Applications of intelligent methods in solar heaters: an updated review

Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=tcfm20 Engineering Applications of Computational Fluid Mechanics ISSN: (Print) (Online) Journal homepage: www.tandfonline.com/journals/tcfm20 Applications of intelligent methods in solar heaters: an updated review Mohammad Alhuyi Nazari, Azfarizal Mukhtar, Ahmad Shah Hizam Md Yasir, M. M. Rashidi, Mohammad Hossein Ahmadi, Vojtech Blazek, Lukas Prokop & Stanislav Misak To cite this article: Mohammad Alhuyi Nazari, Azfarizal Mukhtar, Ahmad Shah Hizam Md Yasir, M. M. Rashidi, Mohammad Hossein Ahmadi, Vojtech Blazek, Lukas Prokop & Stanislav Misak (2023) Applications of intelligent methods in solar heaters: an updated review, Engineering Applications of Computational Fluid Mechanics, 17:1, 2229882, DOI: 10.1080/19942060.2023.2229882 To link to this article: https://doi.org/10.1080/19942060.2023.2229882 © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. Published online: 31 Jul 2023. Submit your article to this journal Article views: 806 View related articles View Crossmark data ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 2023, VOL. 17, NO. 1, 2229882 https://doi.org/10.1080/19942060.2023.2229882 REVIEW ARTICLE Applications of intelligent methods in solar heaters: an updated review Mohammad Alhuyi Nazaria, Azfarizal Mukhtar b, Ahmad Shah Hizam Md Yasirc,M.M.Rashidi d, Mohammad Hossein Ahmadie, Vojtech Blazekf, Lukas Prokopfand Stanislav Misakf aFaculty of New Sciences and Technologies, University of Tehran, Tehran, Iran; bInstitute of Sustainable Energy, Putrajaya Campus, Universiti Tenaga Nasional, Kajang, Malaysia; cFaculty of Resilience, Rabdan Academy, Abu Dhabi, United Arab Emirates; dInstitute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, People’s Republic of China; eFaculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran; fENET Centre, VSB—Technical University of Ostrava, Ostrava, Czech Republic ABSTRACT Heating and thermal comfort have remarkable share of final energy consumption. Until now, most of the demand for heating applications in buildings is supplied by fossil fuels and electrical technologies. Concerning the exhaustion of fossil fuels in the future and the environmental problems related to their consumption, making use of renewable energy sources can be a practical alternative. On this point, solar energy is an appropriate source to be applied for heating by utilizing different technologies. The function and output of solar heaters depends on numerous factors, and this causes difficulties in the prediction of their performance and modelling. In this scenario, intelligent techniques are helpful and have been used by several scholars in recent years. This paper reviews proposed models for the prediction of the performance of different solar heaters. The literature review reveals that artificial neural Networks represent one of the most used approaches for the performance prediction of solar heaters; however, other intelligent techniques, namely support vector machines, have been used for this purpose too. Moreover, it is found that these methods have the ability to predict with great precision by applying the appropriate approach and architecture. In addition, it can be noted that the function of the models generated based on intelligent techniques are associated with some elements such as the employed function and architecture of the model. ARTICLE HISTORY Received 23 January 2023 Accepted 21 June 2023 KEYWORDS Solar heaters; intelligent methods; artificial neural network; renewable energy 1. Introduction Building sector decarbonization is significantly crucial to mitigating climate change since this sector is responsible for around 40% of overall energy utilization and 35% of total emission of greenhouse gases in the world (Ahmed et al., 2022). Heating has a notable rôle in the amount of energy consumption in the world, especially in the residential sector. Around 50% of building energy demand in 2021 was for water and space heating, which led to the direct emission of 2450 Mt CO2. Despite the growing trend for making use of clean energy technologies for heating, fossil fuels are responsible for more than 60% of heating demand in the world (Goodson et al., 2022). Regarding net zero scenario milestones, it is necessary to accelerate decarbonization in heating by 2030 (Goodson et al., 2022), which necessitates substituting current technologies with cleaner ones. For this purpose, making use of promising systems with lower emissions such as district heating, heat pumps and renewable-energy-based technologies have been recommended. Renewable-energy sources can be applied CONTACT Azfarizal Mukhtar [email protected]y for heating by implementing different technologies and tools. For instance, biofuels can be used in heat pumps in order to supply thermal energy to buildings in an efficient and environmentally-friendly way (Blázquez et al., 2021). Aside from biofuels, other renewable energies like solar and geothermal are applicable as the heat source for heat pumps (Fang et al., 2020;Selfetal.,2013;Soltani et al., 2019). Besides single-source heat pumps, it is possible to integrate heat pumps with more than one renewable energy source, e.g. solar and geothermal (Choi et al., 2014). In addition to indirect heat generation using renewable energy sources, it is possible to extract thermal contentdirectlyanduseitforspaceorwaterheating. Solar heaters are among the clean and renewable energy-based systems applicable for air, space or waterheating (Kashyap et al., 2023;Pateletal.,2023). Several studies have analysed the function of solar heaters and the elements influencing their output. For instance, Said, Ghodbane, et al. (2021)investigatedtheperformance of a Linear Fresnel solar Reflector (LFR) water heating system. Their findings revealed that the maximum © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent. 2M. A. NAZARI ET AL. temperature was observed on the tube of receiver and afterithotwaterhadthehighesttemperature.Inaddition,theynotedthat,fortheconsideredsystemwiththe ability to heat 0.4 m3ofwaterperday,theCO 2mitigation was equal to 247.14 kg. Al-Askaree and Al-Muhsen (2023) analysed the function of a Solar Water Heater (SWH) consisting of a serpentine fin core heat exchanger. Itwasstatedthatanincreaseinthewaterflowspeed caused adecrease inefficiency, sincethe acceleratedwater period in large quantities was not enough to heat that amount of water. There are some ideas for the enhancement of the performance of SWHs. For instance, Nazari etal.(2022)applieda CuOnanostructurecoatingtoaserpentine tube flat plate SWH. They stated that, by using the coating on the absorber surface, the absorption of solar radiation was increased, which led to an increase in the outlet temperature. This caused an improvement in the exergy efficiency of the collector by 11.2% in comparison with the absorber without a coating. Thangavelu et al. (2021) analysed the effect of the area of a solar collector on the exergetic dimensions of an SWH usable on a domestic scale. They noted that an increase in the collecting area would decrease the exergy efficiency. Furthermore, it was concluded that the exergy destruction cost rate was higher in cases where collectors with larger area were used. Gunasekaran et al. (2021)investigatedthe influence of the utilization of twisted tape on the function of an evacuated tube collector SWH. They concluded that the insertion of twisted tape having twist ratios of 2 and 3 induced efficiency modification by 6.8% and 4.6%, respectively. Said, Ghodbane, et al. (2021)implemented a 4E (Energy, Exergy, Economic and Environment) analysis of a linear Fresnel reflector usable for hot water production. They noted that the cost of the reflector was US$378.87, which could be recovered after 16 years from first utilization. Moreover, the environmental analysis revealed that the CO2mitigation potential of the designedsystem,havingadailyhotwaterproductionof 4m 3, was 247.14 kg. As well as SWHs, heaters used for air have been considered and studied in various research, namely Akhbari et al. (2020) analysed the function of a Solar Air Heater (SAH) with a triangular channel and found that the highest thermohydraulic performance was obtainable with an internal peak angle of the channel equal to 60°, for cases between 35° and 60°. Moreover, it was observed that, for a certain thermal efficiency, the designed air heater needed alowersurfaceareaincomparisonwithaflatplateheater. Jouybari and Lundström (2020)investigatedtheperformance of an SAH by using a thin porous material as a coverfortheabsorberplate.Thehighestincrementinthe thermohydraulic and thermal performance of the system with porous material was more than five times that of the systems without that medium. Hassan et al. (2020) proposed a new architecture for SAH by replacing the flat absorber plate with adjacent tubes and found that, by using the new design, the system mean daily efficiency increases by up to 132.6% in the case of an air mass flow rate of 0.075kg/s. D. Wang et al. (2020)appliedan ‘S’-shapedribsgaponanSAHandfoundanotableelevation in the efficiency in comparison with the system with a smooth plate. Afshari et al. (2020)assessedthe influence of turbulators modification on the function of an SAH and found that heater maximum efficiency can reach up to 72.41%. Shetty et al. (2020)didastudyon theimpactofperforationontheoutputofacrossflow SAH and reported that an increment in the quantity of perforations induced a remarkable increment in the thermohydraulic efficiency, despite a marginal reduction in the thermal efficiency. Some researchers have focused on SAHs with storage units (Baig & Ali, 2019). For instance, Sajawal et al. (2019) experimentally analysed a double passSAHwithafinnedtubePhaseChangeMaterial (PCM). They reported that the utilization of PCM in the system increased the performance and output of the SAH. Complex system modelling can be performed by applying intelligent methods, namely Support VectorMachines(SVMs)andArtificialNeuralNetworks (ANNs) (M.M. Rashidi et al., 2021). These techniques have been applied in modelling different thermal and renewable energy systems and utilized materials (Razavi et al., 2019). For instance, Alotaibi et al. (2020)made useofGroupMethodsofDataHandling(GMDH)and Multivariate Adaptive Regression Splines (MARSs) for estimating the thermal conductivity of some nanofluids and reported significantly good performance of GMDH in the modelling. In other research (M.H. Ahmadi et al., 2019), GMDH was employed for forecasting the thermal resistance and effective thermal conductivity of oscillating heat pipes and it was seen that this method was able to predict the mentioned variables with acceptable precision. Regarding the dependency of solar systems on different elements and parameters, these approaches have been applied for modelling them by different scholars. For example, Sridharan (2020) made use of a generalized regression neural network to forecast the output of asolardryer.Itwasdiscoveredthatthemodelwasable to predict the performance of the system with an overall accuracy of 96.29%. Tripathy and Kumar (2009)applied an ANN to predict the temperature of food in the process of drying in a mixed mode solar dryer. The results indicated perfect exactness of the predictive model with an R2of 0.952. Abujazar et al. (2018)employedanANNfor ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 3 proposing a model for a stepped solar still and generated amodelwithaRootMeanSquareError(RMSE)of 22.48%. Wang, Kandeal, et al. (2021)appliedthreemethods including ANNs, random forests and multilinear regression for solar still function modelling. Determination coefficients of the mentioned models were 0.9614, 0.9758 and 0.9267, respectively. Sohani et al. (2022)made useofanANNtomodelthedynamicperformanceofan enhanced solar still. The created model was able to forecast daily water production with an error in the range 2.41–5.84%. D. Wang et al. (2020)usedanANNtoestimate Photovoltaic (PV) performance by using the data from numerical simulation. The highest relative deviation between the values of the ANN model and the numerical results was around 0.04%. Literature reviews of the utilization of intelligent methods for modelling different solar systems have shown their great performance and high reliability in making predictions. There are some review papers on the usage of these methods for solar systems. For instance, Voyant et al. (2017) provided a review on the usage of machine learning techniques for forecasting solar radiation. In another review study, Mahmood and J.L. Wang (2021) focused on the applications of these techniques to organic solar cells. E. Engel and N. Engel (2022)reviewed the usage of machine learning methods for solar plants. S. Rashidi et al. (2022) provided a review study on the utilization of intelligent techniques for the assessment of solar desalination technologies. Aside from the abovementioned solar systems, these methods are applicable for different kinds of solar heater. For instance, Li et al. (2017) summarized their recent work and proposed a general framework for the design of solar water heaters by making use of a high-throughput screening method corresponding to machine learning approaches. In spite of the existence of different intelligent techniques for modelling solar heaters, no comprehensive and updated review has been found on this subject. In this regard, this study reviews the scientific publications on the employment of intelligent procedures for modelling the characteristics and performance of solar heaters. The main applications of intelligent methods for modelling solar heaters are the performance prediction of these systems with acceptable exactness and precision by a fast procedure. Moreover, the proposed models can be useful in the process of designing new systems to evaluate their performance and feasibility. In this regard, providing a comprehensive review of previous studies would be useful for scholars, engineers and designers working on solar heaters. In addition, some recommendations are produced for application in upcoming works in this area of science. 2. Intelligent methods Different kinds of model on the basis of machine learning methods have been proposed for engineering problems. Thesemodels,onthebasisofthemachinelearningmethods, are attractive for scholars and researchers regarding their advantages, such as remarkable accuracy and fast performance (Ghalandari et al., 2021). In this section, some of the most applicable ones in terms of modelling different solar heaters are briefly introduced. 2.1. MultiLayer Perceptron (MLP) artificial neural network ANNs are among the artificial intelligence concepts inspired by the performance of the human brain in phenomena identification. In MLP ANNs, neurons are located in three or more layers. The 1st, 2nd and 3rd layers are called the input, hidden and output layers. It is possible to use more than one hidden layer in this type of network. A schematic of this network is depicted in Figure 1.X1to Xn(i=1,2, ... ,N)aretheinputsof the network and nrefers to the number of input variables, jrefers to the number of neurons, wji are the weights of neurons and refer to the synapse power of the ith neuron to the jth neuron, yjis the network output, which is the modelling result and target of the model, ujis the combination of the output linear layer and is determined using Equation (1) (khosrojerdi et al., 2016): uj= n  i=1 wjiXi(1) where yj=∅(uj+bj)(2) svj=uj+bj(3) In the above equations, Ø(0)is the activation function and bjrefers to the function tendency. There are various activation functions that are usable in these networks. The Tan-sigmoid and Log-sigmoid are among the most used functions in these models, which are as follows (khosrojerdi et al., 2016): Logsig(x)=1 1−exp(−x)(4) Tansig(x)=2 1+exp(−2x)−1(5) In the abovementioned equations, xis the activation function input. In general, a neural network operates similarly to a function that receives as many inputs as the 4M. A. NAZARI ET AL. Figure 1. MLP ANN schematic. Adapted from khosrojerdi et al. (2016). number of input layer neurons and has as many outputs as the number of output layer neurons (khosrojerdi et al., 2016). 2.2. Group Method of Data Handling (GMDH) Another of the ANN-based model approaches is the GMDH, which is applicable for different systems. In GMDH, the output can be traced back to the variablesutilizedastheinputs.Eachneuroninthisnetwork receives two inputs and provides an output as a function of them. The layers in the GMDH are composed of these types of neuron. Models based on the GMDH are developed and generated by constructing these kinds of layer until a cut-off state is reached. In Figure 2,the basic architecture of a neuron in the GMDH is illustrated. The relationship or function between the inputs andoutputofneuronscanbeofpolynomialtype,suchas parabolic, cubic or linear, as in Equation (6). Linear functionsareveryoftenusedincaseshavingsmalltraining datasets such that the result is not affected by polynomials of higher order. In this condition, the neuron output is determined by employing Equation (6) (Rizvi et al., 2020): Y=C0+C1a+C2b+C3ab (6) In this equation, Yis the output, Cnrefer to the coefficients and aand bare the inputs. In order to determine the output, the coefficients are required. In this regard, to obtain the coefficients, Lagrange interpolation is applied. Two neurons’ inputs are applied to generate a matrix equation (Equation 7) for finding the neurons’ coefficients (Rizvi et al., 2020): ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ m  i=1 1 m  i=1 a m  i=1 b m  i=1 a·b m  i=1 a m  i=1 a2 m  i=1 a·b m  i=1 a2·b m  i=1 b m  i=1 a·b m  i=1 b2 m  i=1 ab2 m  i=1 a·b m  i=1 a2b m  i=1 ab2m i=1a2b2 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ C0 C1 C2 C3 ⎤ ⎥ ⎥ ⎦ = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ m  i=1 Y m  i=1 a·Y m  i=1 b·Y m  i=1 a·b·Y ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ (7) The network input layer acts only as the input provider. The subsequent layer, the 1st hidden layer, receives input from the previous layer when activated. This layer has C(N,2) neurons, in which Nrefers to the number of neurons in the former layer. This network is generated in suchawaythataneuronisthereforeachinputcombination. Each neuron in this layer utilizes the training data for the determination of transfer functions and tries to forecast the testing data output. The standard error is determined by comparing the forecast data with the actual values. In order to avoid network exponential growth,someoftheneuronswithhigherrorsareeliminated. Similarly, the subsequent hidden layer utilizes it ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 5 Figure 2. Schematic of basic neuron architecture (Rizvi et al., 2020). © Elsevier. Reproduced by permission of 5497741000403. as the inputs and the procedure continues to reach the acceptable outputs (Rizvi et al., 2020). 2.3. Least Square Support Vector Machine (LSSVM) Another method applied as intelligent approach in modelling engineering problems and regression is the least square support vector machine. In general, the LSSVM nonlinear function is as shown in Equation (8) (Maleki et al., 2021): f(x)=wTϕ(x)+bias (8) where frefers to the inputs−output relation, wdenotes theweightvectorandϕis employed to convert the inputs into the characteristic vector (M.A. Ahmadi &Mahmoudi,2016; Ramezanizadeh, Ahmadi, Nazari et al., 2019). For topology minimization, a fitting errorfunctionshouldbecalculatedintheprocedure for finding the regression problem output according to Equation (9) (M.A. Ahmadi & Mahmoudi, 2016; Ramezanizadeh, Ahmadi, Nazari et al. 2019): Min J(w,e)=1 2wTw+γ m  k=1 ek2(9) where γis a margin parameter. The limitation equation should be taken into account as follows (Maleki et al., 2021): yk=wTϕ(xk)+b+ek,k=1, 2, ...,m(10) where ekis the looseness variable (M.A. Ahmadi & Mahmoudi, 2016; Ramezanizadeh et al., 2018). Lagrange multipliers, ai, are employed to obtain the optimization process solution. These are defined according to Equation (11) as follows: L(w,b,e,α) =J(w,e)− m  k=1 αi{wTϕ(xk)+b+ek−Yk} (11) Theoptimalstateoftheregressionmaybecalculated by considering the state parameters and implementation of the partial derivatives in the following equation: ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ w= m  k=1 αiϕ(xi) m  k=1 αi=0 αi=γei wTϕ(xi)+b+ei−Yi=0 ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ (12) For linear formulation of these equations, Equation (13) is applied (Maleki et al., 2021): 0−YT YZZ T+1/γ b α=0 1(13) In the above equation, Y,αand Zare defined as {Y=Y1;... ; Yym},α=[α1,... ,α1]andZ=ϕ(X1)T Yi,... ,ϕ(Xm)TYm, respectively. Utilizing the kernel function as K(X,Xk)=ϕ(X)Tϕ(Xk), i=1,2, ... ,m,the LSSVM regression is calculated according to Equation (14) (M.A. Ahmadi & Mahmoudi, 2016; Ramezanizadeh, Ahmadi, Nazari et al., 2019): f(x)= n  k=1 αkK(x,xk)+b(14) One of the most conventional kernels in regression error is the radial basis as in Equation (15) (M.A. Ahmadi & Mahmoudi, 2016; Ramezanizadeh, Ahmadi, Nazari et al., 2019): K(x,xk)=exp −xk−x2 σ2(15) where σ2isthesquaredbandwidth.Thevalueof this parameter is calculated by using an optimization approach in which the Mean Squared Error (MSE) is the objective function of the problem. 2.4. Adaptive Neuro Fuzzy Inference System (ANFIS) A schematic of the Adaptive Neuro Fuzzy Inference System (ANFIS) model in with an output and two inputs is provided in Figure 3.Accordingtothisfigure,there are five layers in this model type. In the first layer, the inputs are converted into fuzzy sets on the basis of fuzzy membership functions. Afterwards, the input signals are created in the next layer and the related weight of the membership functions are checked. Subsequently, in the next stage normalized firing strength is determined for the nodes. In the subsequent layer, the 4th layer, the results are converted into defuzzified sets. In the last layer,theoutputsofthemodelareprovided.Inthislayer, the summation of all the input signals, obtained from thepreviousstage,aredefined(Ramezanizadeh,Ahmadi, Nazari et al., 2019). 6M. A. NAZARI ET AL. Figure 3. ANFIS schematic for one output and two inputs (Ramezanizadeh, Ahmadi, Ahmadi, et al., 2019). ©Elseveier. Reproduced by permission of 5592070599260. 3. Operating principle of solar heaters In solar heaters, the energy content of a solar beam is utilized in order to increase the temperature of the operating fluid. Depending on the required application, different components can be employed in these technologies. Generally, the main applications of solar heaters, particularly in buildings, are increasing the temperature of air or water. In Figure 4, a schematic of a simple SAH is provided. In SAHs, an absorber plate is employed to collect solar irradiance and transmit the thermal energy to the air flow through the duct. Moreover, glazing is employed on the glass top surface to boost solar radiation absorption.Furthermore,insulationisusedtodecreaseheat loss from the system (Ghritlahre et al., 2021). It is one of the simplest SAH configurations; however, some additional components such as baffles, fins, etc. can be utilized to increase the performance. Moreover, it is possible to enhance the performance further by applying some ideas such as making use of corrugations on the absorber or utilizing porous materials. In addition, more passages can be used in SAHs in order to split air streams to decrease the system top loss (Goel et al., 2021). In Figure 5, classifications of SAHs based on the configuration and employed components are provided. Aside from air, solar heaters are applicable for increasing the temperature of other media such as water, which is another type focused on in this research work. Similar to air, solar beam energy is extracted for increasing the energy content of water. Heating of water can be done directly or indirectly as shown in Figure 6.Inthedirect configuration, solar water is circulated in the collector Figure 4. Conventional SAH schematic. Adapted from Ghritlahre et al. (2021). and directly heated up by receiving thermal energy from the collector, while in the indirect type, a heat transfer medium receives heat from the collector and transfers it to water in a heat exchanger. Aside from the heat transfer, other factors affect the classification of SWHs such as the fluid circulation mechanism, active or passive. In active systems, additional components such as pumps are employed for the circulation of water, while in the passive type, circulation is due to buoyancy. Collector ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 7 Figure 5. Classifications of SAHs. Adapted from Oztop et al. (2013). systems are other parameters considered in the classification of SWHs. In Figure 7,theclassificationofSWHsis represented. In both SWHs and SAHs, additional units such as storage components can be used to enhance the output and extend operating hours. Moreover, these systems can be integratedorcoupledwithothertechnologiessuchas auxiliary heaters. 4. Applications of intelligent methods for solar heaters Solar heaters, as clean technologies, are mainly used in buildings for heating water and space (Liu, Li et al., 2015). Similar to other solar systems, there are some complexities in their performance prediction. In addition, different factors are involved in their output that necessitate making use of appropriate methods yielding great exactness of prediction (Calderón-Ramírez et al., 2022; Kalogirou et al., 1999).Despitetheexistenceof some numerical methods and developed software for modelling these systems, there are some advantages in making use of intelligent methods such as less computational time and cost (Ghritlahre et al., 2020a). In this regard, several scholars have applied intelligent methods to generate predictive models for modelling different characteristics of solar heaters. 4.1. Applications of ANNs for modelling solar heaters Predictive models are applicable for solar heaters and their components with different architectures and configurations. Regarding the dependency of the output of these systems on various elements, these factors must be included in the inputs of the models. One of the most important factors in the output of solar systems is solar radiation. Generally, the output of solar systems increases with solar radiation regarding elevation in the absorbed energy. In addition to solar radiation, there are some other factors depending on the system that influence solar systems output. In this regard, different inputs have been considered in the proposed models for solar heaters. For instance, Bhattacharyya, Sarkar et al. (2021) utilized ANNs to predict the Nusselt number (Nu) and efficiency of helical corrugation with a perforated circular SAH tube using five inputs. The architecture of the models is shown in Figure 8. In order to propose a model, theyutilized experimentaldataobtained intheirprevious work (Bhattacharyya et al., 2020; Bhattacharyya, Pathak et al., 2021). In the experimental study, it was found that theNunumberremarkablyenhanceswithelevationin the Re number, showing the increasing convective heat transfer. In addition, it was shown that the rate of energy transfer increases with decreasing spring and hole ratio. Thereasonbehindthiswasshowntobeswirl/secondary flow and increasing pressure gradient along the radial direction owing to the insertion of spring tape. Moreover, tape with holes induced the development of vortices behindthecirculartubethatcausedelevationintheturbulence and boosted heat transfer (Bhattacharyya et al., 2020). In another experimental study (Bhattacharyya, Pathak et al., 2021), it was observed that the Nu number increased with the elevation of corrugation angle, while in the case of constant angle of corrugation, the Nu number decreased with the elevation of corrugation pitch ratio. In the case of Nusselt number prediction, the accuracy of trainingand test sets was 99.90% and 99.96%, 8M. A. NAZARI ET AL. Figure 6. Schematic of (a) direct SWH and (b) indirect SWH. Adapted from Torshizi and Mighani (2017). respectively, while these values were 99.91% and 99.98% for the mentioned sets, respectively. Souliotis et al. (2009) made use of ANNs to forecast the function of an Integrated Collector Storage (ICS) SWH. The inputs of the created model were ambient temperature, month, speed of wind, total radiation and incidence, and the output was the average temperature of the storage tank. A small deviation was observed between the modelled and the actual average temperature. There are some ideas for modification of solar heaters such as using ribs, fins, baffles, etc. (Saravanakumar et al., 2019; Sivakandhan et al., 2020; Yadav et al., 2022). The performance of solar heaters with these modifications is predictable by intelligent methods. Forinstance,inastudy(Jainetal.,2021), experimental data were used for modelling a SAH with a multi-gap V-roughness with staggered elements. The experimental data showed that, at the higher end of Re numbers, the V-geometry with P/e (relative roughness pitch) of 12 provided better thermal efficiency in comparison with the case of P/e’s of 8, 10, 14 and 16, while in cases at ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 15 heaters are integrable with other energy technologies such as thermoelectric generators (Chargui et al., 2022) andgeothermal systems (Qinetal.,2021), it could be suggested to generate models by using intelligent methods for these types of system. Moreover, since the performance of various intelligent techniques depends on different factors, it is useful to consider influential parameters to obtain better models. For instance, in intelligent methods coupled with optimization algorithms, the optimization method can influence the precision of the proposed model. As an example, in a study by Ramezanizadeh, Ahmadi, Ahmadi et al. (2019) on the dynamic viscosity estimation of Al2O3/water nanofluid, different optimization algorithms, namely GAs, PSO, Hybrid GA PSO (HGAPSO) and Imperialist Competitive Algorithms (ICAs) were used in LSSVM methods. Their findings showed that making use of GAs led to the maximum value of the correlation coefficient among the applied algorithms. In another study (Alarifi et al., 2019a), the performance of PSO-ANFISs and GA-ANFISs in the modelling of the thermophysical properties of a hybrid nanofluid was compared, and it was pointed out that the utilization of PSO as optimization algorithm can lead to better performance. It seems that the performance of optimization algorithms and their selection based on the highest accuracy of the generated model are dependent on the problem and applied modelling method. In MLP ANNs, different training and transfer functions can be used that can affect the outputs of the model and their closeness to the actual data. For instance, in a study by M.M. Rashidi et al. (2023) on the thermal conductivity of some nanofluids, Tan-sigmoid and radial basis functions were applied in an MLP ANN and it was reported that utilization of radial basis functions can provide a model with higher accuracy for their case study. Similar to the optimization algorithm, selection of the best function can be case-dependent. 7. Conclusion Intelligent techniques are usable for theperformance forecasting of various kinds of solar heaters. The key conclusions are summarized as follows. •Intelligent procedures are applicable for performance forecasting of both air and water heaters. •Intelligent methods are utilizable for modelling different characteristics of solar heaters including Nusselt number, friction factor, outlet temperature, etc. •Weather data and working conditions are among the mainfactorsincluded as theinputs ofintelligentmethods. •In comparison with linear regression, intelligent techniques provide higher prediction exactness. •The precision of the developed models depends on some elements such as model architecture and the functions used. •Asidefromthestructureandfunction,theinputs impact the exactness of the models. Nomenclature aInput bInput bjFunction tendency CCoefficient of polynomial ekLooseness parameter uCombination of output linear layer WWeight of neuron Xiith input YOutput Greek letters ϕActivation function γMargin parameter σBandwidth Abbreviations ANN Artificial Neural Network ANFIS Adaptive Neuro Fuzzy Inference System GMDH GroupMethodofDataHandling GRNN General Regression Neural Network ICA Imperialist Competitive Algorithm LSSVM Least Square Support Vector Machine MARS Multivariate Adaptive Regression Spline MLP Multilayer Perceptron MLR Multiple Linear Regression MSE Mean Squared Error RBF Radial Basis Function SAH Solar Air Heater SWH Solar Water Heater Disclosure statement No potential conflict of interest was reported by the authors. Funding Thispaper wassupportedbythefollowingproject TN02000025 National Centre for Energy II. ORCID Azfarizal Mukhtar http://orcid.org/0000-0002-7792-0767 16 M. A. NAZARI ET AL. 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