Simon,

Certainly in most marine power plants on ships it would be common practice to use the waste heat from the exhaust to heat water up for several reasons, I have never seen a cooling system for an exhaust (mind you I have never sailed on a sub either). I would suggest that its a protective sleeve around the main exhaust pipe. If the hot exhaust pipe was in direct contact with, or partially submerged/splashed by seawater the metal corrosion would be greatly accelerated. I see it with steam pipes on deck, unlagged and hot they don'y be long turning into a rust mush once they get in contact with seawater.

Regards,

Mark