When you say "enclosed", you may be referring to the barrel ducts on the inner side the discs that have been in vogue for the last couple of years, such as these by the now defunct Arrows team?
I think that the purpose of those is more aero rather than cooling, in that they are meant to control/direct the exit/airflow of heated air from the brakes.
To clean up the exit flow further, Ferrari and others now use an outer barrel/donut as well:
Tim