Multiple Collectors Research Articles

Assessment of Conical Solar Stills Empowered by N-Replicated Partially Shaded PVT-CPC Collectors: Unveiling Exergo-Enviro-Economic Dynamics, Productivity and Cogeneration Efficiency

Abstract The economic and environmental dimensions play a pivotal role in evaluating solar still systems. The aim of this study is to evaluate the performance, efficiency, and viability of conical solar still integrated with multiple identical photovoltaic-thermal compound parabolic collectors (PVT-CPC) through comprehensive analyses of cogeneration efficiency, exergoeconomic and enviroeconomic factors, and productivity metrics. The results of this study were obtained through MATLAB programming, enabling accurate and detailed computations. The model has been validated at N=0 and N=1, showing strong correlation results: 0.96 and 0.97 for water temperature, 0.99 for yield in both cases, and 0.99 and 0.98 for glass temperature respectively. The system has achieved a total carbon emissions mitigation of 108.29 tCO2 based on energy and 12.44 tCO2 based on exergy while recording an annual yield of 2199.61 kg. The annual cogeneration efficiency, exergo-economic parameter, enviro-economic parameter, and annual productivity are 38.96%, 31.98 kWh/,1570.20 and 244.68% respectively. Furthermore, the obtained results have been compared with prior research and concluded that the exergoeconomic and enviroeconomic parameters for the proposed system are increased by 93.54% than the solar still with water cooled condensing surface and 94.71% than solar still containing partially coated condensing cover with thermoelectric cooling.

Experimental study on the operating characteristics of multiple collector direct expansion solar-assisted heat pump

Solar thermal application is one of the most important ways to replace fossil energy. The discontinuous heating character and low heating efficiency are two key factors that limit the large-scale promotion of solar thermal application. Large-scale direct expansion solar heat pump systems (DX-SAHP) can provide high efficiency and low-cost continuous heating. However, the characteristics of multiple collector arrays and the system's performance still need more research and exploration. In this paper, a DX-SAHP system with multiple solar collectors was constructed and the work process of the system under different operation conditions was expressed. An experimental platform with two DX-SAHP system was built and studied, and each system contained a 10HP compressor, 16 set solar collectors and one fin evaporator in parallel. The results show that the coefficient of performance (COP) of the system running with solar collectors was nearly 30 % higher than that with the fin evaporator under constant frequency mode, and nearly 45 % under variable frequency mode, indicating that such a system has better performance under variable frequency operation mode. The refrigerant in the collector/evaporators were distributed uniformly in equal-path connection mode, which was beneficial in promoting the system's performance. The heating performance of the system under sunny and cloudy weather conditions was analyzed and discussed, respectively. The test results indicated that the COP of the system on sunny or cloudy days was higher than 4.0, and the maximum hourly COP can reach 11.3 and the maximum hourly heating capacity was 27 kW.

دراسة عملية لاداء سخان ماء شمسي ذو الدوران الطبيعي المتصل على التوالي

This research paper presents an experimental study on the performance of a natural circulation solar water heater system with two typical collectors connected in series. The paper provides a comprehensive analysis of the system's thermal performance under different load conditions, including no-load, intermittent, and continuous load. Mean storage tank, solar collector means plate (the left) temperature and thermosyphon flow rate in a vertical tank were measured. Results showed that there was variation in solar water tank and collector plate temperature under load and no-load conditions. Analysis of thermal performance of the system was conducted for each condition. The highest plate temperature (100 ˚C or even more) with no circulation of both collector and load conditions, indicate the high quality of the solar collectors even during the cold season. The collector’s arrangement in series connection is of highest gain in energy and higher storage tank mean water temperature. Several characteristic equations obtained to represent the performance of the present natural circulation system under collector connection arrangement in series. In fact, when large amount of hot water was required for a certain purpose (Industrial sector for example - MSF plant or central heating), multiple collectors are to be deployed in series and in parallel to produce the required amount (quantity) and desired temperature (quality) at the same time. Key words: Thermosyphon solar water heater, storage tank profile temperature, Solar Water Heaters (SWHs), instantaneous efficiency, collector flow factor, collector efficiency factor, collector heat removal factor

Research on the traffic flow measurement method of intelligent connected vehicles based on series and cascade technology

At present, the major cities in our country have entered the development of smart cities, the utilization rate and prevalence rate of intelligent connected cars in smart cities have reached a new peak,to manage the real-time traffic flow of intelligent connected vehicles effectively in smart cities. This paper proposes to calculate the flow of intelligent connected vehicles based on series cascade technology. Firstly, this paper collects multi-source heterogeneous data based on multiple collectors; Secondly, a generative adversarial network is employed for data fusion, synthetic data, closely mirroring the original, is generated for handling unknown variables during model training. Next, an autoencoder model generates input data for feature representation. Lastly, CatBoost, a regression model that leverages a cascaded machine learning algorithm, is utilized to forecast the traffic flow of intelligent connected vehicles in smart cities. The results show that the method based on CASCaded machine learning has remarkable effect in predicting smart city traffic flow and alleviating urban road congestion.

The intra- and interrater reliability of isometric muscle contractions using a novel fixation system for a hand-held dynamometer.

A novel fixation system for a hand-held dynamometer (HHD) was designed to enable isometric muscle measurements on various muscle groups of strong, healthy individuals in a field setting. The objective of this study was to evaluate the intra- and interrater reliability of the system and determine its suitability for use by multiple researchers within large-scale data collections during field activities. Four researchers tested eight healthy subjects, who each completed eight different maximal isometric muscle strength assessments using the HHD fixation system. Intraclass correlation coefficients (ICC) results were evaluated with a 95% confidence interval. ICC results for interrater reliability demonstrated excellent agreement of all eight measurements tested. ICC results for intrarater reliability demonstrated excellent agreement for six out of eight measurements. This system provides a new opportunity for several different high-quality maximal muscle strength measurements to be collected by multiple data collectors on large numbers of strong, healthy individuals in a field setting.

Pandemic data quality modelling: a Bayesian approach in the Italian case

AbstractWhen pandemics like COVID-19 spread around the world, the rapidly evolving situation compels officials and executives to take prompt decisions and adapt policies depending on the current state of the disease. In this context, it is crucial for policymakers to always have a firm grasp on what is the current state of the pandemic, and envision how the number of infections and possible deaths is going to evolve shortly. However, as in many other situations involving compulsory registration of sensitive data from multiple collectors, cases might be reported with errors, often with delays deferring an up-to-date view of the state of things. Errors in collecting new cases affect the overall mortality, resulting in excess deaths reported by official statistics only months later. In this paper, we provide tools for evaluating the quality of pandemic mortality data. We accomplish this through a Bayesian approach accounting for the excess mortality pandemics might bring with respect to the normal level of mortality in the population.

A case study of enhanced flotation of coal gasification fine slag by multiple compound collectors

ABSTRACT The flotation mechanism of multiple compound collectors called ZKC-I for coal gasification fine slag (CGFS) was revealed from the flotation kinetics, adsorption properties, bubble–particle interaction, and froth properties. The results were compared to dodecane, which represents the conventional nonpolar hydrocarbon oil collector. The flotation concentrates yield and rate constant of CGFS treated by ZKC-I were 2–3 times than those of CGFS treated by dodecane. Fourier transform infrared spectroscopy and wrap angle results showed that ZKC-I improved the hydrophobicity of residual carbon because of the synergistic adsorption of fatty acids, esters, and aromatic hydrocarbons in the ZKC-I on the heterogeneous surface of residual carbon particles, which enhanced the adhesion between residual carbon particles and bubble. Due to the strong carrying capacity of the bubble to residual carbon particles, the number of residual carbon particles in the froth treated by ZKC-I was more than that of the CGFS froth treated by dodecane. The high content of carbon particles in the froth resulted in great stability of the flotation froth, and the maximum height and half-life of the froth were higher than that of CGFS treated by dodecane. This study has practical and theoretical significance for the separation of coal-based solid waste.

An analysis of the supply chain dynamics of remanufacturing with multiple collectors

This paper addresses how decisions related to the collection of used products (namely the location and number of collection sources) affect the dynamic performance of remanufacturing. More specifically, we address the case where a manufacturer produces both new and remanufactured, as-good-as-new, products and delivers them to the final customers via a supplier (or suppliers). A percentage of these products is collected at the end of their life by multiple collection sources – either the suppliers, third-parties in charge of the collection, or a combination of both – that may differ in the time required to carry out their collection activities. In this scenario and assuming an optimal operation of all nodes in the supply chain, we derive an exact formulation for two well-known indicators of the so-called bullwhip effect, i.e. the amplification of the order variance and the inventory variance experienced by the manufacturer as compared to that of the final customer demand. The analysis of the so-obtained formulae highlights the importance of the collection lead times (which may be employed as a proxy of the location of the collection source, or its effectiveness in the collection process), as only the number of collection sources with different collection lead times affects the bullwhip effect, being irrelevant how collection sources with the same collection lead times allocate their collection quotas of end-of-life products among themselves. An expression for the optimal allocation (in terms of reduction of the bullwhip effect) of the collection quotas of end-of-life products to each collection source is given, showing the positive effect of increasing the number of groups of collection sources with different collection lead times. In order to reap these benefits, it is required to perform a balanced allocation of the collection of end-of-life products among these groups. These results offer a number of managerial insights for the design of a collection system for the end-of-life products in a remanufacturing setting from a dynamic performance perspective.

Impact of Multiple Module Collectors on the Cell Current Distribution within the Battery Pack

Lithium-ion batteries are usually connected in series and parallel to form a pack for meeting the voltage and capacity requirements of energy storage systems. However, different pack configurations and battery module collector positions result in different equivalent connected resistances, leading to pack current inhomogeneity, which seriously reduces the lifetime and safety of the pack. Therefore, in order to quantitatively analyze the influence of the connected resistance on the current distribution, this study researched the initial cell current distribution of the parallel module by developing mathematical models of different configurations. Then, this study explored the influence of multiple module collector positions on the current inhomogeneity of the pack under the dynamic current condition. The results show that the inhomogeneity of cell current and discharge capacity in the pack with parallel modules connected in series can be improved by keeping each cell in a parallel module with the same distance to its module collector. Furthermore, the current homogeneity of the edge parallel modules in the pack is seriously affected by the position of the single module collector. Therefore, this study innovatively proposes the symmetrical multiple module collectors of the pack, which can greatly improve the current homogeneity of the edge parallel modules, thereby improving the lifetime and safety of the pack.

Novel multiple ligand metal-group collectors assembled from benzohydroxamic acid and cupferron

Pb–BHA (lead complexes of benzohydroxamic acid) as metal-group collectors have been recently used for mineral flotation collector. This complex possessed high selectivity but low flotation efficiency due to extensive dosage. To improve the flotation performance of Pb–BHA, we designed a novel multiple ligand complex collector assembled from Pb2+, BHA, and cupferron (CPF) (i.e., Pb–BHA–CPF). The flotation performance of Pb–BHA–CPF was studied through the flotation test. The structure of Pb–BHA–CPF was analyzed by Fourier transform infrared spectroscopy (FTIR) and X-ray photoelectron spectroscopy (XPS), and the adsorption mechanism of Pb–BHA–CPF at the solid–liquid interface was investigated and discussed through the zeta potential, FTIR, XPS, and crystal chemistry analyses. Based on the results, Pb–BHA–CPF exhibited stronger collecting ability and selectivity than Pb–BHA at a lower reagent dosage. Structural analysis revealed that BHA and CPF could coordinate with Pb2+ to form novel multiple ligand complexes with lead groups, and CPF may replace BHA to form the molecular structure of Pb(L1)n(L2)m (HL1 = BHA, NH4L2 = CPF, n > m). The adsorption mechanism analysis indicated that Pb–BHA–CPF had stronger electrostatic attraction than Pb–BHA and showed stronger chemical adsorption strength with the active oxygen atoms on the mineral surface. This study proposed a method for designing and assembling a multiple ligand metal-group collector.

ASSESSING PALEOECOLOGICAL DATA RETENTION AMONG DISPARATE FIELD COLLECTION REGIMES: A CASE STUDY AT THE MYGATT-MOORE QUARRY (MORRISON FORMATION)

ABSTRACT Field work protocols in the recovery of vertebrate fossils can vary between sites, and also within sites, due to differing researcher goals. Disparate researcher priorities can affect the resulting collections in terms of species richness, size distribution, specimen completeness, taphonomic condition, and aesthetic value. We examined paleoecological data, in the form of bone surface modifications (e.g., abrasion, feeding traces, etc.), from a single site worked by multiple collectors to determine the sensitivity of this type of data to collector bias. We examined 2,368 fossils from the Mygatt-Moore Quarry and divided them into two cohorts: 2016–2019 (bulk collection under a single collector) and pre-2016 (mixed collectors and priorities). Frequencies of modified bone surfaces were then calculated in each cohort among the recovered specimens. However, the specimens within the cohorts were of unequal size, completeness, and amount of preserved surface area, making inferences of modified bone surface frequencies difficult. To correct for unequal morphologies and preservation, we estimated the percentage of altered surface area among specimens by overlaying photos with a 4.0 cm2 digital grid to create a digital set of equal sized fragments. With such a large dataset, we took a random 10% subsample of specimens from each cohort for the grid study. We estimated the sample size needed to accurately reflect the frequency of bone surface modifications by specimen and surface area for each cohort. Results show the recovery of modified bone surfaces between the two cohorts was highly disparate, and potentially sensitive to the effects of collector bias when using specimen-level data. However, frequencies based on estimates of surface area were much more consistent and appeared to equalize data between cohorts and showed little influence of collector bias on data recovery. Thus, the traditional method of calculating frequencies using specimen-level data may create an illusion of bias that is removed when frequencies are calculated from estimated bone surface area. We posit that the digital fragmentation method is more informative when comparing paleoecological traces between datasets and should be applied to fossil assemblages going forward, especially when collection protocols between assemblages are significantly different or unknown.

Experiments and dynamic modelling of dry expansion and flooded evaporators in a CO2 solar assisted heat pump

• A direct-type SAHP working with CO 2 and three PV-T collectors is presented. • Flooded evaporation, obtained with natural circulation, avoid mal-distribution issues. • When superheating is present, the performance drops due to lower collector efficiency. • A dynamic numerical model of the heat pump has been realized in Matlab environment. • The model is used to study solutions to control and avoid superheating. In the present study, a dynamic model of evaporators in a CO 2 solar assisted heat pump is presented and experimentally validated. The evaporators are PV-T (photovoltaic-thermal) solar collectors and they can work both in direct expansion mode and flooded mode. Thanks to the PV-T evaporators we convert the solar radiation into electricity in the PV cells, ensure the evaporation of the CO 2 and cool the solar cells to improve the PV conversion efficiency. The evaporators of the heat pump can work under two operative modes, dry expansion and flooded evaporation. When working in dry-expansion mode, the refrigerant mass flow rate after the throttling valve is directly sent to the solar collectors. Alternatively, when operating in flooded mode, the collectors are fed with saturated liquid refrigerant coming from a low-pressure receiver. In real applications, we can have multiple collectors that are fed in parallel and thus the advantage and the main reason for studying the flooded solar evaporators is that, with this schematic, we can feed them with saturated liquid avoiding possible distribution problems that may occur when distributing the liquid-vapor mixture (direct expansion mode). In this article, the operating mechanism of the heat pump is presented and an experimental comparison between the dry expansion and flooded evaporation is discussed. Since the system operation strongly depends on the solar irradiance and its variation, a comprehensive dynamic numerical model of the system is developed and validated. The results of the model show the regulation mechanism of the evaporators and the whole system and allow to study the solution to possible issues that are encountered in this application.

An optimization-based coverage aware path planning algorithm for multiple mobile collectors in wireless sensor networks

An optimization-based coverage aware path planning algorithm for multiple mobile collectors in wireless sensor networks

Potential Function-Based Control Using Neutral Networks in Uncertain WSNs With Mobile Collectors

In wireless sensor networks (WSNs), sink node mobility has been considered an efficient way to alleviate excessive data forwarding at nodes close to the sink node. Since the mobile sinks (or collectors) move around the network collecting data from the sensor nodes, the need for multi-hop forwarding of sensor data is reduced. In WSNs with mobile collectors, efficient path planning of mobile collectors is a major challenge where many algorithms have been proposed. However, they do not consider tracking performance degradation during flight due to environmental factors such as wind, waves, and obstacles. Tracking control algorithms have been proposed to correct the paths of mobile collectors, but existing work do not consider the possibility of collisions between multiple collectors. In this paper, we propose a distributed control approach that can improve tracking performance of mobile collectors while avoiding collisions in unknown and uncertain WSN environments. The proposed algorithm uses a potential field of attraction and repulsion to control individual mobile collector input, which enables mobile collectors to adjust their trajectories with online learning in a distributed fashion. From the theoretical analysis, the upper bound of tracking error and the conditions of the system parameters to guarantee the desired tracking error set by the operator are derived. The simulation results show that the proposed method significantly outperforms existing methods in terms of tracking error, collision rate, system stability, and convergence.

Energy-Efficient Static Data Collector-based Scheme in Smart Cities

In the Internet of Things (IoT)-based smart city applications, employing the Data Collectors (DC) as the data brokers between the nodes and Base Station (BS) can be a promising solution to enhance the energy efficiency of energy-constrained IoT sensor nodes. There are several schemes that utilize mobile DCs to collect the data packets from sensor nodes. However, moving DCs along the hundreds of thousands of sensors sparsely distributed across a smart city is considered a design challenge in such schemes. Another concern lies in how these mobile DCs are being powered. Therefore, to overcome these limitations, we exploit multiple energy-limited Static Data Collectors (SDC) which are deployed at the locations optimized so that the energy consumption of both nodes and SDCs is minimized. Likewise, an Unmanned Aerial Vehicle (UAV)-enabled wireless power transfer is considered for sustaining the SDCs to avoid their energy depletion and data packet loss. The sustainable charging process operates periodically in each cycle so that the UAV flies from a charging station and after recharging the SDCs, it comes back to the station to be recharged. In this study, we formulate a problem to optimize the movement trajectory and charging time of UAV so that sustainable operation of SDCs during a cycle can be achieved. Unlike the prior studies, our proposed scheme determines the optimal trajectory and charging time at the beginning of each cycle which leads to increase accuracy in comparison with long-term optimization-based schemes. The outcomes of simulation experiments show that the proposed scheme achieves improved network performance in terms of data delivery ratio (12.5%); system throughput (6.6%); total energy consumption (59.19%); and network lifetime (58%) as compared to previous related works.

Is Your Collection Ambiguous?

The natural history specimens of the world have been documented on paper labels, often physically attached to the specimen itself. As we transcribe these data to make them digital and more useful for analysis, we make interpretations. Sometimes these interpretations are trivial, because the label is unambiguous, but often the meaning is not so clear, even if it is easily read. One key element that suffers from considerable ambiguity is people’s names. Though a person is indivisible, their name can change, is rarely unique and can be written in many ways. Yet knowing the people associated with data is incredibly useful. Data on people can be used to validate other data, simplify data capture, link together data across domains, reduce duplication-of-effort and facilitate data-gap-analysis. In addition, people data enable the discovery of individuals unique to our collections, the collective charting of the history of scientific researchers and the provision of credit to the people who deserve it (Groom et al. 2020). We foresee a future where the people associated with collections are not ambiguous, are shared globally, and data of all kinds are linked through the people who generate them. The TDWG People in Biodiversity Data Task Group is therefore working on a guide to the disambiguation of people in natural history collections. The ultimate goal is to connect the various strings of characters on specimen labels and other documentation to persistent identifiers (PIDs) that unambiguously link a name “string” to the identity of a person. In working towards this goal, 150 volunteers in the Bionomia project have linked 21 million specimens to persistent identifiers for their collectors and determiners. An additional 2 million specimens with links to identifiers for people have already emerged directly from collections that make use of the recently ratified Darwin Core terms recordedByID and identifiedByID. Furthermore, the CETAF Botany Pilot conducted among a group of European herbaria and museums has connected over 1.4 million specimens to disambiguated collectors (Güntsch et al. 2021). Still, given the estimated 2 billion (Ariño 2010) natural history specimens globally, there is much more disambiguation to be done. The process of disambiguation starts with a trigger, which is often the transcription of a specimen’s label data. Unambiguous identification of the collector may facilitate this transcription, as it offers knowledge of their biographical details and collecting habits, allowing us to infer missing information such as collecting date or locality. Another trigger might be the flagging of inconsistent data during data entry or resulting from data quality processes, revealing for instance that multiple collectors have been conflated. A disambiguation trigger is followed by the gathering of data, then the evaluation of the results and finally by the documentation of the new information. Disambiguation is not always straightforward and there are many pitfalls. It requires access to biographical data, and identifiers to be minted. In the case of living people, they have to cooperate with being disambiguated and we have to follow legal and ethical guidelines. In the case of dead people, particularly those long dead, disambiguation may require considerable research. We will present the progress made by the People in Biodiversity Data Task Group and their recommendations for disambiguation in collections. We want to encourage other institutions to engage with a global effort of linking people to persistent identifiers to collaboratively improve all collection data.

A novel method for making laser cut panel based daylight collector coupled to a tubular light guide

The work in this paper focuses on the development of a daylighting device which can increase the light output for longer lengths of hollow mirrored light pipe. The device proposed is passive, easy to build, and inexpensive. It uses the concept of total internal reflection in acrylic laser cut panels (LCPs) and extends the idea into a complete collector based on mathematical modelling. The novel method of fabricating laser cut panels with steep cutting angles and partial depth cuts has been discussed in this paper. This method has been combined with weight optimisation to make a lightweight yet efficient collector with no laser cuts exposed to the atmosphere. The simulation results of this collector have been compared with a flat acrylic plate coupled to a light pipe and experimental validation of simulation has been performed using a prototype. The simulation results for collector coupled to 80% reflective light pipe have shown up to 4.3 times the illuminance on model room floor as compared to light pipe with a flat plate on 21 December- the low solar altitude season for which the collector was primarily designed. Another simulation of a real dimension office space with multiple collectors shows that at least 175 lx of average illuminance is available on the work surface with 227 cm2 cross-section light pipes.

Analysis of current collection in micro-tubular solid oxide fuel cells: An empirical and mathematical modelling approach for minimised ohmic polarisation

Data from electrochemical impedance spectroscopy (EIS) of a 152 mm long, 6.8 mm outer diameter (OD) segmented-in-series micro-tubular solid oxide fuel cell (μT-SOFC) coupled with equivalent circuit modelling (ECM) support a circuit model and a continuum resistance path model to investigate the ohmic polarisation and current distribution for various current collector configurations on a micro-tube. Minimising the characteristically long axial current conduction pathways of μT-SOFCs is critical to maximise cell performance, particularly of cells more than a few centimetres long. Optimal positioning of a single current collector minimises the performance losses from the electrode. Multiple current collector terminals increase cell performance over a single terminal, but positioning must still be optimised. Sizing of the current collector terminal is critical to limit the loss of active area of the cathode. A trade-off between terminal sizing/spacing and loss of active area can lead to sub-optimal current collection. The models are generalised for all possible current collector configurations. We identify simple criteria to determine the maximum current collection efficiency of single and multiple anode current collectors for a range of cell geometries. The design tool allows early consideration to cell sizing as a function of anode current collection during cell and stack development.

A CMOS Photodetector for Direct Color Imaging

A novel photodetector for imaging in the visible-near infrared range is investigated. Unlike currently used detectors, the proposed device does not require thin film filters for spectral discrimination. Instead, the discrimination relies on the wavelength-dependent absorption property of semiconductor materials. The detector consists of a window exposing the silicon substrate to the electromagnetic signal. Besides the window, multiple collectors separated by polysilicon gates are laid out. Proper voltage biasing establishes a different spectral response for each collector, thus creating a detection color space. Experimental results demonstrate the color detection capability of a three-collector imaging pixel from sensitivity metamerism index calculations. The sensor is fabricated in a standard 0.35-μm CMOS process and presents a peak combined collectors' responsivity of 0.35 A/W.

Techno-Economic Analysis of Glazed, Unglazed and Evacuated Tube Solar Water Heaters

In the residential sector, a great part of the electricity goes into heating water by electric water heaters, which results in high CO2 emissions as well as an unprecedented increase in electricity demand leading to an energy crisis. This study offers solar water heaters as a more economical and efficient replacement for electric water heaters. The present study is aimed at investigating the potential for solar water heaters in the subcontinent, especially in India. A feasibility analysis is performed for seven cities in the subcontinent, namely Mumbai, New Delhi, Kolkata, Assam, Gujrat and Madhya Pradesh. Simulated results are based on a solar fraction, equity payback, multiple collectors (one, two or three), horizontal and tilted, type of collector (evacuated tube, glazed and unglazed), electricity saved and greenhouse gas (GHG) emission reduction. The collector’s area is made such that it should receive at least 50% of the solar fraction. The range of payback period varies from five to 15 years. The results show Gujrat being the most ideal site for solar water heaters.