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Turbo vs. Supercharger. (long, technical, blabla)



As Al pointed out, the intake air is absorbing heat from the impeller.  So, what he refers to as "cooling the impeller" is another way of saying "heating the intake air".  One other thing, 900deg F is a pretty conservative number if the engine is under load for more than a few seconds.  One would not be incorrect if one used the number 1100 or 1200deg F.
  Oh, yes....the heat does transfer through the shaft just as fast as the intake air can absorb it.  In fact, it absorbs it exactly as fast....it called equilibrium. (given steady states of energy, a certain temperature will be reached and maintained indefinitely)

(Don't we sound like a coupla' experts....)
Larry
  - on the flip side (back to the turbo), cool air rapidly flying by a turbine
  impeller blade will quickly cool that blade. the turbine impeller may be hot
  at idle, but it quickly 'cools as it spools' (nice catch phrase, eh? heheh).
  even with a 900f exhaust blade, the heat simply cant transfer across the
  narrow coupling shaft as fast as the cooler intake air can strip heat from
  the intake blading.

  Al