On my little F-106, I used a dualpipe setup similar to what Mr Matt first described. The outer pipe is fed by the interior of the model, not the bypass. The air that feeds the interior of the model comes from a forward facing slot formed by the inlet's boundary layer splitter plate and the fuselage. It's ram air, and should provide cooling around the bypass itself, before exiting the outer tailpipe passage. [8D]

Mr Matt's second concept he described, I think is used on the BVM F-86 with the RAM500 installation, I believe