OK, here we go......
Based on several approximations and assumptions:
For a change in the intake air temp of 50F from 200F, this equates to roughly 7% increased air density, which allows roughly 7% more fuel (the primary mechanism for increased power through cooler charge air) and thus ROUGHLY 7% more crank power (remember I said there were some approximations used here). For a stock 2.7 producing 250hp, this comes out to about 17.5hp increase (YEA!! more power, right?).
HOWEVER....in order to cool the charge air by 50F and using a very generous assumption of 0.1 seconds of exposure of the intake air to the intercooler interface, not to mention an almost perfect thermal transfer coefficient -- I'll spare you guys all the math -- it would require over (drumroll please) 90hp applied to cooling system. OUCH!!
However, again.....But I know what you're thinking: for an actual application in a daily driver type of situation, using the refrigeration (a/c) system to cool the charge air directly wouldn't be necessary since most people are not going to hold full throttle all the time. What a person COULD try is to use an intermediate cooling system, say a second a/c compressor, water pump with antifreeze or similar and a reservoir of some size. The second a/c system would be able to apply a smaller power input continuously, which could potentially provide power gains for short periods of time. But such a setup would require, say, 10hp from the crank NEARLY ALL THE TIME for maybe 5 seconds with an overall 7hp increase. Not to mention the 200+ lbs of weight the secondary cooling system would add to the car.
So now everybody knows the fundamentals at play and why this isn't practical. Bummer! But this also explains why it's important to allow as much air as possible to pass THROUGH the engine's radiator and not around it. Any time there isn't enough airflow through the radiator from the vehicle moving, the engine fan(s) have to compensate which kills gas mileage (so, like, people who think it's a good idea to remove the fan shroud or the front air dam for example).
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