Etymology
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flue (n.)

"smoke channel in a chimney," 1580s, of uncertain origin, perhaps related to Middle English flue, flewe "mouthpiece of a hunting horn" (early 15c.), which is perhaps from Old French fluie "stream;" or the modern word is perhaps from Middle Dutch vluwe, from Germanic *flowan "to flow" (see flow (v.)). Originally a small chimney in a furnace connected to the main chimney.

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fluonomist (n.)
said to be a humorous title for a chimney-sweep, 1947 according to OED, from flue + ending from economist, etc.
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*pleu- 
Proto-Indo-European root meaning "to flow."

It forms all or part of: fletcher; fledge; flee; fleet (adj.) "swift;" fleet (n.2) "group of ships under one command;" fleet (v.) "to float, drift; flow, run;" fleeting; flight (n.1) "act of flying;" flight (n.2) "act of fleeing;" flit; float; flood; flotsam; flotilla; flow; flue; flugelhorn; fluster; flutter; fly (v.1) "move through the air with wings;" fly (n.) "winged insect;" fowl; plover; Pluto; plutocracy; pluvial; pneumo-; pneumonia; pneumonic; pulmonary.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit plavate "navigates, swims;" Greek plynein "to wash," plein "to navigate," ploein "to float, swim," plotos "floating, navigable," pyelos "trough, basin;" Latin plovere "to rain," pluvius "rainy;" Armenian luanam "I wash;" Old English flowan "to flow;" Old Church Slavonic plovo "to flow, navigate;" Lithuanian pilu, pilti "to pour out," plauju, plauti "to swim, rinse."
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flu (n.)
1839, flue, shortening of influenza. Spelling flu attested from 1893. The abstraction of the middle syllable is an uncommon method of shortening words in English; Weekley compares tec for detective, scrip for subscription.
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damper (n.)

"one who or that which dampens," 1748, in the figurative sense, in reference to spirits, enthusiasm, etc., agent noun from damp (v.). In mechanical senses, "device for checking action:" 1783 in reference to a felt-covered piece of wood, etc., which deadens the string after the note is played; 1788 of a chimney, stove, etc., "metal plate in the flue used to control combustion by regulating the draft." Either or both reinforced the figurative senses. The piano damper-pedal (1848) raises the dampers of all the strings so the notes are prolonged and sympathetic vibrations produced.

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fluency (n.)
1620s, "abundance;" 1630s, "smooth and easy flow," from fluent + abstract noun suffix -cy. Replaced earlier fluence (c. 1600).
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fluent (adj.)
1580s, "flowing freely" (of water), also, of speakers, "able and nimble in the use of words," from Latin fluentem (nominative fluens) "lax, relaxed," figuratively "flowing, fluent," present participle of fluere "to flow, stream, run, melt," from extended form of PIE *bhleu- "to swell, well up, overflow" (source also of Latin flumen "river;" Greek phluein "to boil over, bubble up," phlein "to abound"), an extended form of root *bhel- (2) "to blow, swell." Used interchangeably with fluid (adj.) in 17c. in the sense "changeable, not rigid." Related: Fluently.
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chimney (n.)

late 13c., "furnace;" late 14c., "smoke vent of a fireplace, vertical structure raised above a house for smoke to escape to the open air;" from Old French cheminee "fireplace; room with a fireplace; hearth; chimney stack" (12c., Modern French cheminée), from Medieval Latin caminata "a fireplace," from Late Latin (camera) caminata "fireplace; room with a fireplace," from Latin caminatus, adjective of caminus "furnace, forge; hearth, oven; flue," from Greek kaminos "furnace, oven, brick kiln," which is of uncertain origin.

From the persistence of the medial i in OF. it is seen that the word was not an ancient popular word, but a very early adoption of caminata with subsequent phonetic evolution [OED]

Jamieson [1808] notes that in vulgar use in Scotland it typically was pronounced "chimley." From the same source are Old High German cheminata, German Kamin, Russian kaminu, Polish komin. Chimney-corner "space beside a fireplace" is from 1570s. 

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mantel (n.)

c. 1200, "short, loose, sleeveless cloak," variant of mantle (q.v.). Sense of "movable shelter for soldiers besieging a fort" is from 1520s.

The meaning "timber or stone supporting masonry above a fireplace" is attested by 1510s; it is a shortened form of Middle English mantiltre "mantle-tree" (late 15c.) "beam of oak or some other hard wood above a fireplace or oven" (with tree in the now-obsolete sense of "beam"). But the exact meaning of mantle in that had become obscure by the 19c.

In a fire-place, the mantle or mantlepiece, may have been either a covered or chimney-piece; or the part below it to which a hanging, for the sake of making a flue for the wind to draw up the fire, was attached. The details, however, of this are uncertain. [Robert Gordon Latham, "A Dictionary of the English Language," 1882]

Mantel-clock "clock intended to sit on a mantle-shelf," is by 1824.

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