Posted for "Tracy Crook" <lors01@msn.com>:

Bill Schertz & Frank have already done a good job of explaining this so I'll
just add a couple of thoughts to what Frank said.
The heating due to pressure recovery is small and is unavoidable.  The
alternative (no pressure recovery) means no cooling at all so this factor
must be ignored in practical systems.

The best analysis I've seen on the P51 cooling system showed that it reduced
cooling drag to about a 40 HP loss, an astonishingly low value for a 2000 HP
aircraft.  A net gain (thrust) from the cooling system is a theoretical
possibility but still a pipe dream in actual systems.

Tracy Crook