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Adaptive overheating cover for a solar water heater

Adaptive overheating cover for a solar water heater Abstract Solar water heating systems have been widely used around the world. However, exposure to sunlight can overheat the device, affecting the efficiency and durability of the system. This article proposes an adaptive deck controller that protects the system from overheating without compromising the availability of domestic hot water. Solar water heaters are considered one of the most effective ways to reduce a home’s carbon footprint. They are a renewable energy source that reduces reliance on fossil fuels and saves money. Thus, this paper aims to develop a dynamic cover for solar water heaters that prevent overheating using an artificial neural network to optimize the design of control systems. Based on a self-organizing map network, the controller automatically adjusts the temperature of the solar collector through a fabric screen covering the main subsystems, depending on many parameters such as weather conditions, collector temperature and domestic hot water depending on demand. A suggested technique of four different shade percentages (0%, 20%, 25% or 32%) can avoid overheating and maintain the amount of hot water the home needs. Although renewable energy is free, proper controls are required to ensure maximum efficiency or proper use. In addition, the control of renewable energy leads to longer service life. Open in new tabDownload slide durability, efficiency, overheating, solar water heater, self-organizing map (SOM), temperature control Introduction Solar water heater systems absorb energy from solar radiation to produce hot water for several applications. The use of such a system replaces the consumption of fossil fuels and natural gas. Hence, it minimizes global pollution and reduces the associated environmental impact [1]. Common problems of solar water heater (SWH) systems are overheating, water leakage, lack of water storage and other minor technical problems such as corrosion and calcification. While the SWH system is expected to supply hot water during the hot summer season, it appears to be unfavourable and inconvenient due to the moderate demand for hot water during summer. The overheating phenomenon occurs when the boiling point is reached and the heat can no longer be dispersed because the energy delivered by the solar collectors exceeds the heat-storage capacity and the energy demand [2]. Moreover, fatigue failure might occur to the system, increasing the cost of repairs and maintenance and lowering the system life span [3]. Energy-storage capacity is also a minor concern, especially with shared heating systems [4]. Also, power prediction is a minor concern for a short time due to the high capacity of the SWH [5]. Detection and prevention are always better at first [6]. Tiwari et al. developed a photovoltaic thermoelectric flat-plate collector; the model comprised a semi-transparent photovoltaic module combined with thermoelectric modules and a tube-sheet arrangement for the water flow. The proposed system had an electrical energy gain of 3.96–14.38 W and useful thermal energy of 41.14–148.72 W [7]. Sharma et al. designed a flat-plate solar collector for spice drying. Closed-loop air circulation was settled with a single-cover solar collector. The flat plate had a surface of 2.1 m2 to carry 10 kg of cardamom. Simulation results indicated that the maximum absorber temperature was 68°C and the air temperature at the collector’s output varied between 40°C and 55°C for 6 hours per day, which was sufficient for drying spices [8]. Mekali et al. developed a temperature-control system for a SWH. It was a closed-loop control system based on a supplementary heat source to assure obtaining hot water at any desired temperature [9]. Kirpichnikova and Makhsumov suggested a prototype concerning the overheating protection for solar cells. They attached a holographic film to the cell’s surface to reduce the effect of overheating. The study proved the effectiveness of the film by reflecting the infrared spectrum of the solar radiation, which decreased the surface temperature of the covered cell and increased the generated power [10]. Diez et al. operated a flat-plate solar collector with computational intelligence techniques. An artificial neural network was trained to predict the outlet collector temperature using measured ambient and inlet temperatures, solar irradiance and working fluid flow. Several tests with different artificial neural network architectures were carried out to achieve accurate results [11]. Jullian et al. presented an estimation of deep learning models that were trained under several meteorological situations to predict the performance framework of the solar thermal system. A physical simulation was established in the transient system simulation software to generate operational data in nominal circumstances. Different models with several configurations were suggested for temperature assessment [12]. This paper proposes a shading control system. The novelty of the system relies on a low-price implementation of the solution in which only a few pieces of hardware are required. In addition, the application of a self-organizing map (SOM) model can adapt to household utilization. The system design details are discussed in Section 1. Section 2 consists of software implementation. Accordingly, a model for the SWH system and the artificial neural network is discussed. Sections 3 and 4 include the training and testing of the whole system and its validation. Section 5 contains a conclusion and some proposed future perspectives to develop this system. 1 Proposed control system This section presents in detail the proposed design of the control system. Fig. 1 represents the block diagram of the proposed system. The days (working or holiday), the weather conditions, the temperature of the solar thermal collector and the household hot-water demand are measured. Depending on the input values and based on the artificial neural network model, the solar collector will be fully unshaded, 20% covered with a shade, 25% covered or 32% covered using a DC motor. The whole system can be turned off by a push button. Fig. 1: Open in new tabDownload slide Block diagram of the proposed system showing the inputs and output. The system is based on a controller and a DC motor. The latter tends to spread and fold the covering shield. A fabric that is fused to the motor can cover or uncover the solar thermal collector, as illustrated in Fig. 2. While covering the collector, the appropriate shade protects the system from overheating by reflecting the incident solar radiation as well as providing resistance to environmental outdoor conditions. Fig. 2: Open in new tabDownload slide System layout. 2 Software implementation This section will be dedicated to showing the implementation of the system. Thus, a mathematical model for each of the solar thermal collectors and the storage tank will be developed along with the SOM model. The artificial neural network training, its data sets and its results will be presented in this section. 2.1 Solar thermal system model The SWH system can be divided into two subsystems. The primary subsystem collects solar energy and stores it. It contains the heat-transfer fluid, the solar collector and the insulated pipes. The secondary subsystem comprising a thermal storage tank receives the collected energy from the primary circuit and stores the heat for later consumption [13]. Each of the primary and secondary subsystems is mathematically modelled to simplify the simulation configurations in MATLAB®. 2.1.1 Primary subsystem model Fig. 3 illustrates a schematic drawing of the energy flow through a flat-plate solar collector. Typically, the solar radiation crossing the glass cover of the collector is partially reflected and slightly absorbed by the transparent glass. The rest of the sunlight penetrates the glazing and strikes the metal absorber plate. When it reaches the absorber, a further portion is reflected via radiation and the remaining part is well absorbed by the blackened surface [14]. Fig. 3: Open in new tabDownload slide Energy flow through a flat-plate solar collector [14]. Fundamentally, the solar energy Qs received by the collector’s absorber surface is expressed in Equation (1): Qs=IAcηo(1) where I represents the intensity of the solar radiation (W/m2), Ac represents the surface area of the collector (m2) and ηo represents the optimal efficiency, which depends on the transmission of the glass and the absorption of the absorber plate. In conjunction with the solar energy represented in Equation (1), the thermal loss Ql due to reflection, convection and radiation can be determined using Equation (2), taking into account the heat-transfer coefficient U (W/(m2.K)) and the collector temperature. Thus, increasing the temperature and/or the heat-transfer coefficient increments the heat loss Ql: Ql=UAc(Tc−Tambient)(2) Simultaneously, the heat absorbed by the primary circuit of the collector Qp can be determined by the correlation of the logarithmic mean temperature difference (LMTD) method, the heat-loss coefficient of the primary circuit Up (W/(m2.K)) and the surface area of the tube Ar (m2): Qp=UpAr(LMTD)(3) From Equation (3), the LMTD is determined by the difference of the inlet Tcin, outlet Tcout and collector Tc temperatures (K), as displayed in Equation (4) [15]: LMTD=(Tc−Tcout)−(Tc−Tcin)ln(Tc−TcoutTc−Tcin)(4) Hence, the state equation of the collector is calculated in Equation (5) where ρAl represents the density of the aluminium (kg/m3), cAl represents the specific heat capacity of the aluminium (J/(kg.K)) and Vc represents the volume of the collector (m3): (ρAlcAlVc)dTcdt=Qs−Ql−Qp(5) Moreover, the heat absorbed by the fluid Qf ⁠, defined in Equation (6), is determined by the difference in temperature between the outlet collector and the inlet collector, the volumetric flow rate F (L/s), the density of the heat-transfer fluid ρ (kg/L) and its specific heat capacity c (J/(kg.K)) [14]: Qf=Fρc(Tcout−Tcin)(6) Therefore, the energy balance applicable to the primary circuit is shown in Equation (7), where Vf represents the volume of the fluid passing through the collector (L): (ρcVf)dTcoutdt=Qp−Qf(7) 2.1.2 Secondary subsystem model The thermal storage tank is connected to the collector and the load concurrently. It receives the cold water to transmit it to the collector and it supplies the appliances with the collected warm water. In this analysis, losses in the secondary system are neglected. The thermal output of the storage tank Qout ⁠, expressed in Equation (8), depends on the generated temperature difference, the volumetric flow rate of hot-water consumption Fw (L/s), the water density ρw (kg/L) and the water-specific heat capacity cw (J/(kg.K)): Qout=Fwρwcw(Tcin−Tambient)(8) The heat received by the storage tank increases the water’s temperature; the energy balance of the insulated water-storage tank is described in Equation (9): (ρwcwVtank)dTtankdt=Qp−Qout(9) 2.2 SOM model The artificial neural network is a processing model used in machine learning to imitate the biological neural network. The human brain comprises the interconnected neurons that send information to different parts of the body as a reaction to an action performed. The artificial neural network consists of neurons known as nodes connected in parallel; these nodes are the core processing units of the neural network. It is a set of connected units and each connection is associated with a weight [15]. On the other hand, the SOM is a special type of artificial neural network that provides a topology between input and output spaces. It is a technique for dimensionality reduction, as it plots high-dimensional inputs to a 2D discretized representation. Since the entire learning executes without any supervision, the nodes, known as feature maps, are self-organizing and the input vectors are clustered according to their similarities to produce a 2D grid. Fig. 4 illustrates the flowchart for the SOM technique. The algorithm launches by initializing the weight vectors and selecting a sample vector randomly. Then, the Euclidean distance is computed between each node of the weight vector and the current input vector, as determined in Equation (10), where x is the input vector and wij is the weight connecting the node (i,j) with the input: Fig. 4: Open in new tabDownload slide Self-organizing map flowchart. x→−w→ij=∑nt=0[x→(t)−w→ij(t)]2(10) Afterward, the winning node that has the smallest distance is called the best-matching unit and its topological neighbours are determined. The synaptic weights of these neurons are updated using Equation (11): w→ij(t+1)=wij(t)+αij(t)[x(t)−wij(t)](11) where αij represents the learning rate that is expressed in Equation (12), where t represents the current iteration and λ represents the time constant: α(t)=α0e(−tλ)(12) The computation continues until there are no noticeable modifications in the feature map. The SOM constitutes two layers of processing units: an input layer and an output layer, as shown in Fig. 5. The input layer receives five inputs from the environment and contains the days, the solar radiation, the difference between the collector temperature and the ambient temperature, the difference between the collector temperature and its maximum, and the household hot-water demand. It does not have any hidden layers. The output layer determines the predicted cluster that can be fully unshaded, 20% covered with a shade, 25% covered or 32% covered. During the training phase, the SOM adjusts its weights by applying competitive learning, which is opposed to error-correction learning. Fig. 5: Open in new tabDownload slide Self-organizing map architecture. 3 System training The unlabeled training data sets have been recorded, the artificial neural network has been created and trained using unsupervised learning, and its performance has been evaluated using a variety of visualized tools. 3.1 Data sets A total of 2208 samples for the three months of June, July and August are used as a training data set. These inputs are simulated using the model developed in Section 2. And using the parameters shown in Table 1. Particularly, the data have been created employing simulation using the SWH model developed by the authors. The raw inputs are solar radiation in W/m2, ambient air temperature in °C, storage-tank temperature in K, outlet water-collector temperature in K, collector temperature in K and household water consumption in L/h. The solar radiation in W/m2 and ambient air temperature in °C were retrieved from online sources for Beirut, Lebanon for June, July and August 2018 with an hourly frequency [16]. Fig. 6 shows the average collector temperature over the month. The attained peaks were positioned at 15:00. Fig. 6: Open in new tabDownload slide Monthly average collector temperature in K. Fig. 7 shows the monthly average household hot-water consumption per hour for a family of four persons over a day. It is assumed that each person consumes 30–50 L/day of hot water, with respect to the warm-water usage split between morning and evening time, and the variation between weekdays, weekends and holidays. Fig. 7: Open in new tabDownload slide Monthly average household hot-water consumption in L/h. 3.2 Feature extraction The input vector of the artificial neural network has five inputs, which are: days (whether weekday or holiday); solar radiation; difference between the collector’s temperature and the ambient temperature; difference between the collector’s temperature and its maximum; difference between total daily household hot-water demand and total consumption of the day until the present time. Feature extraction is a process used to reduce the set of raw data into more feasible groups. It combines effectively a large number of processing variables into features to minimize the machine’s efforts and accelerate the learning speed without losing information or affecting the accuracy. One of the obtained features is the difference between the temperature of the collector and the ambient air temperature. This feature gives a relative indication of the heating of the collector. Fig. 8 shows the monthly average of this feature as a function of the daytime. Fig. 8: Open in new tabDownload slide Monthly difference between the collector and ambient temperatures. Another important feature is the difference between the collector’s temperature and the maximum temperature that we would like not to exceed. Accordingly, a limit of 80°C or 353.15 K is maintained to ensure a longer lifespan for the SWH. The desired maximum temperature of 80°C has been chosen because it should fall between 60°C (hot-water temperature) and 100°C, which is considered the boiling temperature of water at atmospheric pressure. Fig. 9 shows the average of this feature for the 3 months as a function of the time of day. Fig. 9: Open in new tabDownload slide Monthly difference between the collector temperature and its desired maximum. The difference between the household water consumed for the day until the present and the average daily demand is an additional important feature. The latter we calculated from the data sets. This feature is important to control the system ensuring the availability of hot water for the users (refer to Fig. 10 for more details). Obviously, at the end of the day, this feature goes to zero. Fig. 10: Open in new tabDownload slide Monthly average household hot-water demand difference with the total consumption. 3.3 Artificial neural network training The five input data sets have been defined to be clustered using the SOM network, which comprises a competitive layer using the nntool from MATLAB®. The total number of clusters is four, denoted as A, B, C and D as shown in Fig. 11, as exhibited from the displayed architecture of Fig. 5. While training the artificial neural network, the number of reached epochs is 200 iterations. By different iterations, we managed to find that four clusters best suit the application. Fig. 11: Open in new tabDownload slide The four clusters of the self-organizing map with the number of datapoints in each cluster. 4 System testing and validation After achieving the SWH model and the SOM training, this section will include the testing of the whole system. Hence, three implemented approaches will be evaluated and the validation of the system will be detailed in this section. 4.1 Approaches evaluation Three approaches have been performed with the solar thermal and artificial neural network models to designate the most suitable percentages of the collector shading. The latter has to reduce the temperature of the collector’s plate (below < 80°C) to increase its lifespan, and without affecting hot-water availability. 4.1.1 First approach The first approach has been computed to cover the solar thermal collector A (0%), B (10%), C (20%) or D (21%), adaptively. Case C and Case D are close because it is a first-iteration approach. Case D has been chosen to be low or very close to Case C to keep the hot water available. After simulation, the collector’s temperature is obtained. Fig. 12 shows the difference between the collector’s temperature and the desired maximum. The peaks of the temperature were 373.4, 370.55 and 362.06 K in June, July and August, respectively. The temperatures of the collector plate surpassed the desired maximum (80°C) by ~20.4, ~17.55 and ~9 K. The overheating occurred from 11:00 to 18:00 during June and July and from 12:00 to 17:00 during August. Fig. 12: Open in new tabDownload slide Difference between the collector’s temperature and its desired maximum for the first approach. On the other hand, Fig. 13 represents the results of the difference between the storage tank and the desired temperatures. During June, July and August, the temperature of the warm water insulated in the storage tank exceeded its desired temperature (60°C) by ~18.9°C, ~18°C and ~10.5°C, respectively. During the night, the tank-water temperature maintained acceptable values of ~20°C below the desired temperature. Fig. 13: Open in new tabDownload slide Difference between the tank and desired temperatures for the first approach. 4.1.2 Second approach A new approach has been proposed to minimize the collector’s temperature by covering the primary circuit with A (0%), B (20%), C (30%) or D (40%). After simulation, the collector’s temperature is obtained. Fig. 14 shows the difference between the collector’s temperature and the desired maximum (80°C). The collector’s temperature did not attain its maximum. During June, July and August, the temperatures were lower than their maximum by ~3.36, ~3.33 and ~8.16 K, respectively. Fig. 14: Open in new tabDownload slide Difference between the collector’s temperature and its desired maximum for the second approach. The results of the difference between the temperature of the hot water stored in the insulated tank and the desired temperature are displayed in Fig. 15. During the night, the tank-water temperature decreases to unacceptable values of ~33°C below the desired temperature. Fig. 15: Open in new tabDownload slide Difference between the tank and desired temperatures for the second approach. 4.1.3 Third approach The third approach has been set to control the temperature of the SWH system by covering the solar thermal collector A (0%), B (20%), C (25%) or D (32%), autonomously. After simulation, the collector’s temperature is obtained. Fig. 16 shows the difference between the collector’s temperature and the desired maximum (80°C). During June and July, it exceeded the maximum temperature limit of approximately ~2.05°C and 1.5°C for a very short period, whereas the temperatures over August did not pass the maximum. Fig. 16: Open in new tabDownload slide Difference between the collector temperature and its maximum for the third approach. The results of the difference between the temperature of the hot water stored in the insulated tank and the desired temperature are displayed in Fig. 17. During the night, the tank-water temperature maintains acceptable values of ~26°C below the desired temperature. Fig. 17: Open in new tabDownload slide Difference between the tank and desired temperatures for the third approach. While covering 0%, 20%, 25% or 32%, adaptively, of the solar thermal collector, its temperature is well reduced and it does not pass excessively its maximum temperature, as well as the household hot water maintains its desired temperature. Therefore, the third approach suits well the objectives of the proposed control system. 4.2 Functional evaluation The three approaches affect the temperatures of the storage tank, the outlet’s collector and the collector plate compared with the original SWH system. The computed results were conducted on the monthly average effect. Also, detailed discussions on the system functionality are presented using the proposed algorithm. The three approaches that control the system are compared with the uncontrolled one on three consecutive days: 18, 19 and 20 August 2019. The temperatures of the household hot-water storage tank exceeded its desirable value for each of the original systems (refer to Fig. 18 for more details). However, the proposed approach showed good agreement with the desired temperature as well as saving the system from any failure. Fig. 18: Open in new tabDownload slide Comparison between three approaches for the desirable tank temperatures for 3 days. The collector’s temperatures were lower than their undesired point while covering the primary subsystem with the second approach and the third one, as manifested in Fig. 19, for 72 consecutive hours. Fig. 19: Open in new tabDownload slide Comparison between three approaches for the desirable collector temperatures for 3 days. Using a SOM network, and with proper configuration, the applied method can be applied to different fields of energy systems. The energy flow between a microgrid and the main grid can be controlled adequately. We can control the charge and discharge of batteries or electric vehicles. The main disadvantage of renewable-energy systems and clean energy relies on their intermittence and their complex control. Artificial intelligence methods can be held in this regard. 5 Conclusion To conclude, the objective of this paper is to propose a suitable solution to protect the SWH from overheating, improve its performance and maximize its lifespan, by lowering the temperature of the solar thermal collector without disturbing the individual’s behaviour. An adaptive controller has been designed to insulate and protect efficiently the solar thermal collector without varying the system. Also, the main components of the SWH system have been modelled as well as the artificial neural network for the computational arrangement. The artificial neural network that is based on a SOM model has been trained using unsupervised machine learning with a total of 2208 training samples. The SOM network was able to group the data sets into four clusters. Finally, it is clearly shown that the proposed system can cover autonomously the primary subsystem of the SWH depending on the days, the solar radiations, the ambient temperatures, the collector temperatures and the household hot-water demand. The approach in which the solar collector can be fully unshaded, 20% covered with a shade, 25% covered or 32% shaded has been chosen as the most suitable and efficient process since it protects the system from overheating and maintains the required temperature of the household hot water. From a future perspective, a thermal simulation of the SWH can be performed to check any possible hotspot formation. Table 1: Simulation parameters of the primary and secondary subsystems [14] Parameter . Value . The surface area of the collector (m2) 2.31 Surface area of the tube (m2) 0.14 Collector volume (m3) 0.12 Optical efficiency 0.81 Collector heat-loss coefficient (W/(m2.K)) 4.5 Volumetric flow rate (L/s) 0.02 Fluid volume (L) 1.41 Fluid specific heat capacity (J/(kg.K)) 3300 Fluid density (kg/L) 1.07 Primary circuit heat-loss coefficient (W/(m2.K)) 150 Aluminium specific heat capacity (J/(kg.K)) 921 Aluminium density (kg/L) 2710 Tank volume (L) 30 Water-specific heat capacity (J/(kg.K)) 4200 Water density (kg/L) 1 Parameter . Value . The surface area of the collector (m2) 2.31 Surface area of the tube (m2) 0.14 Collector volume (m3) 0.12 Optical efficiency 0.81 Collector heat-loss coefficient (W/(m2.K)) 4.5 Volumetric flow rate (L/s) 0.02 Fluid volume (L) 1.41 Fluid specific heat capacity (J/(kg.K)) 3300 Fluid density (kg/L) 1.07 Primary circuit heat-loss coefficient (W/(m2.K)) 150 Aluminium specific heat capacity (J/(kg.K)) 921 Aluminium density (kg/L) 2710 Tank volume (L) 30 Water-specific heat capacity (J/(kg.K)) 4200 Water density (kg/L) 1 Open in new tab Table 1: Simulation parameters of the primary and secondary subsystems [14] Parameter . Value . The surface area of the collector (m2) 2.31 Surface area of the tube (m2) 0.14 Collector volume (m3) 0.12 Optical efficiency 0.81 Collector heat-loss coefficient (W/(m2.K)) 4.5 Volumetric flow rate (L/s) 0.02 Fluid volume (L) 1.41 Fluid specific heat capacity (J/(kg.K)) 3300 Fluid density (kg/L) 1.07 Primary circuit heat-loss coefficient (W/(m2.K)) 150 Aluminium specific heat capacity (J/(kg.K)) 921 Aluminium density (kg/L) 2710 Tank volume (L) 30 Water-specific heat capacity (J/(kg.K)) 4200 Water density (kg/L) 1 Parameter . Value . The surface area of the collector (m2) 2.31 Surface area of the tube (m2) 0.14 Collector volume (m3) 0.12 Optical efficiency 0.81 Collector heat-loss coefficient (W/(m2.K)) 4.5 Volumetric flow rate (L/s) 0.02 Fluid volume (L) 1.41 Fluid specific heat capacity (J/(kg.K)) 3300 Fluid density (kg/L) 1.07 Primary circuit heat-loss coefficient (W/(m2.K)) 150 Aluminium specific heat capacity (J/(kg.K)) 921 Aluminium density (kg/L) 2710 Tank volume (L) 30 Water-specific heat capacity (J/(kg.K)) 4200 Water density (kg/L) 1 Open in new tab Acknowledgements The authors would like to thank the Higher Center for Research (HCR) of the Holy Spirit University of Kaslik (USEK), and the National Council for Scientific Research in Lebanon (CNRS-L) for funding this project. Conflict of interest statement All authors declare that they have no conflicts of interest. References [1] Azzouzi M . Control of solar water heater design . 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Google Scholar Crossref Search ADS WorldCat [13] Energy Saving Trust. Solar Water Heating Systems, Guidance for Professional, Conventional Indirect Models Report. London, England . http://www.simssolar.co.uk/assets/pdf_docs/S0017%20EST-solarWaterHeating.pdf ( March 2021 , date last accessed). [14] Boedecker K. HL313 Domestic Water Heating with Flat Collector. Laboratory Manual . Barsbüttel : Gunt , 2013 . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC [15] Mosallat F , ElMekkawy TY, Friesen DL, et al. Modeling, simulation and control of flat panel solar collectors with thermal storage for heating and cooling applications . In: ANT/SEIT , Nova Scotia , Canada , 1 January 2013 , 686 – 693 . [16] Weather Underground [Online]. https://www.wunderground.com/history/daily/OLBA/date/2018-6-1 ( 12 December 2019 , date last accessed). © The Author(s) 2022. Published by Oxford University Press on behalf of National Institute of Clean-and-Low-Carbon Energy This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (https://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com © The Author(s) 2022. Published by Oxford University Press on behalf of National Institute of Clean-and-Low-Carbon Energy http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Clean Energy Oxford University Press

Adaptive overheating cover for a solar water heater

Adaptive overheating cover for a solar water heater

Clean Energy , Volume 6 (4): 12 – Aug 1, 2022

Abstract

Abstract Solar water heating systems have been widely used around the world. However, exposure to sunlight can overheat the device, affecting the efficiency and durability of the system. This article proposes an adaptive deck controller that protects the system from overheating without compromising the availability of domestic hot water. Solar water heaters are considered one of the most effective ways to reduce a home’s carbon footprint. They are a renewable energy source that reduces reliance on fossil fuels and saves money. Thus, this paper aims to develop a dynamic cover for solar water heaters that prevent overheating using an artificial neural network to optimize the design of control systems. Based on a self-organizing map network, the controller automatically adjusts the temperature of the solar collector through a fabric screen covering the main subsystems, depending on many parameters such as weather conditions, collector temperature and domestic hot water depending on demand. A suggested technique of four different shade percentages (0%, 20%, 25% or 32%) can avoid overheating and maintain the amount of hot water the home needs. Although renewable energy is free, proper controls are required to ensure maximum efficiency or proper use. In addition, the control of renewable energy leads to longer service life. Open in new tabDownload slide durability, efficiency, overheating, solar water heater, self-organizing map (SOM), temperature control Introduction Solar water heater systems absorb energy from solar radiation to produce hot water for several applications. The use of such a system replaces the consumption of fossil fuels and natural gas. Hence, it minimizes global pollution and reduces the associated environmental impact [1]. Common problems of solar water heater (SWH) systems are overheating, water leakage, lack of water storage and other minor technical problems such as corrosion and calcification. While the SWH system is expected to supply hot water during the hot summer season, it appears to be unfavourable and inconvenient due to the moderate demand for hot water during summer. The overheating phenomenon occurs when the boiling point is reached and the heat can no longer be dispersed because the energy delivered by the solar collectors exceeds the heat-storage capacity and the energy demand [2]. Moreover, fatigue failure might occur to the system, increasing the cost of repairs and maintenance and lowering the system life span [3]. Energy-storage capacity is also a minor concern, especially with shared heating systems [4]. Also, power prediction is a minor concern for a short time due to the high capacity of the SWH [5]. Detection and prevention are always better at first [6]. Tiwari et al. developed a photovoltaic thermoelectric flat-plate collector; the model comprised a semi-transparent photovoltaic module combined with thermoelectric modules and a tube-sheet arrangement for the water flow. The proposed system had an electrical energy gain of 3.96–14.38 W and useful thermal energy of 41.14–148.72 W [7]. Sharma et al. designed a flat-plate solar collector for spice drying. Closed-loop air circulation was settled with a single-cover solar collector. The flat plate had a surface of 2.1 m2 to carry 10 kg of cardamom. Simulation results indicated that the maximum absorber temperature was 68°C and the air temperature at the collector’s output varied between 40°C and 55°C for 6 hours per day, which was sufficient for drying spices [8]. Mekali et al. developed a temperature-control system for a SWH. It was a closed-loop control system based on a supplementary heat source to assure obtaining hot water at any desired temperature [9]. Kirpichnikova and Makhsumov suggested a prototype concerning the overheating protection for solar cells. They attached a holographic film to the cell’s surface to reduce the effect of overheating. The study proved the effectiveness of the film by reflecting the infrared spectrum of the solar radiation, which decreased the surface temperature of the covered cell and increased the generated power [10]. Diez et al. operated a flat-plate solar collector with computational intelligence techniques. An artificial neural network was trained to predict the outlet collector temperature using measured ambient and inlet temperatures, solar irradiance and working fluid flow. Several tests with different artificial neural network architectures were carried out to achieve accurate results [11]. Jullian et al. presented an estimation of deep learning models that were trained under several meteorological situations to predict the performance framework of the solar thermal system. A physical simulation was established in the transient system simulation software to generate operational data in nominal circumstances. Different models with several configurations were suggested for temperature assessment [12]. This paper proposes a shading control system. The novelty of the system relies on a low-price implementation of the solution in which only a few pieces of hardware are required. In addition, the application of a self-organizing map (SOM) model can adapt to household utilization. The system design details are discussed in Section 1. Section 2 consists of software implementation. Accordingly, a model for the SWH system and the artificial neural network is discussed. Sections 3 and 4 include the training and testing of the whole system and its validation. Section 5 contains a conclusion and some proposed future perspectives to develop this system. 1 Proposed control system This section presents in detail the proposed design of the control system. Fig. 1 represents the block diagram of the proposed system. The days (working or holiday), the weather conditions, the temperature of the solar thermal collector and the household hot-water demand are measured. Depending on the input values and based on the artificial neural network model, the solar collector will be fully unshaded, 20% covered with a shade, 25% covered or 32% covered using a DC motor. The whole system can be turned off by a push button. Fig. 1: Open in new tabDownload slide Block diagram of the proposed system showing the inputs and output. The system is based on a controller and a DC motor. The latter tends to spread and fold the covering shield. A fabric that is fused to the motor can cover or uncover the solar thermal collector, as illustrated in Fig. 2. While covering the collector, the appropriate shade protects the system from overheating by reflecting the incident solar radiation as well as providing resistance to environmental outdoor conditions. Fig. 2: Open in new tabDownload slide System layout. 2 Software implementation This section will be dedicated to showing the implementation of the system. Thus, a mathematical model for each of the solar thermal collectors and the storage tank will be developed along with the SOM model. The artificial neural network training, its data sets and its results will be presented in this section. 2.1 Solar thermal system model The SWH system can be divided into two subsystems. The primary subsystem collects solar energy and stores it. It contains the heat-transfer fluid, the solar collector and the insulated pipes. The secondary subsystem comprising a thermal storage tank receives the collected energy from the primary circuit and stores the heat for later consumption [13]. Each of the primary and secondary subsystems is mathematically modelled to simplify the simulation configurations in MATLAB®. 2.1.1 Primary subsystem model Fig. 3 illustrates a schematic drawing of the energy flow through a flat-plate solar collector. Typically, the solar radiation crossing the glass cover of the collector is partially reflected and slightly absorbed by the transparent glass. The rest of the sunlight penetrates the glazing and strikes the metal absorber plate. When it reaches the absorber, a further portion is reflected via radiation and the remaining part is well absorbed by the blackened surface [14]. Fig. 3: Open in new tabDownload slide Energy flow through a flat-plate solar collector [14]. Fundamentally, the solar energy Qs received by the collector’s absorber surface is expressed in Equation (1): Qs=IAcηo(1) where I represents the intensity of the solar radiation (W/m2), Ac represents the surface area of the collector (m2) and ηo represents the optimal efficiency, which depends on the transmission of the glass and the absorption of the absorber plate. In conjunction with the solar energy represented in Equation (1), the thermal loss Ql due to reflection, convection and radiation can be determined using Equation (2), taking into account the heat-transfer coefficient U (W/(m2.K)) and the collector temperature. Thus, increasing the temperature and/or the heat-transfer coefficient increments the heat loss Ql: Ql=UAc(Tc−Tambient)(2) Simultaneously, the heat absorbed by the primary circuit of the collector Qp can be determined by the correlation of the logarithmic mean temperature difference (LMTD) method, the heat-loss coefficient of the primary circuit Up (W/(m2.K)) and the surface area of the tube Ar (m2): Qp=UpAr(LMTD)(3) From Equation (3), the LMTD is determined by the difference of the inlet Tcin, outlet Tcout and collector Tc temperatures (K), as displayed in Equation (4) [15]: LMTD=(Tc−Tcout)−(Tc−Tcin)ln(Tc−TcoutTc−Tcin)(4) Hence, the state equation of the collector is calculated in Equation (5) where ρAl represents the density of the aluminium (kg/m3), cAl represents the specific heat capacity of the aluminium (J/(kg.K)) and Vc represents the volume of the collector (m3): (ρAlcAlVc)dTcdt=Qs−Ql−Qp(5) Moreover, the heat absorbed by the fluid Qf ⁠, defined in Equation (6), is determined by the difference in temperature between the outlet collector and the inlet collector, the volumetric flow rate F (L/s), the density of the heat-transfer fluid ρ (kg/L) and its specific heat capacity c (J/(kg.K)) [14]: Qf=Fρc(Tcout−Tcin)(6) Therefore, the energy balance applicable to the primary circuit is shown in Equation (7), where Vf represents the volume of the fluid passing through the collector (L): (ρcVf)dTcoutdt=Qp−Qf(7) 2.1.2 Secondary subsystem model The thermal storage tank is connected to the collector and the load concurrently. It receives the cold water to transmit it to the collector and it supplies the appliances with the collected warm water. In this analysis, losses in the secondary system are neglected. The thermal output of the storage tank Qout ⁠, expressed in Equation (8), depends on the generated temperature difference, the volumetric flow rate of hot-water consumption Fw (L/s), the water density ρw (kg/L) and the water-specific heat capacity cw (J/(kg.K)): Qout=Fwρwcw(Tcin−Tambient)(8) The heat received by the storage tank increases the water’s temperature; the energy balance of the insulated water-storage tank is described in Equation (9): (ρwcwVtank)dTtankdt=Qp−Qout(9) 2.2 SOM model The artificial neural network is a processing model used in machine learning to imitate the biological neural network. The human brain comprises the interconnected neurons that send information to different parts of the body as a reaction to an action performed. The artificial neural network consists of neurons known as nodes connected in parallel; these nodes are the core processing units of the neural network. It is a set of connected units and each connection is associated with a weight [15]. On the other hand, the SOM is a special type of artificial neural network that provides a topology between input and output spaces. It is a technique for dimensionality reduction, as it plots high-dimensional inputs to a 2D discretized representation. Since the entire learning executes without any supervision, the nodes, known as feature maps, are self-organizing and the input vectors are clustered according to their similarities to produce a 2D grid. Fig. 4 illustrates the flowchart for the SOM technique. The algorithm launches by initializing the weight vectors and selecting a sample vector randomly. Then, the Euclidean distance is computed between each node of the weight vector and the current input vector, as determined in Equation (10), where x is the input vector and wij is the weight connecting the node (i,j) with the input: Fig. 4: Open in new tabDownload slide Self-organizing map flowchart. x→−w→ij=∑nt=0[x→(t)−w→ij(t)]2(10) Afterward, the winning node that has the smallest distance is called the best-matching unit and its topological neighbours are determined. The synaptic weights of these neurons are updated using Equation (11): w→ij(t+1)=wij(t)+αij(t)[x(t)−wij(t)](11) where αij represents the learning rate that is expressed in Equation (12), where t represents the current iteration and λ represents the time constant: α(t)=α0e(−tλ)(12) The computation continues until there are no noticeable modifications in the feature map. The SOM constitutes two layers of processing units: an input layer and an output layer, as shown in Fig. 5. The input layer receives five inputs from the environment and contains the days, the solar radiation, the difference between the collector temperature and the ambient temperature, the difference between the collector temperature and its maximum, and the household hot-water demand. It does not have any hidden layers. The output layer determines the predicted cluster that can be fully unshaded, 20% covered with a shade, 25% covered or 32% covered. During the training phase, the SOM adjusts its weights by applying competitive learning, which is opposed to error-correction learning. Fig. 5: Open in new tabDownload slide Self-organizing map architecture. 3 System training The unlabeled training data sets have been recorded, the artificial neural network has been created and trained using unsupervised learning, and its performance has been evaluated using a variety of visualized tools. 3.1 Data sets A total of 2208 samples for the three months of June, July and August are used as a training data set. These inputs are simulated using the model developed in Section 2. And using the parameters shown in Table 1. Particularly, the data have been created employing simulation using the SWH model developed by the authors. The raw inputs are solar radiation in W/m2, ambient air temperature in °C, storage-tank temperature in K, outlet water-collector temperature in K, collector temperature in K and household water consumption in L/h. The solar radiation in W/m2 and ambient air temperature in °C were retrieved from online sources for Beirut, Lebanon for June, July and August 2018 with an hourly frequency [16]. Fig. 6 shows the average collector temperature over the month. The attained peaks were positioned at 15:00. Fig. 6: Open in new tabDownload slide Monthly average collector temperature in K. Fig. 7 shows the monthly average household hot-water consumption per hour for a family of four persons over a day. It is assumed that each person consumes 30–50 L/day of hot water, with respect to the warm-water usage split between morning and evening time, and the variation between weekdays, weekends and holidays. Fig. 7: Open in new tabDownload slide Monthly average household hot-water consumption in L/h. 3.2 Feature extraction The input vector of the artificial neural network has five inputs, which are: days (whether weekday or holiday); solar radiation; difference between the collector’s temperature and the ambient temperature; difference between the collector’s temperature and its maximum; difference between total daily household hot-water demand and total consumption of the day until the present time. Feature extraction is a process used to reduce the set of raw data into more feasible groups. It combines effectively a large number of processing variables into features to minimize the machine’s efforts and accelerate the learning speed without losing information or affecting the accuracy. One of the obtained features is the difference between the temperature of the collector and the ambient air temperature. This feature gives a relative indication of the heating of the collector. Fig. 8 shows the monthly average of this feature as a function of the daytime. Fig. 8: Open in new tabDownload slide Monthly difference between the collector and ambient temperatures. Another important feature is the difference between the collector’s temperature and the maximum temperature that we would like not to exceed. Accordingly, a limit of 80°C or 353.15 K is maintained to ensure a longer lifespan for the SWH. The desired maximum temperature of 80°C has been chosen because it should fall between 60°C (hot-water temperature) and 100°C, which is considered the boiling temperature of water at atmospheric pressure. Fig. 9 shows the average of this feature for the 3 months as a function of the time of day. Fig. 9: Open in new tabDownload slide Monthly difference between the collector temperature and its desired maximum. The difference between the household water consumed for the day until the present and the average daily demand is an additional important feature. The latter we calculated from the data sets. This feature is important to control the system ensuring the availability of hot water for the users (refer to Fig. 10 for more details). Obviously, at the end of the day, this feature goes to zero. Fig. 10: Open in new tabDownload slide Monthly average household hot-water demand difference with the total consumption. 3.3 Artificial neural network training The five input data sets have been defined to be clustered using the SOM network, which comprises a competitive layer using the nntool from MATLAB®. The total number of clusters is four, denoted as A, B, C and D as shown in Fig. 11, as exhibited from the displayed architecture of Fig. 5. While training the artificial neural network, the number of reached epochs is 200 iterations. By different iterations, we managed to find that four clusters best suit the application. Fig. 11: Open in new tabDownload slide The four clusters of the self-organizing map with the number of datapoints in each cluster. 4 System testing and validation After achieving the SWH model and the SOM training, this section will include the testing of the whole system. Hence, three implemented approaches will be evaluated and the validation of the system will be detailed in this section. 4.1 Approaches evaluation Three approaches have been performed with the solar thermal and artificial neural network models to designate the most suitable percentages of the collector shading. The latter has to reduce the temperature of the collector’s plate (below < 80°C) to increase its lifespan, and without affecting hot-water availability. 4.1.1 First approach The first approach has been computed to cover the solar thermal collector A (0%), B (10%), C (20%) or D (21%), adaptively. Case C and Case D are close because it is a first-iteration approach. Case D has been chosen to be low or very close to Case C to keep the hot water available. After simulation, the collector’s temperature is obtained. Fig. 12 shows the difference between the collector’s temperature and the desired maximum. The peaks of the temperature were 373.4, 370.55 and 362.06 K in June, July and August, respectively. The temperatures of the collector plate surpassed the desired maximum (80°C) by ~20.4, ~17.55 and ~9 K. The overheating occurred from 11:00 to 18:00 during June and July and from 12:00 to 17:00 during August. Fig. 12: Open in new tabDownload slide Difference between the collector’s temperature and its desired maximum for the first approach. On the other hand, Fig. 13 represents the results of the difference between the storage tank and the desired temperatures. During June, July and August, the temperature of the warm water insulated in the storage tank exceeded its desired temperature (60°C) by ~18.9°C, ~18°C and ~10.5°C, respectively. During the night, the tank-water temperature maintained acceptable values of ~20°C below the desired temperature. Fig. 13: Open in new tabDownload slide Difference between the tank and desired temperatures for the first approach. 4.1.2 Second approach A new approach has been proposed to minimize the collector’s temperature by covering the primary circuit with A (0%), B (20%), C (30%) or D (40%). After simulation, the collector’s temperature is obtained. Fig. 14 shows the difference between the collector’s temperature and the desired maximum (80°C). The collector’s temperature did not attain its maximum. During June, July and August, the temperatures were lower than their maximum by ~3.36, ~3.33 and ~8.16 K, respectively. Fig. 14: Open in new tabDownload slide Difference between the collector’s temperature and its desired maximum for the second approach. The results of the difference between the temperature of the hot water stored in the insulated tank and the desired temperature are displayed in Fig. 15. During the night, the tank-water temperature decreases to unacceptable values of ~33°C below the desired temperature. Fig. 15: Open in new tabDownload slide Difference between the tank and desired temperatures for the second approach. 4.1.3 Third approach The third approach has been set to control the temperature of the SWH system by covering the solar thermal collector A (0%), B (20%), C (25%) or D (32%), autonomously. After simulation, the collector’s temperature is obtained. Fig. 16 shows the difference between the collector’s temperature and the desired maximum (80°C). During June and July, it exceeded the maximum temperature limit of approximately ~2.05°C and 1.5°C for a very short period, whereas the temperatures over August did not pass the maximum. Fig. 16: Open in new tabDownload slide Difference between the collector temperature and its maximum for the third approach. The results of the difference between the temperature of the hot water stored in the insulated tank and the desired temperature are displayed in Fig. 17. During the night, the tank-water temperature maintains acceptable values of ~26°C below the desired temperature. Fig. 17: Open in new tabDownload slide Difference between the tank and desired temperatures for the third approach. While covering 0%, 20%, 25% or 32%, adaptively, of the solar thermal collector, its temperature is well reduced and it does not pass excessively its maximum temperature, as well as the household hot water maintains its desired temperature. Therefore, the third approach suits well the objectives of the proposed control system. 4.2 Functional evaluation The three approaches affect the temperatures of the storage tank, the outlet’s collector and the collector plate compared with the original SWH system. The computed results were conducted on the monthly average effect. Also, detailed discussions on the system functionality are presented using the proposed algorithm. The three approaches that control the system are compared with the uncontrolled one on three consecutive days: 18, 19 and 20 August 2019. The temperatures of the household hot-water storage tank exceeded its desirable value for each of the original systems (refer to Fig. 18 for more details). However, the proposed approach showed good agreement with the desired temperature as well as saving the system from any failure. Fig. 18: Open in new tabDownload slide Comparison between three approaches for the desirable tank temperatures for 3 days. The collector’s temperatures were lower than their undesired point while covering the primary subsystem with the second approach and the third one, as manifested in Fig. 19, for 72 consecutive hours. Fig. 19: Open in new tabDownload slide Comparison between three approaches for the desirable collector temperatures for 3 days. Using a SOM network, and with proper configuration, the applied method can be applied to different fields of energy systems. The energy flow between a microgrid and the main grid can be controlled adequately. We can control the charge and discharge of batteries or electric vehicles. The main disadvantage of renewable-energy systems and clean energy relies on their intermittence and their complex control. Artificial intelligence methods can be held in this regard. 5 Conclusion To conclude, the objective of this paper is to propose a suitable solution to protect the SWH from overheating, improve its performance and maximize its lifespan, by lowering the temperature of the solar thermal collector without disturbing the individual’s behaviour. An adaptive controller has been designed to insulate and protect efficiently the solar thermal collector without varying the system. Also, the main components of the SWH system have been modelled as well as the artificial neural network for the computational arrangement. The artificial neural network that is based on a SOM model has been trained using unsupervised machine learning with a total of 2208 training samples. The SOM network was able to group the data sets into four clusters. Finally, it is clearly shown that the proposed system can cover autonomously the primary subsystem of the SWH depending on the days, the solar radiations, the ambient temperatures, the collector temperatures and the household hot-water demand. The approach in which the solar collector can be fully unshaded, 20% covered with a shade, 25% covered or 32% shaded has been chosen as the most suitable and efficient process since it protects the system from overheating and maintains the required temperature of the household hot water. From a future perspective, a thermal simulation of the SWH can be performed to check any possible hotspot formation. Table 1: Simulation parameters of the primary and secondary subsystems [14] Parameter . Value . The surface area of the collector (m2) 2.31 Surface area of the tube (m2) 0.14 Collector volume (m3) 0.12 Optical efficiency 0.81 Collector heat-loss coefficient (W/(m2.K)) 4.5 Volumetric flow rate (L/s) 0.02 Fluid volume (L) 1.41 Fluid specific heat capacity (J/(kg.K)) 3300 Fluid density (kg/L) 1.07 Primary circuit heat-loss coefficient (W/(m2.K)) 150 Aluminium specific heat capacity (J/(kg.K)) 921 Aluminium density (kg/L) 2710 Tank volume (L) 30 Water-specific heat capacity (J/(kg.K)) 4200 Water density (kg/L) 1 Parameter . Value . The surface area of the collector (m2) 2.31 Surface area of the tube (m2) 0.14 Collector volume (m3) 0.12 Optical efficiency 0.81 Collector heat-loss coefficient (W/(m2.K)) 4.5 Volumetric flow rate (L/s) 0.02 Fluid volume (L) 1.41 Fluid specific heat capacity (J/(kg.K)) 3300 Fluid density (kg/L) 1.07 Primary circuit heat-loss coefficient (W/(m2.K)) 150 Aluminium specific heat capacity (J/(kg.K)) 921 Aluminium density (kg/L) 2710 Tank volume (L) 30 Water-specific heat capacity (J/(kg.K)) 4200 Water density (kg/L) 1 Open in new tab Table 1: Simulation parameters of the primary and secondary subsystems [14] Parameter . Value . The surface area of the collector (m2) 2.31 Surface area of the tube (m2) 0.14 Collector volume (m3) 0.12 Optical efficiency 0.81 Collector heat-loss coefficient (W/(m2.K)) 4.5 Volumetric flow rate (L/s) 0.02 Fluid volume (L) 1.41 Fluid specific heat capacity (J/(kg.K)) 3300 Fluid density (kg/L) 1.07 Primary circuit heat-loss coefficient (W/(m2.K)) 150 Aluminium specific heat capacity (J/(kg.K)) 921 Aluminium density (kg/L) 2710 Tank volume (L) 30 Water-specific heat capacity (J/(kg.K)) 4200 Water density (kg/L) 1 Parameter . Value . The surface area of the collector (m2) 2.31 Surface area of the tube (m2) 0.14 Collector volume (m3) 0.12 Optical efficiency 0.81 Collector heat-loss coefficient (W/(m2.K)) 4.5 Volumetric flow rate (L/s) 0.02 Fluid volume (L) 1.41 Fluid specific heat capacity (J/(kg.K)) 3300 Fluid density (kg/L) 1.07 Primary circuit heat-loss coefficient (W/(m2.K)) 150 Aluminium specific heat capacity (J/(kg.K)) 921 Aluminium density (kg/L) 2710 Tank volume (L) 30 Water-specific heat capacity (J/(kg.K)) 4200 Water density (kg/L) 1 Open in new tab Acknowledgements The authors would like to thank the Higher Center for Research (HCR) of the Holy Spirit University of Kaslik (USEK), and the National Council for Scientific Research in Lebanon (CNRS-L) for funding this project. Conflict of interest statement All authors declare that they have no conflicts of interest. References [1] Azzouzi M . Control of solar water heater design . In: 2011 10th International Conference on Environment and Electrical Engineering , Rome, Italy , 8 May 2011 , 1 – 5 . [2] Papadimitratos A , Sobhansarbandi S, Pozdin V, et al. Evacuated tube solar collectors integrated with phase change materials . Sol Energy , 2016 , 129 : 10 – 19 . Google Scholar Crossref Search ADS WorldCat [3] Frank E , Mauthner F, Fischer S. Overheating prevention and stagnation handling in solar process heat applications . International Energy Agency-Solar Heating and Cooling Task , 49 , 2015 . https://task49.iea-shc.org/Data/Sites/7/frank_iea_shc_task49_overheatingstagnationreport_approved_v-2-3.pdf ( 22 December 2019 , date last accessed). Google Scholar OpenURL Placeholder Text WorldCat [4] Zhou Y , Hu W, Min Y, et al. Integrated power and heat dispatch considering available reserve of combined heat and power units . IEEE Trans Sustainable Energy , 2019 , 10 : 1300 – 1310 . Google Scholar Crossref Search ADS WorldCat [5] Asrari A , Wu TX, Ramos B. A hybrid algorithm for short-term solar power prediction—sunshine state case study . IEEE Trans Sustainable Energy , 2017 , 8 : 582 – 591 . Google Scholar Crossref Search ADS WorldCat [6] Nehme B , Youness R, Hanna TA, et al. Developing a skin conductance device for early Autism Spectrum Disorder diagnosis . In: 2016 3rd Middle East Conference on Biomedical Engineering (MECBME) , Beirut, Lebanon , 6 October 2016 , 139 – 142 . [7] Tiwari A , Alashqar OA, Dimri N. Modeling and validation of photovoltaic thermoelectric flat plate collector (PV-TE-FPC) . Energy Convers Manage , 2020 , 205 : 112378 . Google Scholar Crossref Search ADS WorldCat [8] Sharma D , Rajesh VR. Modeling and design of a flat plate solar collector with closed air circulation for drying spices . In: 2018 4th International Conference on Electrical Energy Systems (ICEES) , Chennai, India , 7 February 2018 , 352 – 357 . [9] Mekali HV , Somashekhar KR, Gowda Baragur A, et al. Design and development of automatic temperature control system for solar water heater system . In: 2018 IEEE 7th International Conference on Power and Energy (PECon) , Kuala Lumpur, Malaysia , 3 December 2018 , 19 – 22 . [10] Kirpichnikova IM , Makhsumov IB. Investigation of surface temperature of solar modules using holographic overheating protection . In: 2019 IEEE Russian Workshop on Power Engineering and Automation of Metallurgy Industry: Research & Practice (PEAMI) , Magnitogorsk, Russia , 4 October 2019 , 80 – 84 . [11] Diez FJ , Navas-Gracia LM, Martínez-Rodríguez A A, et al. Modelling of a flat-plate solar collector using artificial neural networks for different working fluid (water) flow rates . Sol Energy , 2019 , 188 : 1320 – 1331 . Google Scholar Crossref Search ADS WorldCat [12] Correa-Jullian C , Cardemil JM, Droguett EL, et al. Assessment of deep learning techniques for prognosis of solar thermal systems . Renew Energy , 2020 , 145 : 2178 – 2191 . Google Scholar Crossref Search ADS WorldCat [13] Energy Saving Trust. Solar Water Heating Systems, Guidance for Professional, Conventional Indirect Models Report. London, England . http://www.simssolar.co.uk/assets/pdf_docs/S0017%20EST-solarWaterHeating.pdf ( March 2021 , date last accessed). [14] Boedecker K. HL313 Domestic Water Heating with Flat Collector. Laboratory Manual . Barsbüttel : Gunt , 2013 . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC [15] Mosallat F , ElMekkawy TY, Friesen DL, et al. Modeling, simulation and control of flat panel solar collectors with thermal storage for heating and cooling applications . In: ANT/SEIT , Nova Scotia , Canada , 1 January 2013 , 686 – 693 . [16] Weather Underground [Online]. https://www.wunderground.com/history/daily/OLBA/date/2018-6-1 ( 12 December 2019 , date last accessed). © The Author(s) 2022. Published by Oxford University Press on behalf of National Institute of Clean-and-Low-Carbon Energy This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (https://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com © The Author(s) 2022. Published by Oxford University Press on behalf of National Institute of Clean-and-Low-Carbon Energy

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Abstract

Abstract Solar water heating systems have been widely used around the world. However, exposure to sunlight can overheat the device, affecting the efficiency and durability of the system. This article proposes an adaptive deck controller that protects the system from overheating without compromising the availability of domestic hot water. Solar water heaters are considered one of the most effective ways to reduce a home’s carbon footprint. They are a renewable energy source that reduces reliance on fossil fuels and saves money. Thus, this paper aims to develop a dynamic cover for solar water heaters that prevent overheating using an artificial neural network to optimize the design of control systems. Based on a self-organizing map network, the controller automatically adjusts the temperature of the solar collector through a fabric screen covering the main subsystems, depending on many parameters such as weather conditions, collector temperature and domestic hot water depending on demand. A suggested technique of four different shade percentages (0%, 20%, 25% or 32%) can avoid overheating and maintain the amount of hot water the home needs. Although renewable energy is free, proper controls are required to ensure maximum efficiency or proper use. In addition, the control of renewable energy leads to longer service life. Open in new tabDownload slide durability, efficiency, overheating, solar water heater, self-organizing map (SOM), temperature control Introduction Solar water heater systems absorb energy from solar radiation to produce hot water for several applications. The use of such a system replaces the consumption of fossil fuels and natural gas. Hence, it minimizes global pollution and reduces the associated environmental impact [1]. Common problems of solar water heater (SWH) systems are overheating, water leakage, lack of water storage and other minor technical problems such as corrosion and calcification. While the SWH system is expected to supply hot water during the hot summer season, it appears to be unfavourable and inconvenient due to the moderate demand for hot water during summer. The overheating phenomenon occurs when the boiling point is reached and the heat can no longer be dispersed because the energy delivered by the solar collectors exceeds the heat-storage capacity and the energy demand [2]. Moreover, fatigue failure might occur to the system, increasing the cost of repairs and maintenance and lowering the system life span [3]. Energy-storage capacity is also a minor concern, especially with shared heating systems [4]. Also, power prediction is a minor concern for a short time due to the high capacity of the SWH [5]. Detection and prevention are always better at first [6]. Tiwari et al. developed a photovoltaic thermoelectric flat-plate collector; the model comprised a semi-transparent photovoltaic module combined with thermoelectric modules and a tube-sheet arrangement for the water flow. The proposed system had an electrical energy gain of 3.96–14.38 W and useful thermal energy of 41.14–148.72 W [7]. Sharma et al. designed a flat-plate solar collector for spice drying. Closed-loop air circulation was settled with a single-cover solar collector. The flat plate had a surface of 2.1 m2 to carry 10 kg of cardamom. Simulation results indicated that the maximum absorber temperature was 68°C and the air temperature at the collector’s output varied between 40°C and 55°C for 6 hours per day, which was sufficient for drying spices [8]. Mekali et al. developed a temperature-control system for a SWH. It was a closed-loop control system based on a supplementary heat source to assure obtaining hot water at any desired temperature [9]. Kirpichnikova and Makhsumov suggested a prototype concerning the overheating protection for solar cells. They attached a holographic film to the cell’s surface to reduce the effect of overheating. The study proved the effectiveness of the film by reflecting the infrared spectrum of the solar radiation, which decreased the surface temperature of the covered cell and increased the generated power [10]. Diez et al. operated a flat-plate solar collector with computational intelligence techniques. An artificial neural network was trained to predict the outlet collector temperature using measured ambient and inlet temperatures, solar irradiance and working fluid flow. Several tests with different artificial neural network architectures were carried out to achieve accurate results [11]. Jullian et al. presented an estimation of deep learning models that were trained under several meteorological situations to predict the performance framework of the solar thermal system. A physical simulation was established in the transient system simulation software to generate operational data in nominal circumstances. Different models with several configurations were suggested for temperature assessment [12]. This paper proposes a shading control system. The novelty of the system relies on a low-price implementation of the solution in which only a few pieces of hardware are required. In addition, the application of a self-organizing map (SOM) model can adapt to household utilization. The system design details are discussed in Section 1. Section 2 consists of software implementation. Accordingly, a model for the SWH system and the artificial neural network is discussed. Sections 3 and 4 include the training and testing of the whole system and its validation. Section 5 contains a conclusion and some proposed future perspectives to develop this system. 1 Proposed control system This section presents in detail the proposed design of the control system. Fig. 1 represents the block diagram of the proposed system. The days (working or holiday), the weather conditions, the temperature of the solar thermal collector and the household hot-water demand are measured. Depending on the input values and based on the artificial neural network model, the solar collector will be fully unshaded, 20% covered with a shade, 25% covered or 32% covered using a DC motor. The whole system can be turned off by a push button. Fig. 1: Open in new tabDownload slide Block diagram of the proposed system showing the inputs and output. The system is based on a controller and a DC motor. The latter tends to spread and fold the covering shield. A fabric that is fused to the motor can cover or uncover the solar thermal collector, as illustrated in Fig. 2. While covering the collector, the appropriate shade protects the system from overheating by reflecting the incident solar radiation as well as providing resistance to environmental outdoor conditions. Fig. 2: Open in new tabDownload slide System layout. 2 Software implementation This section will be dedicated to showing the implementation of the system. Thus, a mathematical model for each of the solar thermal collectors and the storage tank will be developed along with the SOM model. The artificial neural network training, its data sets and its results will be presented in this section. 2.1 Solar thermal system model The SWH system can be divided into two subsystems. The primary subsystem collects solar energy and stores it. It contains the heat-transfer fluid, the solar collector and the insulated pipes. The secondary subsystem comprising a thermal storage tank receives the collected energy from the primary circuit and stores the heat for later consumption [13]. Each of the primary and secondary subsystems is mathematically modelled to simplify the simulation configurations in MATLAB®. 2.1.1 Primary subsystem model Fig. 3 illustrates a schematic drawing of the energy flow through a flat-plate solar collector. Typically, the solar radiation crossing the glass cover of the collector is partially reflected and slightly absorbed by the transparent glass. The rest of the sunlight penetrates the glazing and strikes the metal absorber plate. When it reaches the absorber, a further portion is reflected via radiation and the remaining part is well absorbed by the blackened surface [14]. Fig. 3: Open in new tabDownload slide Energy flow through a flat-plate solar collector [14]. Fundamentally, the solar energy Qs received by the collector’s absorber surface is expressed in Equation (1): Qs=IAcηo(1) where I represents the intensity of the solar radiation (W/m2), Ac represents the surface area of the collector (m2) and ηo represents the optimal efficiency, which depends on the transmission of the glass and the absorption of the absorber plate. In conjunction with the solar energy represented in Equation (1), the thermal loss Ql due to reflection, convection and radiation can be determined using Equation (2), taking into account the heat-transfer coefficient U (W/(m2.K)) and the collector temperature. Thus, increasing the temperature and/or the heat-transfer coefficient increments the heat loss Ql: Ql=UAc(Tc−Tambient)(2) Simultaneously, the heat absorbed by the primary circuit of the collector Qp can be determined by the correlation of the logarithmic mean temperature difference (LMTD) method, the heat-loss coefficient of the primary circuit Up (W/(m2.K)) and the surface area of the tube Ar (m2): Qp=UpAr(LMTD)(3) From Equation (3), the LMTD is determined by the difference of the inlet Tcin, outlet Tcout and collector Tc temperatures (K), as displayed in Equation (4) [15]: LMTD=(Tc−Tcout)−(Tc−Tcin)ln(Tc−TcoutTc−Tcin)(4) Hence, the state equation of the collector is calculated in Equation (5) where ρAl represents the density of the aluminium (kg/m3), cAl represents the specific heat capacity of the aluminium (J/(kg.K)) and Vc represents the volume of the collector (m3): (ρAlcAlVc)dTcdt=Qs−Ql−Qp(5) Moreover, the heat absorbed by the fluid Qf ⁠, defined in Equation (6), is determined by the difference in temperature between the outlet collector and the inlet collector, the volumetric flow rate F (L/s), the density of the heat-transfer fluid ρ (kg/L) and its specific heat capacity c (J/(kg.K)) [14]: Qf=Fρc(Tcout−Tcin)(6) Therefore, the energy balance applicable to the primary circuit is shown in Equation (7), where Vf represents the volume of the fluid passing through the collector (L): (ρcVf)dTcoutdt=Qp−Qf(7) 2.1.2 Secondary subsystem model The thermal storage tank is connected to the collector and the load concurrently. It receives the cold water to transmit it to the collector and it supplies the appliances with the collected warm water. In this analysis, losses in the secondary system are neglected. The thermal output of the storage tank Qout ⁠, expressed in Equation (8), depends on the generated temperature difference, the volumetric flow rate of hot-water consumption Fw (L/s), the water density ρw (kg/L) and the water-specific heat capacity cw (J/(kg.K)): Qout=Fwρwcw(Tcin−Tambient)(8) The heat received by the storage tank increases the water’s temperature; the energy balance of the insulated water-storage tank is described in Equation (9): (ρwcwVtank)dTtankdt=Qp−Qout(9) 2.2 SOM model The artificial neural network is a processing model used in machine learning to imitate the biological neural network. The human brain comprises the interconnected neurons that send information to different parts of the body as a reaction to an action performed. The artificial neural network consists of neurons known as nodes connected in parallel; these nodes are the core processing units of the neural network. It is a set of connected units and each connection is associated with a weight [15]. On the other hand, the SOM is a special type of artificial neural network that provides a topology between input and output spaces. It is a technique for dimensionality reduction, as it plots high-dimensional inputs to a 2D discretized representation. Since the entire learning executes without any supervision, the nodes, known as feature maps, are self-organizing and the input vectors are clustered according to their similarities to produce a 2D grid. Fig. 4 illustrates the flowchart for the SOM technique. The algorithm launches by initializing the weight vectors and selecting a sample vector randomly. Then, the Euclidean distance is computed between each node of the weight vector and the current input vector, as determined in Equation (10), where x is the input vector and wij is the weight connecting the node (i,j) with the input: Fig. 4: Open in new tabDownload slide Self-organizing map flowchart. x→−w→ij=∑nt=0[x→(t)−w→ij(t)]2(10) Afterward, the winning node that has the smallest distance is called the best-matching unit and its topological neighbours are determined. The synaptic weights of these neurons are updated using Equation (11): w→ij(t+1)=wij(t)+αij(t)[x(t)−wij(t)](11) where αij represents the learning rate that is expressed in Equation (12), where t represents the current iteration and λ represents the time constant: α(t)=α0e(−tλ)(12) The computation continues until there are no noticeable modifications in the feature map. The SOM constitutes two layers of processing units: an input layer and an output layer, as shown in Fig. 5. The input layer receives five inputs from the environment and contains the days, the solar radiation, the difference between the collector temperature and the ambient temperature, the difference between the collector temperature and its maximum, and the household hot-water demand. It does not have any hidden layers. The output layer determines the predicted cluster that can be fully unshaded, 20% covered with a shade, 25% covered or 32% covered. During the training phase, the SOM adjusts its weights by applying competitive learning, which is opposed to error-correction learning. Fig. 5: Open in new tabDownload slide Self-organizing map architecture. 3 System training The unlabeled training data sets have been recorded, the artificial neural network has been created and trained using unsupervised learning, and its performance has been evaluated using a variety of visualized tools. 3.1 Data sets A total of 2208 samples for the three months of June, July and August are used as a training data set. These inputs are simulated using the model developed in Section 2. And using the parameters shown in Table 1. Particularly, the data have been created employing simulation using the SWH model developed by the authors. The raw inputs are solar radiation in W/m2, ambient air temperature in °C, storage-tank temperature in K, outlet water-collector temperature in K, collector temperature in K and household water consumption in L/h. The solar radiation in W/m2 and ambient air temperature in °C were retrieved from online sources for Beirut, Lebanon for June, July and August 2018 with an hourly frequency [16]. Fig. 6 shows the average collector temperature over the month. The attained peaks were positioned at 15:00. Fig. 6: Open in new tabDownload slide Monthly average collector temperature in K. Fig. 7 shows the monthly average household hot-water consumption per hour for a family of four persons over a day. It is assumed that each person consumes 30–50 L/day of hot water, with respect to the warm-water usage split between morning and evening time, and the variation between weekdays, weekends and holidays. Fig. 7: Open in new tabDownload slide Monthly average household hot-water consumption in L/h. 3.2 Feature extraction The input vector of the artificial neural network has five inputs, which are: days (whether weekday or holiday); solar radiation; difference between the collector’s temperature and the ambient temperature; difference between the collector’s temperature and its maximum; difference between total daily household hot-water demand and total consumption of the day until the present time. Feature extraction is a process used to reduce the set of raw data into more feasible groups. It combines effectively a large number of processing variables into features to minimize the machine’s efforts and accelerate the learning speed without losing information or affecting the accuracy. One of the obtained features is the difference between the temperature of the collector and the ambient air temperature. This feature gives a relative indication of the heating of the collector. Fig. 8 shows the monthly average of this feature as a function of the daytime. Fig. 8: Open in new tabDownload slide Monthly difference between the collector and ambient temperatures. Another important feature is the difference between the collector’s temperature and the maximum temperature that we would like not to exceed. Accordingly, a limit of 80°C or 353.15 K is maintained to ensure a longer lifespan for the SWH. The desired maximum temperature of 80°C has been chosen because it should fall between 60°C (hot-water temperature) and 100°C, which is considered the boiling temperature of water at atmospheric pressure. Fig. 9 shows the average of this feature for the 3 months as a function of the time of day. Fig. 9: Open in new tabDownload slide Monthly difference between the collector temperature and its desired maximum. The difference between the household water consumed for the day until the present and the average daily demand is an additional important feature. The latter we calculated from the data sets. This feature is important to control the system ensuring the availability of hot water for the users (refer to Fig. 10 for more details). Obviously, at the end of the day, this feature goes to zero. Fig. 10: Open in new tabDownload slide Monthly average household hot-water demand difference with the total consumption. 3.3 Artificial neural network training The five input data sets have been defined to be clustered using the SOM network, which comprises a competitive layer using the nntool from MATLAB®. The total number of clusters is four, denoted as A, B, C and D as shown in Fig. 11, as exhibited from the displayed architecture of Fig. 5. While training the artificial neural network, the number of reached epochs is 200 iterations. By different iterations, we managed to find that four clusters best suit the application. Fig. 11: Open in new tabDownload slide The four clusters of the self-organizing map with the number of datapoints in each cluster. 4 System testing and validation After achieving the SWH model and the SOM training, this section will include the testing of the whole system. Hence, three implemented approaches will be evaluated and the validation of the system will be detailed in this section. 4.1 Approaches evaluation Three approaches have been performed with the solar thermal and artificial neural network models to designate the most suitable percentages of the collector shading. The latter has to reduce the temperature of the collector’s plate (below < 80°C) to increase its lifespan, and without affecting hot-water availability. 4.1.1 First approach The first approach has been computed to cover the solar thermal collector A (0%), B (10%), C (20%) or D (21%), adaptively. Case C and Case D are close because it is a first-iteration approach. Case D has been chosen to be low or very close to Case C to keep the hot water available. After simulation, the collector’s temperature is obtained. Fig. 12 shows the difference between the collector’s temperature and the desired maximum. The peaks of the temperature were 373.4, 370.55 and 362.06 K in June, July and August, respectively. The temperatures of the collector plate surpassed the desired maximum (80°C) by ~20.4, ~17.55 and ~9 K. The overheating occurred from 11:00 to 18:00 during June and July and from 12:00 to 17:00 during August. Fig. 12: Open in new tabDownload slide Difference between the collector’s temperature and its desired maximum for the first approach. On the other hand, Fig. 13 represents the results of the difference between the storage tank and the desired temperatures. During June, July and August, the temperature of the warm water insulated in the storage tank exceeded its desired temperature (60°C) by ~18.9°C, ~18°C and ~10.5°C, respectively. During the night, the tank-water temperature maintained acceptable values of ~20°C below the desired temperature. Fig. 13: Open in new tabDownload slide Difference between the tank and desired temperatures for the first approach. 4.1.2 Second approach A new approach has been proposed to minimize the collector’s temperature by covering the primary circuit with A (0%), B (20%), C (30%) or D (40%). After simulation, the collector’s temperature is obtained. Fig. 14 shows the difference between the collector’s temperature and the desired maximum (80°C). The collector’s temperature did not attain its maximum. During June, July and August, the temperatures were lower than their maximum by ~3.36, ~3.33 and ~8.16 K, respectively. Fig. 14: Open in new tabDownload slide Difference between the collector’s temperature and its desired maximum for the second approach. The results of the difference between the temperature of the hot water stored in the insulated tank and the desired temperature are displayed in Fig. 15. During the night, the tank-water temperature decreases to unacceptable values of ~33°C below the desired temperature. Fig. 15: Open in new tabDownload slide Difference between the tank and desired temperatures for the second approach. 4.1.3 Third approach The third approach has been set to control the temperature of the SWH system by covering the solar thermal collector A (0%), B (20%), C (25%) or D (32%), autonomously. After simulation, the collector’s temperature is obtained. Fig. 16 shows the difference between the collector’s temperature and the desired maximum (80°C). During June and July, it exceeded the maximum temperature limit of approximately ~2.05°C and 1.5°C for a very short period, whereas the temperatures over August did not pass the maximum. Fig. 16: Open in new tabDownload slide Difference between the collector temperature and its maximum for the third approach. The results of the difference between the temperature of the hot water stored in the insulated tank and the desired temperature are displayed in Fig. 17. During the night, the tank-water temperature maintains acceptable values of ~26°C below the desired temperature. Fig. 17: Open in new tabDownload slide Difference between the tank and desired temperatures for the third approach. While covering 0%, 20%, 25% or 32%, adaptively, of the solar thermal collector, its temperature is well reduced and it does not pass excessively its maximum temperature, as well as the household hot water maintains its desired temperature. Therefore, the third approach suits well the objectives of the proposed control system. 4.2 Functional evaluation The three approaches affect the temperatures of the storage tank, the outlet’s collector and the collector plate compared with the original SWH system. The computed results were conducted on the monthly average effect. Also, detailed discussions on the system functionality are presented using the proposed algorithm. The three approaches that control the system are compared with the uncontrolled one on three consecutive days: 18, 19 and 20 August 2019. The temperatures of the household hot-water storage tank exceeded its desirable value for each of the original systems (refer to Fig. 18 for more details). However, the proposed approach showed good agreement with the desired temperature as well as saving the system from any failure. Fig. 18: Open in new tabDownload slide Comparison between three approaches for the desirable tank temperatures for 3 days. The collector’s temperatures were lower than their undesired point while covering the primary subsystem with the second approach and the third one, as manifested in Fig. 19, for 72 consecutive hours. Fig. 19: Open in new tabDownload slide Comparison between three approaches for the desirable collector temperatures for 3 days. Using a SOM network, and with proper configuration, the applied method can be applied to different fields of energy systems. The energy flow between a microgrid and the main grid can be controlled adequately. We can control the charge and discharge of batteries or electric vehicles. The main disadvantage of renewable-energy systems and clean energy relies on their intermittence and their complex control. Artificial intelligence methods can be held in this regard. 5 Conclusion To conclude, the objective of this paper is to propose a suitable solution to protect the SWH from overheating, improve its performance and maximize its lifespan, by lowering the temperature of the solar thermal collector without disturbing the individual’s behaviour. An adaptive controller has been designed to insulate and protect efficiently the solar thermal collector without varying the system. Also, the main components of the SWH system have been modelled as well as the artificial neural network for the computational arrangement. The artificial neural network that is based on a SOM model has been trained using unsupervised machine learning with a total of 2208 training samples. The SOM network was able to group the data sets into four clusters. Finally, it is clearly shown that the proposed system can cover autonomously the primary subsystem of the SWH depending on the days, the solar radiations, the ambient temperatures, the collector temperatures and the household hot-water demand. The approach in which the solar collector can be fully unshaded, 20% covered with a shade, 25% covered or 32% shaded has been chosen as the most suitable and efficient process since it protects the system from overheating and maintains the required temperature of the household hot water. From a future perspective, a thermal simulation of the SWH can be performed to check any possible hotspot formation. Table 1: Simulation parameters of the primary and secondary subsystems [14] Parameter . Value . The surface area of the collector (m2) 2.31 Surface area of the tube (m2) 0.14 Collector volume (m3) 0.12 Optical efficiency 0.81 Collector heat-loss coefficient (W/(m2.K)) 4.5 Volumetric flow rate (L/s) 0.02 Fluid volume (L) 1.41 Fluid specific heat capacity (J/(kg.K)) 3300 Fluid density (kg/L) 1.07 Primary circuit heat-loss coefficient (W/(m2.K)) 150 Aluminium specific heat capacity (J/(kg.K)) 921 Aluminium density (kg/L) 2710 Tank volume (L) 30 Water-specific heat capacity (J/(kg.K)) 4200 Water density (kg/L) 1 Parameter . Value . The surface area of the collector (m2) 2.31 Surface area of the tube (m2) 0.14 Collector volume (m3) 0.12 Optical efficiency 0.81 Collector heat-loss coefficient (W/(m2.K)) 4.5 Volumetric flow rate (L/s) 0.02 Fluid volume (L) 1.41 Fluid specific heat capacity (J/(kg.K)) 3300 Fluid density (kg/L) 1.07 Primary circuit heat-loss coefficient (W/(m2.K)) 150 Aluminium specific heat capacity (J/(kg.K)) 921 Aluminium density (kg/L) 2710 Tank volume (L) 30 Water-specific heat capacity (J/(kg.K)) 4200 Water density (kg/L) 1 Open in new tab Table 1: Simulation parameters of the primary and secondary subsystems [14] Parameter . Value . The surface area of the collector (m2) 2.31 Surface area of the tube (m2) 0.14 Collector volume (m3) 0.12 Optical efficiency 0.81 Collector heat-loss coefficient (W/(m2.K)) 4.5 Volumetric flow rate (L/s) 0.02 Fluid volume (L) 1.41 Fluid specific heat capacity (J/(kg.K)) 3300 Fluid density (kg/L) 1.07 Primary circuit heat-loss coefficient (W/(m2.K)) 150 Aluminium specific heat capacity (J/(kg.K)) 921 Aluminium density (kg/L) 2710 Tank volume (L) 30 Water-specific heat capacity (J/(kg.K)) 4200 Water density (kg/L) 1 Parameter . Value . The surface area of the collector (m2) 2.31 Surface area of the tube (m2) 0.14 Collector volume (m3) 0.12 Optical efficiency 0.81 Collector heat-loss coefficient (W/(m2.K)) 4.5 Volumetric flow rate (L/s) 0.02 Fluid volume (L) 1.41 Fluid specific heat capacity (J/(kg.K)) 3300 Fluid density (kg/L) 1.07 Primary circuit heat-loss coefficient (W/(m2.K)) 150 Aluminium specific heat capacity (J/(kg.K)) 921 Aluminium density (kg/L) 2710 Tank volume (L) 30 Water-specific heat capacity (J/(kg.K)) 4200 Water density (kg/L) 1 Open in new tab Acknowledgements The authors would like to thank the Higher Center for Research (HCR) of the Holy Spirit University of Kaslik (USEK), and the National Council for Scientific Research in Lebanon (CNRS-L) for funding this project. Conflict of interest statement All authors declare that they have no conflicts of interest. References [1] Azzouzi M . Control of solar water heater design . 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Published by Oxford University Press on behalf of National Institute of Clean-and-Low-Carbon Energy This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (https://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com © The Author(s) 2022. Published by Oxford University Press on behalf of National Institute of Clean-and-Low-Carbon Energy

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Clean EnergyOxford University Press

Published: Aug 1, 2022

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