An air-to-air intercooler is constructed similarly to a car's radiator. It has a large, airtight volume inside with a large surface area. Compressed air from the turbocharger flows into the intercooler and transfers heat to the intercooler by conduction. The intercooler itself is generally mounted in the front of the automobile where fresh air passes through its vanes and bleeds off the heat. The cooled air then exits the intercooler and is fed into the intake system of the automobile.

Intercoolers are different from radiators in that they must be airtight, i.e. free of boost leaks, and they should present as little restriction to the airflow as possible.

Intercoolers are generally rated on their efficiency, or on how well they remove heat from the compressed air. It should be obvious from this discussion that using such a setup, it will be impossible to cool the compressed air to less than the temperature of the ambient air. Therefore, air-to-air intercoolers will work much better in the cooler months than in the dead heat of summer. An excellent intercooler will get you close to ambient temperature.

Air/water intercoolers circulate water through the intercooler housing to remove the heat instead of relying on the ambient airstream.

Warning: YAFWU ahead! :)
A couple of notes about intercoolers:

Intercoolers can have multiple cores, much like high performance radiators. Think of what you know a radiator is, then think of a second one stacked in front of it, with the input and output connected in paralell accross them.

The primary advantage of this design is that you can both increase the surface area exposed to the open air (or liquid, depending on design), while decreasing the over all pressure drop across the whole intercooler. Obviously, this means better cooling, and higher pressure output, which equates to better boost performance at the intake manifold.

The secondary advantage of this method is that you can optimize for space in your design easier. ie: if you have much more room for depth than width, instead of building a wide single core intercooler, you could build a half-width double core intercooler.

Intercooler placement is often critical to overall performance of a vehicle. If the intercooler is front-mounted, it will cause greater drag. Thus, the practice of side-mounting intercoolers, like in the Audi S4. This allows for less drag in an air to air system, and still provide decent (and sometimes superior) cooling .

Yes, Boyle's Ideal Gas Law relates the various aspects of a given air charge, ie: pressure, volume, and temperature.

See intercooling for the theory on these devices.

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