Solar Heating Applications Research Articles

Thermo-economic analysis of a solar district heating plant with an air-to-water heat pump

Solar district heating systems are essential in reducing carbon emissions and alleviating the energy crisis. By integrating with air-to-water heat pumps, it is possible to enhance the system’s efficiency and flexibility. However, the complementary mechanisms and coupling effects between the heat pump and the other components of the system are not clear. To address these issues, it is necessary to investigate the thermo-economic performance of the system, taking into account energy price fluctuations to achieve a more efficient and economically viable operational model. This study focuses on a solar district heating system in the Danish city of Ørum and investigates the impact of integrating a large-scale air-to-water heat pump. Based on energy and economic analyses, the impact of the heat pump on the system efficiency and the levelized cost of heat are investigated for 2020 and 2022. The results show that the heat pump can convert low-cost electricity into heat which will be stored in the tank, increasing the tank’s heat storage content by 1.2 times. The medium to low-temperature water in the tank can preheat the heat pump’s compressor, raising the COP of the heat pump from 3.3 to 3.5 and increasing the annual utilization cycle of the tank by 1.4 times by reducing the return water temperature to the bottom of the tank. Additionally, the system performance has been improved due to the installation of the heat pump, which increased the system COP from 1.22 in 2020 to 2.62 in 2022. Subsequently, the CO2 emission has been decreased from 192 kg/MWh to 74 kg/MWh with a larger share of sustainable energy. Due to the heat pump operation, the system-levelized cost of heat could be reduced to 68.6 EUR/MWh, compared to 94 EUR/MWh if the heat pump is removed. The investigation also revealed that the heat pump improved the flexibility of the heating system in response to energy prices, especially during the 2022 energy crisis in Europe. The findings of the paper provide a good reference for large solar heating applications.

Towards maximum cost-effectiveness: multi-objective design optimisation of insulating glass flat-plate collectors

A significant challenge in the advancement of solar thermal heating systems lies in the unexplored techno-economic potential of insulating glass flat-plate collectors. These collectors are constructed in accordance with the specifications of standard insulating glass units and have emerged over the past decade as a promising design concept for enhancing the cost-effectiveness of solar thermal systems. However, substantial findings regarding the techno-economic viability of their production are still pending. The aim of this paper is to optimise insulating glass collector designs for solar district heating applications by identifying key design parameters that maximise cost-effectiveness. This study employed a five-stage methodology. It included thermo-hydraulic collector modelling using MATLAB/Simscape and the CARNOT Toolbox. The model was validated against experimental performance tests. A Latin hypercube computational design with 250,000 samples was set up to train supervised machine learning metamodels and perform a multi-objective optimisation using an elitist genetic algorithm. The study identified the argon concentration, collector length, and width as critical parameters influencing efficiency. Larger, thinner collectors demonstrated superior performance due to reduced convective losses and increased aperture-to-surface ratios. The optimisation revealed that the insulating glass collectors could achieve a 7.7 percentage point increase in efficiency, a 19.4 % reduction in material cost, and a 14.5 % decrease in weight compared to market-available flat-plate collectors. However, the direct economic comparison was not considered strong in evidence due to a lack of economic data from technology providers. The most cost-effective designs featured an argon concentration of 99 %, sealing thickness of 31.2 mm, and a glazing thickness of 4.1 mm, and 4.5 mm, while collector length and width varied more significantly. The research findings indicate the techno-economic potential of insulating glass collectors, demonstrating their ability to outperform conventional flat-plate collectors in terms of cost-effectiveness and efficiency. Future studies should focus on producing and testing larger modules and incorporating production costs to fully realise their potential for solar district heating applications. This study provides valuable guidelines for IGU designers and producers aiming to develop cost-effective and efficient solar thermal collectors for district heating systems.

A novel heating system of solar-assisted enhanced jet enthalpy air source heat pump for cold regions

Solar energy and air source heat pumps are common heat sources for clean heating, but at lower ambient temperatures, the performance of solar energy and air source heat pumps will decline significantly, which can be ameliorated by integrating the two heat sources. However, the range of solar radiation and ambient temperature variation is very wide, and the existing integration methods cannot guarantee that they are optimal over a wide range. Therefore, this paper proposes a novel integration method of solar energy and jet enthalpy air source heat pump suitable for cold regions, where solar energy is used to heat the refrigerant in the jet branch to increase the flow rate of the jet branch, which enhances the effect of jet enthalpy. Under varying outdoor temperatures and solar radiations, the performances of the new integrated system and the traditional integrated systems are compared by simulation method. The results show that within the scope of this study (outdoor temperatures ranging from −30 °C to 10 °C, and radiations from 200 to 800 W/m2), the heat output and coefficient of performance of the new system are higher than those of the existing integrated systems. At an outdoor temperature of −30 °C and a radiation of 500 W/m2, the new system increases heat output by 45.8 % and coefficient of performance by 22.5 % compared with the existing two systems. This research can promote the application of solar energy and air source heat pump heating in cold regions.

Graphene-based Cr-GaAs-Ag multilayer absorber structure for solar heating applications

The optimization of the solar absorber is very important to develop the efficiency of the solar absorber. We have designed here one solar absorber which is optimized using variation in different physical parameters. The design of this absorber is based on Cr-GaAS-Ag materials which is also based on a thin film graphene material. The designed solar structure is used for heating applications which can be applied in industrial use. The highest absorption of more than 99 % is achieved for different wavelengths. The design also shows the 97.1 % absorption for the 1000 nm wavelength. The optimization section is also provided in this research at the end of results section. The conclusions are obtained using absorption for the different layer structures in this research. Layer by layer analysis for the absorption is provided in this manuscript. The research is aimed at renewable energy use in the industries by providing sustainable heating applications.

Development and Investigation of Nitrate Phase Change Filler Material for Solar Process Heating Applications

Thermocline thermal energy storage system is an imperial system for solar process heating applications. The thermal energy storage system comprises filler material and heat transfer fluid. In the present study, the commercial phase change material (PCM) (filler material) solar salt (60%NaNO3+40%KNO3) is synthesized, and it is encapsulated with a 1mm thickness of stainless steel 316L encapsulation with the macro-size of 60mm; the encapsulated PCMs is considered as a single particle in the thermocline thermal energy storage system. The performance of the single encapsulated PCM is studied with a constant heat transfer fluid (Therminol-VP1) flow rate of 0.00015 kg/s during the charging process. The specific heat of the solar salt is measured in Differential Scanning Calorimeter (DSC) in the solid phase is found as 1.381 J/gK, and liquid phase is identified as 1.551 J/g-K, the enthalpy during the phase change process is found as 116.72 J/g. As well, the thermal conductivity of the solar salt is measured in Transient Heat Conduction method, and the thermal conductivity follows the linear relationship of -0.0025(T)+0.4023 (45ºC<T<100ºC) in the sensible region. The temperature variations and the phase change phenomena for the solar salt is identified and the contours are provided. The charging time for the encapsulated solar salt is identified as ~138 minutes. The energy storage cost for the single filler material (Solar Salt + SS316L encapsulation) is identified as Rs.5.93/- (USD 0.071) for the period of charging duration.

Impact of Temperature and Optical Error on the Combined Optical and Thermal Efficiency of Solar Tower Systems for Industrial Process Heat

Concentrating solar thermal (CST) power towers can provide high flux concentrations at commercial scale. As a result, CST towers exhibit potential for high-temperature solar industrial process heat (SIPH) applications. However, at higher operating temperatures, thermal radiation losses can be significant. This study explores the trade-off between thermal and optical losses for SIPH applications using a collection of three case studies at operating temperatures that range from 900-1,550 °C. We assume blackbody radiation to represent the thermal losses at the receiver and we use ray tracing to estimate the optical losses. The results show the impact of process temperature on the maximum attainable system efficiency, as well as the higher flux concentration requirements as the temperature increases.

Preparation and characterization of palmitic acid/polymer composite phase change materials supported with cross-linked poly(limonene-co-ethylene glycol dimethacrylate) copolymers for low-temperature thermal applications

Limonene-based polymers have a growing interest as being renewable source-derived materials. Here, highly cross-linked porous polymers were synthesized by free radical copolymerization of water-in-oil (w/o) high internal phase emulsions (HIPEs) of limonene and ethylene glycol dimethacrylate (EGDMA). The bio-derived monomer content in the total monomer composition was set to 50 vol%. To vary the openness and permeability of the resulting porous copolymers, synthesized poly(limonene-co-EGDMA) (PLE-x) copolymers were processed via two different approaches as extraction (E) and lyophilization (L). Ultimately, the ring-porous PLE-E or PLE-L copolymers with different degrees of permeability were used as supporting matrices for the development of form-stable palmitic acid@poly(limonene-co-EGDMA) (PA@PLE-E and PA@PLE-L) composite phase change materials (PCMs). The chemical structure, pore morphology, specific surface area, and thermal properties of the PLE based supports and PA@PLE-E / PA@PLE-L composite PCMs were explored. BET specific surface areas of the ring-porous PLE-E and PLE-L frameworks were measured to be 20.5 m2.g−1 and 4.8 m2.g−1. In addition to that, the latent heats of the resulting composite PCMs were found to be 77.4 J.g−1 and 64.1 J.g−1, while the peak melting temperatures were 63.4 °C and 60.7 °C, for PA@PLE-E and PA@PLE-L, respectively. The bio-derived matrices based thermally stable leak-proof PA@PLE-x composite PCMs with proper latent heat storage (LHS) characteristics are ideal candidates as energy materials for passive solar heating applications due to their favorable phase change temperatures.

Thermal performance enhancement of lauric acid using nanomaterials as composite phase change material.

In the present work, lauric acid was taken as a phase change material (PCM), and different nanoparticles (NPs) such as SiO2, TiO2, CuO, and ZnO were taken as the supporting materials. CuO NPs were prepared through the co-precipitation technique; SiO2, TiO2, and ZnO NPs were synthesized via the sol-gel technique. These NPs with different weight fractions were dispersed into molten lauric acid, individually. The variations in thermal properties (phase change temperature and latent heat for solid and liquid) of the prepared composite PCMs due to the dispersion of NPs were observed by DSC analyses. An increase in thermal conductivity of the composite PCMs was observed with the increasing weight fraction of NPs. In order to ascertain the long-term utility, a thermal reliability test was conducted on the composite PCMs with repeated heating and cooling cycles. Also, the specific heats of the pure PCM and the composite PCMs were determined as a function of temperature. Further, the experimental investigation was performed on the pure PCM and the prepared composite PCMs to assess their phase change behavior, and the test results clearly proved that the time required for the complete melting and freezing process of the composite PCMs was less when compared to pure PCM. By considering the above facts, the newly prepared composite PCMs can be recommended as a potential candidate for low-temperature solar heating applications.

An Integrated Light Pipe Receiver and Thermal Energy Storage

An integrated light pipe receiver and thermal energy storage (TES) architecture is proposed for solar process heat applications. Simulations demonstrate the benefits of increased heat transfer area to a low conductivity TES medium and reduced surface radiation losses. When compared against a baseline design with a hemispherical absorber, the integrated light pipe receiver enables up to a factor of three higher energy storage for distributed absorption relative to localized absorption at the top of the TES. For a lower thermal conductivity TES medium or baselining to a flat-top absorber, an increase in thermal energy storage up to a factor of five results.

Impacts, Barriers, and Future Prospective of Metal Hydride‐Based Thermochemical Energy Storage System for High‐Temperature Applications: A Comprehensive Review

This article summarizes various thermochemical energy storage (TCES) systems based on their thermochemical properties, operating temperature, and storage density. Metal hydride (MH)‐based TCES is a potential energy storage system due to its higher energy storage density (>100 kWh m−3), higher operating temperature (>500 °C), relatively better reaction kinetics, and minimal or no energy losses (theoretically). MHs operate at various temperature ranges, and based on temperature, they are classified as low‐temperature MH and high‐temperature MH. This article highlights potential metal alloys operating above 300 °C, with an energy storage density of more than 100 kWh m−3, suitable for concentrated solar thermal power generation and industrial process heating applications. Magnesium (Mg) alloy‐based hydrides have shown good cyclic stability (up to 1500 cycles) at a temperature above 400 °C. The lower cost of material, higher energy storage capacity, better reversibility, and higher thermal stability of Mg‐based alloys have been explored in several small‐scale experimental investigations. The thermal energy storage (TES) efficiency of MH‐based TCES systems is reported ≈ 90%, which is significantly higher than sensible and latent TES systems. Challenges associated with MH‐based TES systems, such as heat transfer enhancement, cost reduction, and chemical and thermal stability, have been discussed in detail.

Strengths, Weaknesses, Opportunities, and Threats Analysis for the Strengthening of Solar Thermal Energy in Colombia

Colombia has made different efforts to contribute to fulfilling its international commitments to curb climate change by reducing emissions and promoting technological development and project financing. However, the existing policies and regulatory framework primarily focus on promoting the photovoltaic industry for electricity production. Likewise, the energy sector has neglected the potential of solar thermal energy as a heat source. In this sense, it is necessary to redouble efforts through new public policies that integrate solar thermal energy in the residential and productive sectors. Using solar thermal energy for heating can contribute to the energy transition and meet its sustainable development goals. Therefore, the main objective of this work was to analyze Strengths, Weaknesses, Opportunities, and Threats to determine the potential application of thermal solar heat in Colombia while considering the local context. Factors such as their environmental conditions, policies, and regulations; the existence of international agreements; and their political status in general were analyzed. The analysis revealed Colombia’s significant solar heat potential, enabling over 1.3 million cold-climate households to access hot water or reduce firewood use. Industrially, applying solar heat in 5% of the current industry could decrease fossil fuel consumption by 13 PJ. The findings highlight that Colombia’s potential in thermal solar energy necessitates collaborative efforts, legislative reinforcement, climate-adaptive measures, and the resolution of political and social challenges.

Opportunities and Barriers to the Application of Solar Heat For Industrial Processes Technologies to Turkish Industrial Parks: The Case of Kayseri Industrial Park

Turkiye's industrial parks (IP) represent more than one-third of the country's exports and employ 2.1 million people, almost one-third of the country's total industrial employment. As an effective means of implementing macro policies, IPs are essential for inclusive and sustainable industrialisation by improving efficiency and lowering costs. Given Turkiye's vulnerability to climate change and natural disasters, investments in renewable energy (RE) are poised on the national climate change agenda for a steady and reliable energy supply. As an upper-middle-income country, Turkiye has a good start transitioning to RE mainly. Although one of the top 5 countries with total solar capacity, solar heat for industrial processes (SHIP) is one of the not-fully discovered areas for energy generation. With this background, this study examines drivers and barriers to adopting SHIP technologies. The method uses the lessons from prosumer experience in developing and applying SHIP technologies. For this purpose, the field research was conducted in two phases, and the two different data sets were collected by the methods of 'Semi-structured in-depth interviews with prosumers' and 'Survey on solar energy usage with members of IP'. The current barriers and drivers in decision-making for investment and installation of photovoltaics implications and their maintenance were identified. Then, a survey built on the lessons learned from the analysis of the interviews was made to determine why there is no improvement in the deployment of SHIP implications. Finally, essential barriers and sub-barriers are listed under the headings of ‘legal, regulatory, procedural, economic, financial, Social, and technical'. The results of the data analysis show that 'insufficient government support, lack of financial support, inadequate capacity and expertise with modern technologies, and inefficient infrastructure' are identified as significant barriers to the diffusion of SHIP technologies in the IP context in Turkiye.

Performance enhancement of flat-plate and parabolic trough solar collector using nanofluid for water heating application

Flat plate solar collector (FPSC) and parabolic trough solar collector (PTSC) are widely used for residential solar water heating (SWH) applications. This work studied two different solar collector systems. Nanofluid and its influence on the residential solar water heating (SWH) systems were investigated. The two SWH systems were designed, installed, tested, and compared at varying mass flow rates (mf) of 0.47, 1.05, and 1.75 kg min−1 in ambient environmental conditions. The comparative study was conducted according to thermal efficiency (ηth), useful energy gain (QU), stored energy (QS), outlet hot water temperature (To), and difference temperature (ΔT) between the cold inlet and hot outlet water from the collectors. The analysis of outcomes showed that the PTSC was more efficient than FPSC. The FPSC and PTSC systems performance were investigated using two different types of nanofluids. Carbon nanotubes in water and ethylene glycol were utilized. A remarkable improvement in the average thermal efficiency 64.1 % and 80.6 % of FPSC and PTSC systems using ethylene glycol nanofluid were obtained respectively. The total reduction in CO2 emissions was 31.26 kg/day and 39.28 kg/day for the FPSCs and PTSCs, respectively in the presence of ethylene glycol nanofluid. A significant saving in CO2 release is owing to the renewable clean energy of solar collectors.

Numerical simulation of the melting and solidification processes of stearic acid/carbon fiber composite phase change material for solar water heating applications

Phase Change Materials (PCMs) are one of the most promising materials for storing thermal energy and supplying stored energy for Domestic Hot Water (DHW) applications. This paper presents a detailed numerical analysis to describe transient heat transfer in a phase-change composite thermal energy-storage system. The composite was composed of 92.5 % stearic acid, 7.5 % carbon fiber, and a heat transfer fluid (ethylene cellulose). Numerics were implemented using ‘The Integrated Computer Engineering and Manufacturing code for Computational Fluid Dynamics’. The results were validated using experimental data and demonstrated acceptable agreement and an accurate representation of this specific transient heat transfer problem. The difference between the simulation and experimental results was so small that we considered the simulation results reliable. When the phase change heat storage process is about 800 s, the heat is transferred to the entire phase change heat storage tank, and when the phase change heat storage process is about 10800s, the temperature of all composite phase change materials reaches the phase change temperature. When the phase change heat storage process is about 8 h, the temperature of the composite phase change material in the whole phase change heat storage tank reaches 90 ℃. The temperature tends to be stable after the phase transition heat release process for about 500 s, and there is no large fluctuation in temperature with the passage of time. When the phase change heat release process reaches 7200 s, the cold-water inlet temperature is 15 ℃, 20 ℃ and 25 ℃, and the outlet temperature is 25.8 ℃, 30.8 ℃ and 35.7 ℃, respectively, indicating that the application of composite phase change materials in phase change heat storage water tank has a good effect.

Experimental investigation of the solar latent heat thermal energy storage system integrated with salt hydrate phase-change materials

To achieve rational utilization of renewable energy sources, a solar latent heat thermal energy storage system for hot water application was developed in this study. The feasibility of the salt hydrates using in the solar heating was assessed and the comparative experimental investigation was conducted under various operating conditions. It shows that the higher flow rate and radiation accelerate the melting process of the phase-change material. The time taken for the storage medium to reach phase transition was reduced by approximately 48.9%; meanwhile, the collector efficiency was enhanced by approximately 10.2% as the flow rate increased from 10 g/s to 30 g/s. The accumulated charging energy increased by approximately 10.9% when the radiation increased from 850 W/m2 to 920 W/m2, resulting in a prolonged heat release process. The test results suggest the promising potential of the salt hydrates for the solar water heating applications.

Study on the thermal performance of double pass solar air heater with PCM-based thermal energy storage system

The solar air heater (SAH) is an efficient, eco-friendly, and cost-effective way for solar drying, space heating, crop yielding, and HVAC applications. However, SAH has two drawbacks: low heat transfer coefficient and the intermittent nature of solar energy. Different roughness elements were employed to enhance the heat transfer coefficient, while different PCM arrangements were used to increase thermal efficiency and operational hours. Accordingly, the composite geometry of semicircular PCM tubes and perforated blocks are investigated at non-dimensional parameters such as tube amplitude ratios (a/H) from 0.2 to 0.5 and relative blockage height ratios (e/H) from 0.4 to 0.8. In this study, the three-dimensional transient numerical investigation is carried out along with experimental validation. The effect of a/H and e/H on the thermal efficiency, heat storage rate and pumping power are analyzed at a mass flow rate (ṁ) from 0.011 kg/s to 0.047 kg/s. For the range of parameters studied, the maximum thermal efficiency is determined to be 97 %, corresponding to mass flow rate of 0.047 kg/s, a/H value of 0.2 and e/H value of 0.4, while the maximum heat storage rate is determined to be 637 W at a/H value of 0.5, mass flow rate of 0.011 kg/s and e/H value of 0.4. The improvement in thermal performance is considered at the expense of pumping power. Moreover, the maximum pumping power is determined to be 38.9 W at e/H value of 0.8, mass flow rate of 0.047 kg/s and a/H value of 0.3.

A scalable phase change material-based system enhanced by multi-walled carbon nanotubes and fins for efficient solar water heating applications

Phase change material (PCM)-based harvesting and storage systems are promising solutions to solar energy's intermittence and non-uniformity issues. Previous efforts have focused on the absorption, conversion, and storage capability of PCMs. However, efficiently utilizing the stored thermal energy within PCMs remains challenging. Herein, we devise a facile and scalable PCM-based system with heat transfer and light absorption enhancement simultaneously by fins and multi-walled carbon nanotubes (MWCNTs) for solar water heating applications. Photothermal conversion experiments demonstrate that the water temperature of the PCM-based system with MWCNT and fins is up to 79.0 °C under the stationary condition, which is increased by 58.6 % and 55.2 % compared to the original composite and the MWCNT-doped one, respectively. Furthermore, numerical simulations indicate that fins act as a bridge between PCM and water, facilitating rapid heat transport and improving the thermal energy storage pattern, enabling efficient solar water heating. The water temperature can keep above 40.0 °C for 51 min at a flow rate of 11.34 l/h under ambient cooling conditions, and the maximum thermal efficiency is up to 89.2 %, which is higher than most flat plate and tubular solar collectors, demonstrating the superiority of the proposed system.

Design and Fabrication of Hybrid Charging Station

A solar collector is a device that transforms solar radiation from the Sun into heat, which is then transferred to working fluid. The use of solar collectors reduces energy costs over time as they do not use fossil fuels or electricity like in traditional waterheating. As well as in domestic settings, a large number of these collectors can be combined in an array and used to generate electricity in solar thermal power plants. There are a number of different types of solar collector designs that use the energy of the sun to heat working fluid. Parabolic dish reflector provides a better alternative way in order to generate higher temperatures with better efficiency. The parabolic dish reflector is a solar energy collector designed to capture the sun’s direct solar radiation over a large surface area and focus or “concentrate it” onto a small focal point area, increasing the solar energy received by more than a factor of two. In the present project we will do the design & development of Parabolic Dish collector with automatic solar trackingfor water heating application. Keywords: Solar energy, water heating application, parabolic dish collector, automatic solar tracking.

Potential maps for combined nocturnal radiative cooling and diurnal solar heating applications in Europe

Radiative cooling is a process where a surface cools down by radiating thermal energy into the outer space. Radiative cooling and solar heating applications can be combined in one single device named Radiative Collector and Emitter (RCE) which can generate heat during the day and cold at night. The power generated by these devices varies depending on the location's weather conditions. In this paper we predict the power and energy production potential using Kriging interpolations and give detailed prediction maps of the solar heating and radiative cooling potential using data from weather stations in Europe. On average, and considering ideal conditions, the annual radiative cooling potential in Europe is 50.24 W/m2 and 212.21 kWh/m2·year, and the solar heating potential is 225.08 W/m2 and 1152.36 kWh/m2·year. We also combine both potentials to create suitability maps of RCE technology, which show the south of Europe as having the most potential for RCE implementation. Of these regions, southern Turkey and southern Spain have a score in the suitability index higher than 70% in all the defined criteria, while with a medium filtering criterion for radiative cooling production and solar heating, most of the continent is suitable for the application of RCE technology.

Preparation, stabilization, and thermal characterization of CuO/water nanofluids applicable to domestic solar water heater

In this contribution, an experimental investigation has been carried out to analyze the stability and light absorbance characteristics of CuO/water nanofluids applicable to domestic solar water heaters. Nanofluids are prepared at 0.01–0.05 wt% by dispersing dry CuO nanopowder in water in presence of Gum Acacia (GA) stabilizer via ultrasonic agitation. The stability of the nanofluids is examined through gravity sedimentation. The samples are exposed to natural sunlight as well as LED light to examine their light absorbance potential by virtue of temperature rise. The light absorbance potential of nanofluids as compared to water is expressed as Temperature Variation Ratio (TVR). The nanofluids remain stable for six months. The sedimentation is more in higher concentration relative to their dilute counterparts. The absorbance capacities of the nanofluids augment with the nanoparticle addition to base fluid. However, 0.01 and 0.05 wt% samples show relatively lower absorbance due to a higher sedimentation rate. Maximum absorbance is observed with 0.03 wt% which shows a maximum temperature rise up to 60 °C under sunlight and 56 °C under LED light. Whereas, water shows a maximum increase up to 52 °C under sunlight and 48 °C under LED. The TVR shows the highest values of 2.3 and 1.86 with 0.03 wt% sample when kept under sunlight and LED lights respectively. Hence, nanofluids are recommended as working fluids in solar water heating applications.