Flue

A flue is a duct, pipe, or opening designed to convey exhaust gases, such as smoke and combustion byproducts, from heating appliances like fireplaces, furnaces, boilers, or industrial equipment to the external environment. In engineering, it ensures safe venting, dilution, and dispersal of gases to prevent indoor buildup of harmful substances. The term has been in use since at least 1582, with uncertain etymology.^[1]^[2] Flues also refer to air channels in certain musical instruments, such as flue pipes in organs that produce sound through vibration of air. Historically associated with chimney evolution in medieval Europe, flues are constructed from materials like clay, brick, or modern corrosion-resistant alloys, and are subject to building codes for safety and efficiency.^[3]

Overview

Definition

A flue is a duct, pipe, or opening designed specifically for conveying exhaust gases, smoke, or combustion byproducts from sources such as fireplaces, furnaces, boilers, or generators to the outdoors, thereby preventing their accumulation indoors and ensuring safe operation of heating or combustion systems.^[4]^[5] Unlike a chimney, which serves as the enclosing structure that connects a fireplace or appliance to the external environment, a flue refers specifically to the internal passageway within that structure through which gases travel.^[6]^[7] The operation of a flue relies on basic principles of buoyancy and pressure differences, where hot gases, being less dense than the surrounding cooler air, naturally rise and create a draft that pulls combustion byproducts upward and outward.^[8]

Function and Principles

A flue operates primarily through the natural draft mechanism driven by the stack effect, where hot combustion gases within the flue rise due to their lower density compared to cooler surrounding air, creating an upward airflow that evacuates exhaust from the combustion chamber.^[9] This buoyancy-induced movement relies on temperature-induced density differences: the heated gases expand and become less dense, generating a pressure differential that draws fresh air into the system while propelling byproducts outward.^[10] The draft pressure \Delta P can be approximated by the equation

\Delta P = \rho_{\text{air}} g h \left(1 - \frac{T_{\text{air}}}{T_{\text{flue}}}\right),

where \rho_{\text{air}} is the density of ambient air, g is gravitational acceleration (approximately 9.81 m/s²), h is the flue height, T_{\text{air}} is the ambient air temperature, and T_{\text{flue}} is the flue gas temperature (both in absolute units, such as Kelvin).^[9] This formula highlights how greater height and temperature differentials enhance draft strength, ensuring efficient gas evacuation without mechanical assistance.^[11] In combustion processes, the flue plays a critical role by facilitating the supply of oxygen to the fire through induced inflow of replacement air, while simultaneously removing combustion byproducts such as carbon dioxide, water vapor, and particulates to sustain efficient burning and prevent incomplete combustion.^[12] The upward draft created by the rising hot gases establishes a partial vacuum at the base of the flue, pulling ambient air into the combustion zone to replenish oxygen depleted during fuel oxidation, thereby maintaining the air-fuel ratio necessary for optimal energy release.^[13] This dual function—intake of reactant air and expulsion of waste gases—minimizes the accumulation of toxic residues and supports steady-state combustion efficiency.^[14] The velocity of gases within the flue is influenced by factors including height, cross-sectional area, and temperature, with higher flues and hotter gases promoting faster flow to overcome frictional losses. These dynamics ensure that the flue's design balances sufficient speed for complete evacuation against excessive turbulence that could hinder overall system performance.^[15] Common operational issues in flues include backdraft or downdraft, where external winds or intrusions of cold air reverse the natural upward flow, causing smoke and gases to spill back into the living space.^[16] Such reversals often stem from atmospheric pressure imbalances, such as gusts creating downward forces at the flue top or sudden cooling of flue gases reducing buoyancy, leading to hazardous indoor air quality degradation.^[17] Mitigation typically involves ensuring adequate insulation to preserve gas temperatures, though material choices can subtly affect thermal retention without altering core airflow principles.^[18]

History

Origins in Ancient and Medieval Times

The earliest precursors to flues can be traced to prehistoric cave dwellings during the Lower Paleolithic period, around 170,000 years ago, where open central hearths were commonly positioned to facilitate natural smoke venting through roof openings or cave entrances. Archaeological evidence from sites like Lazaret Cave in France indicates that early humans strategically placed these hearths to optimize air circulation, directing smoke toward the cave opening while minimizing inhalation risks and allowing heat to distribute effectively within the space. These rudimentary setups, lacking enclosed channels, served as proto-flues by relying on natural drafts for smoke expulsion, marking the initial human adaptation to fire management in enclosed environments.^[19]^[20] In ancient civilizations, particularly Rome around 500 BCE, architectural features like atria and compluvia evolved to enhance smoke escape from domestic hearths. The atrium, a central open-roofed courtyard in Roman houses, featured a compluvium—a square opening in the roof—that not only collected rainwater but also permitted smoke from the adjacent hearth to rise and dissipate outdoors, improving indoor air quality in urban dwellings. This design represented an advancement over prehistoric methods by integrating smoke venting into structured architecture. Complementing these, early flues appeared in Roman hypocaust systems, which circulated hot air and smoke beneath floors and through wall channels for underfloor heating in bath-houses, serving as a precursor to dedicated flue networks.^[21] The medieval period, from the 12th to 13th centuries, saw the emergence of purpose-built chimneys and enclosed flues in European castles and monasteries, transitioning from open fires to directed smoke channels constructed of stone or brick. In England, Norman castles from the 1180s onward incorporated these innovations, such as vertical stone flues rising from central fireplaces to expel smoke above the roofline, reducing indoor pollution and enabling larger enclosed halls. This shift was widespread across medieval Europe, with adoption in monastic and elite structures by the mid-12th century, reflecting social changes like increased privacy and comfort in domestic spaces. A key innovation was the enclosure of flues, which minimized smoke accumulation compared to open hearths, as evidenced by Venetian records from 1348 documenting regulations for chimney construction following an earthquake that highlighted the need for standardized, durable designs.^[22]^[23] Early flue-like systems also appeared in non-European contexts, such as the heated flooring (kang) with underfloor flues in ancient Chinese homes dating back to the Han dynasty (around 200 BCE–200 CE), which directed smoke from hearths through channels beneath sleeping platforms for efficient heating.^[24]

Evolution in the Modern Era

During the Renaissance and Enlightenment periods, innovations in flue design focused on enhancing draft control and thermal efficiency in residential fireplaces. Benjamin Franklin introduced the Pennsylvanian fireplace in the 1740s, featuring a dedicated flue passage behind a false back and a damper known as the "Register," a wrought-iron plate that adjusted airflow to prevent excessive draft and heat loss.^[25] This design allowed for wider effective flue openings compared to traditional narrow chimneys, improving smoke evacuation while retaining room heat. Later, in 1796, Sir Benjamin Thompson, Count Rumford, developed the Rumford fireplace, which narrowed the flue throat to accelerate smoke velocity and direct it upward more efficiently, reducing fuel consumption by up to 50% in tests and minimizing room smoke.^[26] The Industrial Revolution in 19th-century England spurred the widespread adoption of multi-flue chimneys in factories to handle the exhaust from multiple coal-fired boilers, enabling scaled-up manufacturing processes like textile production and iron smelting. These tall, multi-flue structures, often exceeding 100 feet in height, dispersed flue gases over wider areas to mitigate local pollution while supporting the high-volume combustion required for steam engines.^[27] Safety concerns from chimney maintenance prompted regulatory intervention, with the Chimney Sweepers and Chimneys Regulation Act of 1840 prohibiting the use of children under 21 for climbing flues, aiming to curb exploitative labor practices and reduce accidents in increasingly complex industrial chimney systems.^[28] Although enforcement was limited, the act marked an early step toward standardized safety in flue construction and upkeep. In the 20th century, post-World War II housing booms accelerated the shift to prefabricated metal flues in modular homes, such as the enameled steel Lustron houses produced from 1947 to 1950, which integrated durable, factory-assembled metal venting to streamline installation and resist corrosion in mass-built residences.^[29] By the 1950s, building codes began mandating insulated flue liners, typically clay or metal with thermal barriers, to prevent condensation and fires in unlined masonry chimneys, as outlined in updates to the National Building Code that addressed rising incidents of chimney-related hazards in suburban developments.^[30] Environmental pressures further reshaped flue engineering; the U.S. Clean Air Act of 1970 imposed emission standards on stationary sources, necessitating advanced flue gas treatments like desulfurization scrubbers on industrial stacks to capture pollutants such as sulfur dioxide, influencing designs to incorporate filtration and monitoring features.^[31] A key milestone came in the 1980s with the broad adoption of forced-draft systems in gas appliances, where fans actively pushed combustion air through the flue, enhancing reliability over natural convection and complying with updated voluntary standards for safer venting in residential furnaces and boilers.^[32]

Design and Construction

Materials and Components

Flues are constructed from a variety of materials selected for their ability to withstand high temperatures, corrosion, and structural stresses associated with combustion byproducts. Common primary materials include clay tiles, often made from terracotta, which provide durability in traditional masonry chimneys but can be brittle under impact or thermal shock.^[33] Concrete blocks are another affordable option, frequently used in precast chimney systems for their cost-effectiveness and ease of installation in modern residential applications.^[34] Metals such as stainless steel (for high-temperature applications) and aluminum (for gas appliances) are prevalent in contemporary installations due to their corrosion resistance.^[33] Key structural components ensure the safe and efficient operation of a flue. The flue liner serves as an inner tube that contains combustion gases and prevents leakage into surrounding masonry or building materials, typically constructed from clay, metal, or approved composites.^[35] The damper, a movable metal plate located near the base of the flue, regulates airflow and draft to control combustion efficiency and minimize heat loss when the fireplace is not in use.^[36] A thimble provides a secure connection point between the flue and heating appliances, such as wood stoves or furnaces, allowing for safe passage through walls or chimneys while maintaining structural integrity.^[37] At the top, a cap or crown terminates the flue, protecting it from rain, debris, and animals while permitting the escape of smoke.^[36] Construction of flues incorporates specific considerations to handle extreme conditions. Insulation layers, such as ceramic fiber blankets, are often applied around the liner to maintain structural stability and withstand temperatures up to 1,800°F, reducing external heat transfer and preventing condensation on outer surfaces.^[33] Expansion joints or flexible sections are integrated to accommodate thermal expansion and contraction, mitigating stress cracks from repeated heating and cooling cycles.^[38] Durability of flue materials is significantly influenced by their resistance to acid condensation, where flue gases can form corrosive liquids with a pH of approximately 4, accelerating deterioration if not addressed.^[39] Clay tile liners typically offer a lifespan of over 50 years with proper maintenance, owing to their chemical inertness, though they may crack under physical stress.^[40] Metal liners, particularly stainless steel, provide 20 to 40 years of service, benefiting from enhanced resistance to both thermal and chemical degradation in modern fuel environments.^[41]

Material	Key Properties	Typical Lifespan
Clay Tiles (Terracotta)	Durable, acid-resistant, brittle	50+ years^[40]
Concrete Blocks	Affordable, structural support	Varies
Stainless Steel	Corrosion-resistant, flexible	20-40 years^[41]

Types of Flues

Masonry flues, also known as traditional or Class 1 flues, consist of brick or stone linings that form vertical passages within a chimney structure, designed to facilitate natural convection for exhaust gases.^[42] These flues are prevalent in residential settings, where they support multiple appliances through separate channels separated by at least 4 inches of solid masonry bonding.^[43] Subtypes include single-wall configurations, which rely on the surrounding masonry for insulation and heat retention, and double-wall variants that incorporate an air space or additional lining for enhanced thermal performance and reduced heat loss.^[44] Their vertical orientation maximizes draft through buoyancy, making them suitable for solid fuel and wood-burning systems in older constructions. Prefabricated metal flues, often referred to as Class 2 or factory-built systems, utilize modular sections of stainless steel piping, typically UL-listed for safety and ease of assembly. These systems are constructed from interlocking components, allowing for straightforward installation and common use in retrofitting existing structures without extensive masonry work.^[45] Key subtypes include Class A flues, which are all-fuel capable and insulated (often double- or triple-wall) to handle high temperatures up to 1000°F continuously, suitable for wood, coal, or oil appliances, and Class B flues, designed specifically for vented gas appliances with double-wall construction consisting of an aluminum inner wall and galvanized steel outer wall for lower-temperature operations.^[46]^[47] Their lightweight design and prefabricated nature reduce labor costs compared to masonry, though they require precise support and clearance to combustibles as per UL 103 standards.^[48] Specialized flue types address specific installation constraints and appliance needs beyond traditional vertical systems. Balanced flues are sealed, room-air-independent setups for gas appliances, employing a concentric twin-wall pipe where the inner tube exhausts combustion products and the outer draws in external combustion air, ensuring no indoor air dilution and compliance with standards like BS 5440 Part 1.^[49] Power flues, or fan-assisted systems, incorporate an electric blower to induce draft, enabling horizontal or shorter venting paths that bypass natural convection limitations, though they depend on reliable electricity and interlocks to prevent operation during fan failure.^[50] Flueless designs, primarily for gas fires, eliminate external ducting entirely by integrating a catalytic converter—a honeycomb structure coated with platinum or palladium—that oxidizes carbon monoxide into carbon dioxide and water vapor at the point of combustion, allowing safe indoor operation without venting, subject to room ventilation requirements per manufacturer guidelines.^[51] Performance variations among flue types stem primarily from their draft mechanisms and configurations. Vertical masonry flues generate the strongest natural draft through thermal buoyancy, achieving pressures up to 20-30 Pa in typical residential setups with adequate height and temperature differentials, promoting efficient exhaust without mechanical aid.^[52] In contrast, power flues compensate for reduced vertical rise or horizontal runs by mechanically producing comparable or higher draft via fans, but their efficacy relies on power supply and may introduce noise or maintenance needs.^[9] Prefabricated metal and balanced systems offer reliable performance in constrained spaces, with draft optimized by insulation to maintain gas temperatures, though they generally yield lower natural pressures than unlined masonry without assistance.^[53]

Applications

In Heating and Combustion Systems

In heating and combustion systems, flues serve as the primary exhaust pathways for combustion byproducts, ensuring safe venting of hot gases while facilitating efficient heat transfer in appliances such as fireplaces, boilers, and furnaces. In wood-burning and gas fireplaces, the flue acts as the core channel within the chimney, drawing smoke and gases upward via natural draft created by the buoyancy of heated air; typical residential flues are sized with diameters of 8 to 12 inches to accommodate varying fireplace openings, such as 8 inches for small stoves or open fires and 12 inches for larger setups.^[54]^[55] Multi-flue chimney stacks enable venting for multiple appliances or fireplaces within a single structure, with building codes requiring separating masonry wythes—at least 4 inches thick—between adjacent flues to prevent gas leakage and ensure structural integrity.^[56] In boilers and furnaces, flues direct hot combustion gases through firetubes or heat exchangers to maximize heat transfer to water or air before final venting, a process central to steam systems where gases from fuel combustion pass through submerged tubes to generate steam efficiently.^[57] Traditional flued boilers rely on natural or fan-assisted draft to propel these gases, but modern condensing boilers cool exhaust below the dew point in a secondary heat exchanger to recover latent heat, achieving efficiencies of 90% to 98.5% AFUE; these systems use durable plastic flues, such as high-temperature polypropylene, for the cooler, acidic exhaust, contrasting with metal flues in non-condensing units.^[57] Industrial applications, particularly in coal- and oil-fired power plants, employ large-scale flues to convey massive volumes of combustion gases to emission control systems, where scrubbers and other technologies mitigate pollutants before atmospheric release. For instance, flue gas desulfurization (FGD) systems like limestone forced oxidation scrubbers remove up to 98% of SO₂ by injecting sorbents into the flue stream, while selective catalytic reduction (SCR) units achieve 90% NOx reduction by catalyzing reactions with ammonia in the flue pathway.^[58] These flues integrate with electrostatic precipitators or fabric filters to capture particulates, ensuring compliance with environmental regulations for high-output combustion processes.^[58] Flue sizing in these systems adheres to standards based on the appliance's BTU output to maintain adequate draft and prevent backdrafting; precise calculations use code tables accounting for height, lateral offsets, and appliance type—for example, a 150,000 BTU natural draft furnace typically requires a 6-inch diameter vent at 20 feet height.^[59]^[60] These standards, drawn from references like the National Fuel Gas Code (NFPA 54), ensure safe operation by balancing airflow with combustion demands.^[59]

In Musical Instruments

In pipe organs, flue pipes generate sound through the vibration of air molecules as compressed air passes through a narrow channel called the flue and strikes a sharp edge known as the labium at the pipe's mouth, producing flute-like tones reminiscent of a recorder or whistle.^[61] This acoustic mechanism relies on the interaction between the air jet and the labium, creating periodic vortices that excite the air column within the pipe to resonate at specific frequencies.^[61] Flue pipes typically constitute approximately 80% of the total pipes in a standard pipe organ, forming the foundational basis for most tonal ranks.^[62] Flue pipes are constructed from either metal or wood, with metal pipes often featuring cylindrical or conical bodies for precise resonance, while wooden pipes are typically rectangular in cross-section to facilitate construction and tonal warmth.^[63] They are categorized as open or stopped: open pipes resonate along their full length, producing a fundamental frequency determined by the pipe's dimensions, whereas stopped pipes, capped at one end, effectively halve the resonating length and thus sound an octave higher for the same physical length.^[63] Both types include a foot for air entry and a body that shapes the sound wave, with variations in scaling—such as diameter relative to length—further influencing timbre, from broad flutes to narrow string-like tones.^[61] Voicing techniques refine the tonal quality of flue pipes by adjusting parameters like flue width, which controls the air jet's velocity and volume, and cut-up height, the vertical distance from the flue exit to the labium, which modulates the attack and harmonic content for desired color.^[64] Narrower flue widths produce brighter, more piercing tones with enhanced higher harmonics, while higher cut-up allows for a fuller, more fundamental-rich sound; these adjustments are empirically tuned to balance power and clarity.^[64] The edge tone frequency at the labium, which drives the pipe's resonance, depends on the air jet speed v and the geometry of the mouth, approximately following models like f \approx \frac{v}{2.7 d} where d is the jet-to-edge distance. The pipe resonates at its fundamental frequency f = \frac{c}{2L} for open pipes, with c the speed of sound, establishing the oscillatory feedback that sustains the pipe's resonance.^[65] Flue pipes evolved within medieval church organs starting in the 14th century, where portable and positive organs featured simple ranks of flue pipes for liturgical support, laying the groundwork for complex ensembles.^[66] By this period, foundational ranks such as the principal or diapason—open metal flue pipes providing clear, robust tones—emerged as core elements, enabling the blockwerk organs' powerful, unified sound that defined early European sacred music.^[67] These developments marked a shift from rudimentary wind instruments to sophisticated acoustic systems integral to organ design.^[66]

In Architectural Heating Systems

In ancient Roman architecture, flues played a central role in the hypocaust heating systems of public bath-houses, dating back to around 100 BCE. These systems featured raised floors supported by pilae—stacks of stone or ceramic tiles—that created a subfloor cavity through which hot air from a praefurnium furnace circulated, with temperatures reaching up to 40°C in the caldarium. Vertical and horizontal flues, constructed from ceramic box tiles known as tubuli integrated into the walls, directed the heated air upward and allowed it to radiate warmth while venting through the roof, ensuring even distribution and preventing moisture buildup.^[68]^[69] During the medieval and Renaissance periods, flues were commonly integrated into the thick stone walls of European castles to facilitate room heating, often serving multiple fireplaces within a single structure. In sites such as Mallow Castle and Kanturk Castle in County Cork, Ireland, these flues were mined through existing masonry, allowing smoke and heat from central hearths to rise and distribute warmth across interconnected chambers without compromising structural integrity. Shared chimney stacks connected disparate fireplaces, optimizing heat flow in large halls and private quarters, a practice that evolved from earlier defensive architecture to prioritize occupant comfort by the 15th and 16th centuries.^[70] In the 19th century, flues supported boiler-based heating in Victorian public baths and institutional buildings like asylums, enabling steam distribution for whole-building warmth. Public wash-houses and baths featured boiler flues that channeled hot air or steam into drying chambers and bathing areas, maintaining temperatures above 200°F to support laundering and therapeutic soaking, as seen in Manchester's facilities established under the 1846 Public Baths Act. Similarly, in asylums such as the Iowa Insane Hospital (built 1873), brick partition walls incorporated dedicated heating and ventilating flues connected to central boilers, promoting uniform warmth and air circulation in patient wards to align with moral treatment philosophies emphasizing environmental hygiene.^[71]^[72]^[73] Distinct from vertical chimney flues, historical architectural heating systems often employed horizontal or sloped flues to achieve even heat distribution across floors and walls. In Roman hypocausts, horizontal channels under suspended floors and sloped wall passages facilitated convective flow, minimizing hot spots and enhancing efficiency in expansive bath complexes. Medieval castle designs similarly used sloped flues within walls to direct heat laterally between rooms, while 19th-century asylum and bath installations incorporated gently sloped boiler flues to balance pressure and prevent steam condensation, prioritizing architectural integration over direct vertical exhaust.^[69]^[70]^[72]

Heat Management and Efficiency

Heat Retention Techniques

In traditional open fireplaces, up to 90% of the generated heat can escape through the flue due to convection, as warm air rises and carries heat away via buoyant flue gases.^[74] This heat loss is primarily quantified using the sensible heat transfer equation Q = m \cdot C_p \cdot \Delta T, where [Q](/page/Q) represents the heat loss rate, m is the mass flow rate of flue gases, C_p is the specific heat capacity of the gases, and \Delta T is the temperature difference between the flue gases and the ambient environment.^[75] Such losses highlight the need for targeted retention methods to enhance overall heating efficiency. Key retention strategies include the use of dampers, which restrict airflow and draft when the fire is low or extinguished, thereby minimizing unnecessary heat escape through the chimney. Insulation techniques, such as lining the flue with vermiculite, reduce conductive heat transfer to surrounding materials by providing a thermal barrier that maintains higher internal temperatures.^[76] Additionally, heat reclaimers function as external heat exchangers that capture warmth from flue gases, circulating heated air back into the living space without direct contact with combustion byproducts.^[77] Modern technologies further improve retention in high-efficiency systems. Sealed combustion flues, common in condensing furnaces, draw combustion air from outside and exhaust gases through sealed pathways, preventing indoor heat dilution and achieving annual fuel utilization efficiencies (AFUE) exceeding 95%.^[78] Variable-speed blowers in power-vented flues optimize gas flow rates based on demand, reducing excess draft and associated heat losses during operation.^[79] These techniques significantly impact system performance; for instance, insulating a flue can reduce conductive losses by 20-30% compared to an uninsulated one, leading to better draft stability and higher overall efficiency in combustion appliances.^[80] Certain flue materials, such as those with low thermal conductivity, complement these methods by inherently aiding heat retention within the system.

Safety and Maintenance Considerations

One of the primary safety risks associated with flues, particularly in wood-burning systems, is the accumulation of creosote, a tarry byproduct of incomplete combustion that can ignite within the flue, leading to chimney fires. Creosote has an auto-ignition temperature of 451°F (233°C), and such fires can reach temperatures exceeding 2,000°F (1,093°C), potentially damaging flue linings and spreading to the structure.^[81] To prevent this, the National Fire Protection Association (NFPA) Standard 211 recommends annual professional cleaning and inspection of chimneys and flues for solid-fuel appliances to remove creosote buildup. Carbon monoxide (CO) poisoning represents a significant health hazard from flues, as blocked, damaged, or improperly installed flues can prevent proper venting of this colorless, odorless gas produced by combustion. Exposure to CO at concentrations as low as 0.1% (1,000 ppm) can be lethal within hours, causing symptoms mimicking the flu and leading to approximately 230 deaths annually in the U.S. from non-fire-related CO incidents (2019–2021 average), though this number has declined from over 400 in earlier decades due to improved safety standards and technologies.^[82]^[83] Modern building codes, such as the International Residential Code (IRC) Section R315, mandate the installation of CO alarms in homes with fuel-burning appliances to provide early detection and alert occupants. Structural integrity issues in flues often arise from corrosion caused by acidic condensate formed during combustion, especially in unlined masonry flues where flue gases with a pH below 5 directly contact the interior surfaces. This acidity, primarily from sulfur dioxide and water vapor, accelerates deterioration, leading to cracks, spalling (flaking of masonry), and potential collapse over time.^[84] Regular inspections are essential to identify these issues early, with visual and camera assessments recommended to check for deterioration that could compromise venting or structural stability.^[85] Maintenance protocols for flues emphasize routine cleaning and adherence to clearance requirements to mitigate risks. For wood- and oil-burning flues, annual cleaning is advised to remove soot and debris, while gas-fired flues typically require cleaning every three years or as needed based on usage.^[86] Additionally, the International Residential Code (IRC) Section R1003.18 requires a minimum 2-inch (51 mm) clearance between flue exteriors and combustible materials to prevent heat transfer and fire spread. Professional sweeps certified under NFPA 211 should perform these tasks to ensure compliance and safety.