number 98.22%

Test accuracy for thermohydraulic efficiency 96.83%Sustainability 2021, 13, x FOR PEER REVIEW 13 of 20

Figure 6. Predicted and experimental Nu values for corrugated tube with insert.

Figure 7. Predicted and experimental efficiency values for corrugated tube with insert.

Figure 6. Predicted and experimental Nu values for corrugated tube with insert.

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Figure 6. Predicted and experimental Nu values for corrugated tube with insert.

Figure 7. Predicted and experimental efficiency values for corrugated tube with insert.

Figure 7. Predicted and experimental efficiency values for corrugated tube with insert.

Some recent work on solar air-heaters with various types of turbulator inserts are re-ported by many researchers [69–73], but the authors failed to predict unknown parameters.Predicting unknown parameters is very important. So, next, for achieving a better result,a noble work effort is shown, where a set of unknown input parameters were generated topredict the values for Nu and efficiency. The detailed statistical analysis of the generateddata is shown in Table 7, which includes a count of the data, mean, and standard deviation,that elaborates the range or the distribution of the generated data.

Table 7. Analysis of generated data.

CorrugationAngle

CorrugationPitch Ratio

PerforationRatio

Perforated DiscPitch Ratio

ReynoldsNumber

Count 22,679 22,679 22,679 22,679 22,679Mean 53.33 0.88 0.255 1.06 37,017.94

StandardDeviation 22.11 0.37 0.14 1.16 28,473.95

The newly generated parameters for prediction are shown in Table 8. The Nus-selt number and thermohydraulic efficiency results of the generated data are shown inTables 9 and 10. Here, different combinations of inputs were taken and fed to the model.The inputs are new to the model and hence the accuracy is measured to their outcomes.

Table 8. New generated parameters for prediction.

Sl. No. Parameters Values

1 Corrugation angle (θ) 20◦, 25◦, 40◦, 45◦, 50◦, 65◦, 70◦, 75◦, and 90◦

2 Perforation ratio (k) 0.08, 0.10, 0.20, 0.30, 0.40, and 0.453 Corrugation pitch ratio (y) 0.4, 0.6, 0.8, 1.2, and 1.44 Perforated disc pitch ratio (s) 0.14, 0.20, 0.28, 0.35, 1.0, 2.0, and 3.55 Reynolds number (Re) 8000–70,000

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Table 9. Predicted result of Nusselt number on generated data.

Sl. No. CorrugationAngle

CorrugationPitch Ratio

PerforationRatio

Perforated DiscPitch Ratio

ReynoldsNumber

NusseltNumber

1 20◦ 0.4 0.08 0.14 9000 119.742 20◦ 0.6 0.45 0.2 70,000 157.083 25◦ 0.8 0.1 0.28 70,000 160.014 25◦ 1.2 0.4 0.35 8000 93.875 40◦ 1.4 0.1 2.0 60,000 138.316 40◦ 0.4 0.2 0.2 65,000 172.107 45◦ 0.6 0.3 0.14 9500 122.918 45◦ 0.8 0.08 1.0 9000 120.679 50◦ 1.2 0.2 3.5 60,000 144.72

10 50◦ 1.4 0.45 0.28 65,000 150.3611 65◦ 0.4 0.3 0.35 8000 138.9712 65◦ 0.6 0.4 1.0 9500 134.6713 70◦ 0.8 0.1 2.0 9000 133.3514 70◦ 1.2 0.08 3.5 70,000 170.1515 75◦ 1.4 0.45 0.14 8000 125.4616 75◦ 0.4 0.4 0.2 60,000 182.0917 90◦ 0.6 0.2 0.35 65,000 193.3818 90◦ 0.8 0.08 2.0 9500 149.04

Table 10. Predicted result of thermohydraulic efficiency on generated data.

Sl. No. CorrugationAngle

CorrugationPitch Ratio

PerforationRatio

Perforated DiscPitch Ratio

ReynoldsNumber Efficiency

1 20◦ 0.4 0.08 0.14 9000 2.102 20◦ 0.6 0.45 0.2 70,000 1.483 25◦ 0.8 0.1 0.28 70,000 1.494 25◦ 1.2 0.4 0.35 8000 1.715 40◦ 1.4 0.1 2.0 60,000 1.466 40◦ 0.4 0.2 0.2 65,000 1.607 45◦ 0.6 0.3 0.14 9500 2.198 45◦ 0.8 0.08 1.0 9000 2.169 50◦ 1.2 0.2 3.5 60,000 1.52

10 50◦ 1.4 0.45 0.28 65,000 2.0011 65◦ 0.4 0.3 0.35 8000 1.8712 65◦ 0.6 0.4 1.0 9500 1.4313 70◦ 0.8 0.1 2.0 9000 1.9914 70◦ 1.2 0.08 3.5 70,000 1.4715 75◦ 1.4 0.45 0.14 8000 1.7316 75◦ 0.4 0.4 0.2 60,000 1.3817 90◦ 0.6 0.2 0.35 65,000 1.4018 90◦ 0.8 0.08 2.0 9500 2.20

Based on the newly generated parameters, Figure 8 is plotted. The 3D plots of HTin terms of Nu and thermohydraulic efficiency are shown in Figure 8a–d, respectively.From Table 5, it may be seen that the accuracy was 98% for Nusselt number and 97% forthermohydraulic efficiency, which indicates that the new ANN model had no complicationsin learning the Nusselt number and thermohydraulic efficiency. From Figure 8a,b, one caneasily observe the Nusselt number (z-axis), Reynolds number (y-axis), and corrugationangle (x-axis) plotted in a 3D graph. In Figure 8a, the Nusselt number is the function ofcorrugation angle and Reynolds number, and is plotted at a constant corrugation pitchratio of 0.4, perforation ratio of 0.08, and perforated disc ratio of 0.14, while in Figure 8b,the Nusselt number is the function of corrugation angle and Reynolds number, and isplotted at a constant corrugation pitch ratio of 1.4, perforation ratio of 0.45, and perforateddisc ratio of 3.5.

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16 75° 0.4 0.4 0.2 60,000 1.38 17 90° 0.6 0.2 0.35 65,000 1.40 18 90° 0.8 0.08 2.0 9500 2.20

Based on the newly generated parameters, Figure 8 is plotted. The 3D plots of HT in terms of Nu and thermohydraulic efficiency are shown in Figure 8a–d, respectively. From Table 5, it may be seen that the accuracy was 98% for Nusselt number and 97% for thermohydraulic efficiency, which indicates that the new ANN model had no complica-tions in learning the Nusselt number and thermohydraulic efficiency. From Figure 8a,b, one can easily observe the Nusselt number (z-axis), Reynolds number (y-axis), and cor-rugation angle (x-axis) plotted in a 3D graph. In Figure 8a, the Nusselt number is the function of corrugation angle and Reynolds number, and is plotted at a constant corru-gation pitch ratio of 0.4, perforation ratio of 0.08, and perforated disc ratio of 0.14, while in Figure 8b, the Nusselt number is the function of corrugation angle and Reynolds number, and is plotted at a constant corrugation pitch ratio of 1.4, perforation ratio of 0.45, and perforated disc ratio of 3.5.

(a) (b)

(c) (d)

Figure 8. 3D plots of Nu at different corrugation angle and Reynolds number: (a) at constant y = 0.4, k = 0.08, and s = 0.14,(b) at constant y = 1.4, k = 0.45, and s = 0.35. 3D plots of thermohydraulic efficiency at different corrugation angle andReynolds number: (c) at constant y = 0.4, k = 0.08, and s = 0.14, (d) at constant y = 1.4, k = 0.45, and s = 0.35.

From Figure 8a,b, it can be detected that the Nu is increasing with the increase ofRe and corrugation angle, and the proposed ANN model very closely shadowed theexperimental pattern [50]. From the figures, one can see that the Nusselt numbers aremaximum when the corrugation angle is varied between 70◦ and 90◦ at Reynolds numbersbetween 60,000 and 70,000.

The thermohydraulic efficiency (η) is another very important factor to evaluate theperformance of the solar air-heater. In Figure 8c,d, efficiency (z-axis), Re (y-axis), and corru-gation angle (x-axis) are plotted in a 3D graph. In Figure 8c, the efficiency is the functionof corrugation angle and Reynolds number, and is plotted at a constant corrugation pitchratio of 0.4, perforation ratio of 0.08, and perforated disc ratio of 0.14, while in Figure 8d,the efficiency is the function of corrugation angle and Re, and is plotted at a constantcorrugation pitch ratio of 1.4, perforation ratio of 0.45, and perforated disc ratio of 3.5.From the figures, it can be detected that the efficiency is decreasing with the increase of Reand increasing corrugation angle, and the new ANN model for this particular study is veryclosely shadowed in the experimental pattern [50]. From the figures, one can see that the

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thermohydraulic efficiency is maximum (η = 2.36 to 2.54) when the corrugation angle is at90◦ and Reynolds numbers are between 8000 and 10,000.

Both the models (for Nusselt number and efficiency) will ease a very huge workload bydetermining the required outputs. With the given test data, as mentioned in Tables 9 and 10,researchers working with a similar experimental setup can use these models to help to tunetheir parameters according to their needs and obtain their required results. It is importantto note and consider an error factor of ±3% while considering the results.

5. Conclusions

Based on the experimental investigated results, a new artificial neural network modelwas offered for the prediction of Nusselt number (Nu) and thermohydraulic efficiency (η)by using machine learning techniques. From the analysis, the following points were made:

1. An ANN model was used for regression analysis to predict the heat transfer andthermohydraulic efficiency.

2. Two different models were trained based on the features of experimental data, which pro-vide an estimation of experimental output based on user-defined input parameters.

3. The models were evaluated to have an accuracy of 97.00% on unknown test data4. The proposed model was able to reasonably forecast the Nu and thermal efficiency.5. Artificial neural networks can be an important method for HT prediction, mainly when

large datasets are being used.6. The proposed models will help researchers working in heat transfer enhancement-

based experiments to understand and predict the output.

Author Contributions: Conceptualization, S.B., S.C. and R.R.; methodology, S.B., D.S., S.C., and R.R.;software, V.G..; validation, E.A. and V.G.; formal analysis, V.G., E.A., S.B. and S.C.; investigation, S.C.,R.R., E.A. and D.S..; resources, E.A.; data curation, S.C. and R.R.; writing—original draft preparation,S.B., S.C. and V.G.; writing—review and editing, V.G. and E.A.; supervision, S.B. and V.G.; projectadministration, E.A. and S.B.; funding acquisition, S.B. All authors have read and agreed to thepublished version of the manuscript.

Funding: The authors would like to gratefully acknowledge Birla Institute of Technology andScience, Pilani, Pilani Campus, for their funding (research grant—ACRG) in this optimization andprediction research.

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Data Availability Statement: Data is contained within the article.

Acknowledgments: The authors would like to gratefully acknowledge Birla Institute of Technologyand Science, Pilani, Pilani Campus, for their funding (research grant—ACRG) in this optimizationand prediction research. Authors also would like to show their gratitude towards Sam Casting,MCKVIE and Devendra Kumar Vishwakarma for helping in this paper.

Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

A cross-sectional areaANN artificial neural networkDh hydraulic diameter, md corrugation depthe cut depth, mf friction factorh heat transfer coefficient, W.m−2·K−1

HT heat transfer

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j Colburn j-factork perforation ratioL tube length, mm mass flow rate of working fluid, kg/sML machine learningNu Nusselt numberP pitchPD pressure dropPr molecular Prandtl numberq heat flux, W·m−2

Re Reynolds numberRw average thermal resistance of wall, ohms perforated disc pitch ratioV bulk velocity, m·s−1

y corrugation pitch ratioGreek Symbols∆P pressure drop, Paη thermohydraulic performance factorθ corrugation angle

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