Waste Heat Sources Research Articles

Research Needs for the Solid Oxide Electrolyzer (SOEC) with a Proton-Conducting SOEC (H-SOEC) Electrochemical Hydrogen Compressor (EHC) Energy Conversion Network (ECN)

A high temperature solid oxide electrolysis cell (SOEC) for electrolysis of water is paired with a H-SOEC for hydrogen compression. SOEC and EHC have been integrated into an ECN in a series configuration and then simulated and analyzed. Adding heat and minimizing area specific resistance (ASR) would be highly desirable for further developing highly-efficient SOEC H-SOEC EHC ECN’s. It is important to note there is a maximum possible heat generation rate with a given ASR when operated below the thermoneutral point. There is a maximal heat addition rate for optimal efficiency of the SOEC, and it is not at thermoneutral. Many developers have expressed interest in the thermal management of electrolyzer cells and in the possible existence such an optimum. It is important to understand in general that heat removal can allow increase hydrogen production rate over the thermoneutral path at constant temperature. For this reason, the SOEC H-SOEC EHC ECN was simulated over a range of currents and ASR’s to determine the heat addition or removal required. If the internal resistance of an SOEC could be lowered sufficiently via the development of new, high-performing materials, the efficiency of hydrogen production could be very high, especially when supplementary heat is provided from solar or other waste heat sources such as nuclear or coal power plants. It is remarkable that a quarter to a third of the energy for the combined high-temperature electrolysis and hydrogen compression system could be provided by solar, nuclear or geothermal energy. The goal of HT electrolysis research and development should be to lower ASR and improve heat conduction or heat transfer into and out of the SOEC. The promise of the H-SOEC electrochemical hydrogen compressors depends on its stability, durability and improved transference numbers. The goal of future research should be to improve the potential of this new SOEC H-SOEC EHC ECN.

Novel District Heating Systems: Methods and Simulation Results

Fifth-generation district heating and cooling (5th DHC) systems offer promising approaches to decarbonizing space heating, cooling and domestic hot water supply. By using these systems, clustered buildings combined with industrial waste heat can achieve a net-zero energy balance on a variety of time scales. Thanks to the low exergy approach, these systems are highly efficient. As part of the Smart Anergy Quarter Baden (SANBA) project, the thermal energy grid simulation tool TEGSim has been further developed and used to design an ultra-low-temperature district heating (ULTDH) network with hydraulic and thermal components fitted to the specific regional characteristics of the investigated case. Borehole thermal energy storage (BTES) used as seasonal storage ensures long-term feasibility. The annual discrepancy of input of thermal energy provided by space cooling and output of energy demanded by space heating and domestic hot water is supplied by an external low-grade industrial waste heat source. This paper presents the functionality of the simulation and shows how to interpret the findings concerning the design of all components and their interplay, energy consumption and efficiencies.

Performance Analysis and Optimization of a Series Heat Exchangers Organic Rankine Cycle Utilizing Multi-Heat Sources from a Marine Diesel Engine.

Organic Rankine Cycle (ORC) is an effective way to recycle waste heat sources of a marine diesel engine. The aim of the present paper is to analyze and optimize the thermoeconomic performance of a Series Heat Exchangers ORC (SHEORC) for recovering energy from jacket water, scavenge air, and exhaust gas. The three sources are combined into three groups of jacket water (JW)→exhaust gas (EG), scavenge air (SA)→exhaust gas, and jacket water→scavenge air→exhaust gas. The influence of fluid mass flow rate, evaporation pressure, and heat source recovery proportion on the thermal performance and economic performance of SHEORC was studied. A single-objective optimization with power output as the objective and multi-objective optimization with exergy efficiency and levelized cost of energy (LCOE) as the objectives are carried out. The analysis results show that in jacket water→exhaust gas and jacket water→scavenge air→exhaust gas source combination, there is an optimal heat recovery proportion through which the SHEORC could obtain the best performance. The optimization results showed that R245ca has the best performance in thermoeconomic performance in all three source combinations. With scavenge air→exhaust, the power output, exergy efficiency, and LCOE are 354.19 kW, 59.02%, and 0.1150 $/kWh, respectively. Integrating the jacket water into the SA→EG group would not increase the power output, but would decrease the LCOE.

Development of Biomass Based-Activated Carbon for Adsorption Dehumidification

The demand for dehumidification in tropical regions contributes to a significant portion of the building energy consumption. Desiccant dehumidification can mitigate energy consumption by recovering the exergy potential from the waste heat and renewable energy sources. Material development is the bottleneck in realizing the full potential of desiccant dehumidification systems beyond conventional adsorbents such as silica gel and zeolite. Therefore, it is necessary to develop novel materials that can be regenerated using the heat source under 70°C. In this study, we developed activated carbons (ACs) as the desiccant materials derived from waste biomass. The ability of activated carbon (AC) to remove the moisture was controlled by carefully preparing the material using several conditions to achieve the right operation window for optimum moisture sorption processes. The porous and surface characteristics of the newly-prepared AC were analyzed and compared with those of silica gel. The adsorption isotherm measurements were conducted, and the data were fitted with Henry-Sips and Do-Do isotherm models. The current AC exhibited an excellent water adsorption capacity (up to 0.41 g/g). The efficacy of the ACs for dehumidification applications was assessed using the weather data from several regions of Indonesia, from North Sumatera to Papua. The results revealed that under the studied conditions, the new desiccant material showed a better dehumidification capacity than silica gel. Moreover, the reported AC can be regenerated using temperatures as low as 40°C, which is readily available from waste heat, including the heat rejection from the condenser of any air-conditioning unit.

Research Needs for the Solid Oxide Electrolyzer (SOEC) with a Proton-Conducting SOEC (H-SOEC) Electrochemical Hydrogen Compressor (EHC) Energy Conversion Network (ECN)

A high temperature solid oxide electrolysis cell (SOEC) for electrolysis of water is paired with a H-SOEC for hydrogen compression (EHC). SOEC and EHC have been integrated into an electrochemical network (ECN) in a flow-series configuration and then simulated and analyzed. Adding heat and minimizing area specific resistance (ASR) would be highly desirable for further developing highly-efficient SOEC+EHC ECN’s. It is important to note there is a maximum possible heat generation rate with a given ASR when operated below the thermoneutral point. There is a maximal heat addition rate for optimal efficiency of the SOEC, and it is not at thermoneutral. Many developers have expressed interest in the thermal management of electrolyzer cells and in the possible existence of such an optimum. It is important to understand in general that heat removal can allow an increased hydrogen production rate over the thermoneutral path at constant temperature. For this reason, the SOEC+EHC ECN was simulated over a range of currents and ASR’s to determine the heat addition or removal required. If the internal resistance of an SOEC could be lowered sufficiently via the development of new, high-performing materials, the efficiency of hydrogen production could be very high, especially when supplementary heat is provided from solar or other waste heat sources such as nuclear or coal power plants. It is remarkable that a quarter to a third of the energy for the combined high-temperature electrolysis and hydrogen compression system could be provided by solar, nuclear, or coal.

(Plenary) Update on the SOFC Program at the DOE’s National Energy Technology Laboratory

The Solid Oxide Fuel Cell (SOFC) Program, managed by the U.S. Department of Energy (DOE) Office of Fossil Energy (FE) and administered by the FE’s National Energy Technology Laboratory (NETL), is currently developing low-cost SOFC power generation systems. SOFC power systems have the potential to achieve greater than 60 percent efficiency. The SOFC’s operating temperature is lower than combustion-based processes and precludes NOx formation; there are near-zero emissions of CO2, criteria pollutants, and particulates. Furthermore, SOFC power systems require approximately one-third the amount of water relative to conventional combustion-based power systems. The Program includes the testing of SOFC with natural gas in distributed applications, including data centers. In addition to SOFC, there are several new projects on various aspects of high temperature solid oxide electrolysis cell (SOEC) for electrolysis of water. The development of efficient systems for hydrogen production is very interesting, especially when supplementary heat is provided from solar or other waste heat sources such as nuclear or coal power plants.

Research on big data analysis model of multi energy power generation considering pollutant emission—Empirical analysis from Shanxi Province

With the development of the integrated energy Internet, energy structure optimization and emission reduction have led to higher requirements for developing various energy sources to enable coordinated and sustainable development. However, data-mining methods are rarely used to study the coordination of multi-energy generation in published research results. In this study, from the perspective of power industry emissions, coordinated generation of various energy sources, and balance of power generation and consumption, a data-mining algorithm was used to analyze the development of thermal power, hydropower, wind power, waste heat, gas, and other power sources. The chi-square automatic interaction detection tree (CHAID), logistic regression, and two-step clustering methods were applied. The results show that: a) CO2 and SO2 emissions were mainly affected by thermal power generation, whereas NOx emissions were jointly affected by thermal power, garbage power, and gas-fired power, and the emissions of various pollutants increased with an increase in power consumption. The optimal power-generation scheme under minimum emission can be obtained. b) There was a strong correlation between thermal power generation and residential electricity consumption, and renewable energy (wind energy, photovoltaic, hydropower) exhibited the highest correlation with the electricity consumption of the tertiary industry, which indicates that renewable energy generation can be promoted by managing electricity consumption in the tertiary industry. c) When the electricity demand of all users was small, the proportion of renewable energy power generation increased; in contrast, the thermal power generation was larger. This indicates the importance of improving the sustainable and stable power supply of renewable energy. This study provides a data analysis model for the coordinated development of multiple energies, which will contribute to the decision-making basis for controlling power emissions, improving the utilization rate of renewable energy, and optimizing the energy structure.

Optimal hydrocarbon based working fluid selection for a simple supercritical Organic Rankine Cycle

In this paper, several hydrocarbons' performance as a working fluid for a supercritical Organic Rankine Cycle are studied. Energy, exergy, and exergoeconomic analysis are conducted for the cycle operating with a low-grade waste heat source. Initially, fifteen different working fluids, primarily hydrocarbons, were considered based on their environmental characteristics, global warming potential, ozone depletion potential, flammability, and toxicity. The cycle efficiency for each working fluid was analyzed for different cycle operating pressures and different inlet heat source temperatures from 400 K to 500 K for a constant turbine work output. Three different trends of cycle performance characteristics were observed for various working fluids with the cycle operating at different evaporator pressures and source inlet temperatures. The working fluids that exhibited similar characteristic trends were then categorized into families for further analysis. Three hydrocarbons, i.e., Dimethyl Ether, R1234yf, and Diethyl Ether, were each selected as the representative of their respective family, along with Isobutane as the reference working fluid for comparison. After detailed energy and exergy analyses, Dimethyl Ether and Isobutane were found to be promising working fluids for the range of pressure and source inlet temperatures considered. Finally, the exergoeconomic analysis showed Dimethyl Ether to be the optimal working fluid based on the unit cost of net work produced and the total cost of exergy destruction, which were calculated to be (59.18 ± 0.49) $/MWh and (8.92 ± 0.48) $/h, respectively, when operating at 450 K.

Parametric analysis and multi-objective optimization of a combined Organic Rankine Cycle and Vapor Compression Cycle

This paper aims to provide a performance examination of combining power and refrigeration system, which consists of an Organic Rankine Cycle driven Vapor Compression Cycle from waste heat source. The following working fluids R123, R11, and R113 were assessed from thermodynamic and economic standpoints. The numerical model of the system is developed under Engineering Equation Solver software. Thermal and exergy efficiencies of the combined system are selected to establish the thermodynamic analysis. The economic evaluation was based on three indicators, namely net earnings, payback period, and levelized cost of energy. In order to examine the trade-off between thermodynamic and economic performance, a multi-objective optimization supported by a decision-making process is investigated. Moreover, a parametric study is carried out to determine the effect of several parameters such as boiler and condenser temperatures and mass flow rate on the system performance. The optimized results indicate that the highest energy and exergy efficiencies using R123 as working fluid are over 1.02 and 0.53 respectively, while the payback period is 6.3 years. Additionally, the levelized cost of energy is 0.06 $/kWh at heat source temperature of 150 °C, condenser temperature of 25 °C and turbine inlet pressure of 2 MPa.

Thermal energy storage sizing for industrial waste-heat utilization in district heating: A model predictive control approach

Thermal energy storage (TES) is a key technology for enabling increased utilization of industrial waste heat in district heating. The ability of TES to equalize offsets in demand and supply depends strongly on the sizing, control and integration in a heating plant. We consider the problem of sizing TES in heating plants utilizing a varying waste-heat source. To this end, we propose a combined dynamic simulation and model predictive control approach that accounts for the dynamics and optimal control of the heating plant with TES. A case study has been carried out on a district-heating plant located in Norway, with 90% of its annual heat production being heat recovered from the off-gas from a ferrosilicon plant. We evaluate the effective peak-heating reduction with different TES sizes and the energy-to-heat-flow-ratio for the TES discharging periods as performance metrics. For the case study, our results suggest that a modest TES tank volume of 1500 m3 is sufficient to achieve a half-year peak-heating reduction of 12% and comparable performance with larger volumes. The proposed methodology constitutes a numerically tractable means of incorporating the impact of model predictive control on the sizing of TES for heating plants with time-varying waste-heat supply and demand.

Supra-Regional District Heating Networks: A Missing Infrastructure for a Sustainable Energy System

In analogy to electricity transmission networks, this paper analyzes the concept of supra-regional district heating networks (SR-DHN), connecting a large number of actors. Using a back-casting approach, a SR-DHN is assumed to exist and thus, implementation challenges, such as economic feasibility and energy losses, are circumvented in the first step (but are analyzed in the discourse). The paper then analyzes, in an interdisciplinary qualitative manner and supported by a case study, what technical, operational, economic and legal issues must have been resolved. Results show that the heat transmission network, being the backbone of the SR-DHN, is an expensive infrastructure, but is likely to become economic in a non-fossil energy system. By decreasing the reliance on single waste heat sources, SR-DHN allows longer payback periods and can thus be an enabler for using industrial waste heat. However, involving many actors requires comprehensive contractual foundations. The derived hypothesis is that SR-DHN, which is predominantly fed by waste heat, shall be operated with lower temperatures in winter (feeding the return while minimizing expensive winter losses) and high temperatures in summer (enabling alternative usages while accepting high but inexpensive summer losses).

Potential Diffusion of Renewables-Based DH Assessment through Clustering and Mapping: A Case Study in Milano

This work aims at developing a methodology for the assessment of district heating (DH) potential through the mapping of energy demand and waste heat sources. The presented method is then applied to the Metropolitan City of Milano as a case study in order to investigate the current and, especially, the future sustainability of DH with the foreseen building refurbishment and consequent heat demand reduction. The first step is the identification of the areas the most interesting from a heat density and an economic point of view through a clustering algorithm, in which lies the main novelty of the work. The potential is then assessed by investigating their synergy with the available heat sources, which are mapped and analyzed in terms of recoverable thermal energy and costs. In future scenarios with foreseen heat demand reduction, low-temperature networks and excess heat sources are considered, such as metro stations and datacenters, together with the conventional sources, such as thermoelectric plants. The outcomes prove that lower heat demand corresponds to higher network costs with consequently reduced district heating potential but also prove that the properties of low-temperature district heating can potentially compensate for the drop in its cost-effectiveness. Another interesting finding is that the renovation of buildings in an area should be not performed evenly but with criteria; for instance, in synergy with DH diffusion.

Experimental validation of a multiple model predictive control for waste heat recovery organic Rankine cycle systems

Waste heat recovery systems are today considered as a valuable solution to increase energy efficiency of industrial applications and heavy-duty vehicles, as it uses a thermodynamic organic Rankine cycle system to recover the heat losses to produce electrical or mechanical power. Optimal performance of such machines is often achieved at conditions where complex time-varying nonlinear dynamics are encountered, making the automatic control strategy a fundamental element to maximise the energy efficiency. In this paper the development of a multiple model predictive controller suitable for industrial implementation is presented, and its effectiveness is experimentally validated for the task of maximising output power of a 11kWel small-scale ORC power unit used in a waste heat recovery application. The main advantage of the proposed controller is the possibility to use different model structures to describe local dynamics without increasing complexity of the optimisation problem. Additionally, experimental results illustrate that the entire operating range of the system might be classified in two regions, a quasi-linear and a highly nonlinear region for ‘high’ and ‘low’ superheating degrees respectively. Closed-loops tests lead to the conclusion that a single linear model predictive controller might only be used under suboptimal operation of low power production (on the quasi-linear region for ‘high’ superheating), otherwise leading to poor performance or even instability. Alternatively, the proposed strategy keeps the cycle stable over the entire range of conditions and allows to increase the net electrical energy produced by at least 6%, even under drastic waste heat source variations, when operating closer to the minimum allowed superheating degree.

Low carbon district heating in China in 2025- a district heating mode with low grade waste heat as heat source

Clean district heating systems are needed in large cities, especially in Northern China. This paper presents a low carbon district heating system that features a low return water temperature, use of low grade waste heat as the main heat source, long distance heat transmission with a large temperature difference, distributed peak heating load addition by natural gas and heat-power decoupling with heat pump and thermal storage. This Low carbon district heating 2025 system is suitable for large cities, large waste heat sources, high heating densities and the utilization of using existing large heating networks in almost all the cities of Northern China. These clean heating systems in Chinese cities have great potential to reduce energy use, reduce emissions and improve the district heating system economics.

Performance evaluation of an absorption heat transformer for industrial heat waste recovery using the characteristic equation

In this paper we report on new experimental results of an absorption heat transformer. In order to have a concise view on the whole performance field the characteristic equation model, a novel version of ideas from the 80ies of the last century is developed. In the model insight from recent research on absorption chillers is used. The 40 kW prototype implements a single effect absorption cycle working with water as refrigerant and an aqueous LiBr solution as the solvent. As a novelty, the parameter set of the characteristic equation model has been obtained from the cycle analysis of the device based on the measurements of one single operating point. The resulting model predicts the prototype performance for driving heat temperature levels of low temperature industrial waste heat sources (60–100 °C), with variations of the temperature of the useful upgraded between 90 and 138 °C that result in gross temperature lifts (GTL) between 20 and 55 K. The measured COP values are between 0.30 and 0.48. An additional regression developed after evaluating the deviations from the model assumptions reduces the uncertainty of the model. The uncertainties for COP and upgraded heat flow rate predictions are below 11% (R2 = 0.812) and 4% (R2 = 0.918) respectively.

Techno-Economic Analysis of Waste Heat Utilization in Data Centers: Application of Absorption Chiller Systems

Modern data centers are playing a pivotal role in the global economic situation. Unlike high-quality source of waste heat, it is challenging to recover the decentralized and low-quality waste heat sourced from data centers due to numerous technological and economic hurdles. As such, it is of the utmost importance to explore possible pathways to maximize the energy efficiency of the data centers and to utilize their heat recovery. Absorption chiller systems are a promising technology for the recovery of waste heat at ultra-low temperatures. In fact, the low temperature heat discharged from data centers cannot be retrieved with conventional heat recovery systems. Therefore, the present study investigated feasibility of waste heat recovery from data centers using an absorption chiller system, with the ultimate goal of electrical energy production. To fulfill this objective, a techno-economic assessment of heat recovery using absorption chiller (AC) technique for the data centers with power consumption range of 4.5 to 13.5 MW is performed. The proposed AC system enables saving electricity for the value of 4,340,000 kWh/year and 13,025,000 kWh/year leading to an annual reduction of 3068 and 9208 tons CO2 equivalent of greenhouse gas (GHG) emissions, respectively. The results of this study suggest an optimum change in the design of the data center while reducing the payback period for the investors.

Thermodynamic, economic, and environmental analysis and multi-objective optimization of a dual loop organic Rankine cycle for CNG engine waste heat recovery

• Thermodynamic, economic, and environmental analysis are presented. • Proposing a multi-model driven NSGA-III method for DORC performance optimization. • A tradeoff appears among thermal efficiency, payback period and CO 2 emission. Waste heat energy exists in the exhaust, intercooler, and coolant during the operation of the compressed natural gas (CNG) engine. The cascade utilization of the waste heat energy of the CNG engine can be realized considering the structural advantages of the dual loop organic Rankine cycle (DORC) system. Operating parameters have an important influence on DORC system performance. Traditional analysis methods have limitations in analyzing the relationship between operating parameters and system performance, and little attention is paid to the environmental impact of the system. The environmental performance of the system plays an important role in saving energy and protecting the environment. Therefore, the bilinear interpolation algorithm is introduced to analyze the waste heat sources of the CNG engine and the thermodynamic, economic, and environmental performances of the DORC system. In addition, the comprehensive operating performance of the DORC system has not been thoroughly and comprehensively optimized. Therefore, this study proposes a multi-model driven NSGA-III method for DORC comprehensive performance optimization. Results show that the optimal thermal efficiency, payback period (PB), and emissions of CO 2 equivalent (ECE) are 11.98%, 4.02 years, and 43.74 ton CO 2,eq , respectively. Moreover, decreasing the thermal efficiency of the system will significantly decrease ECE and increase PB at the same time. This research provides a reliable reference for the analysis, design, evaluation, and optimization of the comprehensive performance of the DORC system.

Integration of membrane distillation as volume reduction technology for in-land desalination brines management: Pre-treatments and scaling limitations

Management of in-land reverse osmosis (RO) desalination brines generated from surface brackish waters is a current challenge. Among the different near-Zero and Zero Liquid Discharge (ZLD) alternatives, Membrane Distillation (MD), in which the transport of water is thermally driven, appears as an attractive technology if a residual heat source is available. The aim of this study was to identify the limits of Direct Contact MD (DCMD) pre-treatments such as acidification and aeration, or the combination of both to quantify the scaling reduction potential when treating a RO brine from surface brackish water. Experimental data were used to evaluate the effectiveness of DCMD to achieve the highest concentration factors, depending on the chosen pre-treatment. Additionally, an economic analysis of the operational cost, taking as case study a site where the current management of the brine is the discharge to the sea, was also carried out. Results showed that pre-treatments enhanced MD performance by increasing the concentration factor achieved and highest volume reductions (about 3 times) were reached with the combination of acidification and aeration pre-treatments. Both processes reduced the precipitation potential of CaCO3(s) by reducing the total inorganic carbon (>90%); however, CaSO4·2H2O(s) precipitated. Results also indicated that even if a waste heat source is available, brine disposal into the sea is the cheapest option, while ZLD alternatives were not attractive in the current regulatory framework since their cost was higher than the discharge to the sea. Other options related to the Minimal Liquid Discharge may be more economically attractive.

Thermodynamic Performance of Adsorption Working Pairs for Low-Temperature Waste Heat Upgrading in Industrial Applications

The present work aims at the thermodynamic analysis of different working pairs in adsorption heat transformers (AdHT) for low-temperature waste heat upgrade in industrial processes. Two different AdHT configurations have been simulated, namely with and without heat recovery between the adsorbent beds. Ten working pairs, employing different adsorbent materials and four different refrigerants, have been compared at varying working boundary conditions. The effects of heat recovery and the presence of a temperature gradient for heat transfer between sinks/sources and the AdHT components have been analyzed. The achieved results demonstrate the possibility of increasing the overall performance when internal heat recovery is implemented. They also highlight the relevant role played by the existing temperature gradient between heat transfer fluids and components, that strongly affect the real operating cycle of the AdHT and thus its expected performance. Both extremely low, i.e., 40–50 °C, and low (i.e., 80 °C) waste heat source temperatures were investigated at variable ambient temperatures, evaluating the achievable COP and specific energy. The main results demonstrate that optimal performance can be achieved when 40–50 K of temperature difference between waste heat source and ambient temperature are guaranteed. Furthermore, composite sorbents demonstrated to be the most promising adsorbent materials for this application, given their high sorption capacity compared to pure adsorbents, which is reflected in much higher achievable specific energy.

Energy Saving and Economic Evaluations of Exhaust Waste Heat Recovery Hot Water Supply System for Resort

The objective of this study is to investigate the energy savings and economics of the hot water supply system for the luxury resort. The hot water was generated using the waste heat from the exhaust gas heat (EGH) of internal combustion engine (ICE) installed at the luxury resort. The capacity and characteristics of waste heat source, flow demand and supply system of hot water were surveyed, and data is collected from the real system. The new heat exchanger system which utilizes the EGH to produce the hot water is designed considering the dew point temperature and the back pressure of exhaust gas system. The results show that the proposed system could supply hot water at a temperature of 55 °C corresponding to the present resort demand of 6 m3/h using EGH of ICE at 20% load. The proposed system could achieve the saving of 400 L/day in diesel oil (DO) fuel consumption and the payback time of new system could be evaluated as 9 months. The proposed system could produce hot water of 14 m3/h at 25% of engine load and 29 m3/h at full engine load which are sufficient to satisfy the regular and maximum hot water demand of resort. The presented results show the capability of the proposed system to satisfy the current hot water demand of resort and suggest the larger potential to save energy by recovering EGH of ICE. The novelty of the present work involves detailed methodology to design heat exchangers and evaluate system economics for hot water supply system based on EGH of ICE.