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The term "flux chiller" definately appears in Franz Joseph's Star Fleet Technical Manual. I expect FJ invented it, although I haven't read Whitfield and could be wrong.
As for what they *DO*, the manual doesn't shed any light. MrNeutron's or Timo's explanations are as good as any.
For what it's worth, FJ's daughter once said in an interview that FJ conceptualised the warp effect as going THROUGH the nacelles, front to back, like some kind of cosmic jet engine (This was back in the 70s, of course, long before the canon explanation).
Interesting trivia note: FJ's single-nacelle designs do have flux chillers. They're on the bottom of the nacelle.