Right, wrong or otherwise I've seen the wall opened up behind the cooktop on a 1st floor kitchen in a 2 story house where the cooktop was not on an exterior wall, and new ducting was run between studs, then underneath the cabinets to tie in to the existing ductwork. The house was on a concrete slab and the downdraft duct ran through it.

Whether this was good or bad I'm not sure, only that where someone was presented with the challenge this was the step they took.

It could be done, but how efficient it will be is another question.
Assuming there will be a minimum of three 90 degree turns in the duct; from up, to back, to down, to out. And what size the existing ducting is will also play a role...

The best path for any duct is straight up and out, with a short run that does not diminish in size. Any deviation from that will cause increased turbulence, noise, and decrease performance. Adding unnecessary turns and restrictions is not a good idea. If you have no other choice, then that's a whole other situation.

Thanks a lot Schiksal, ctycdm, live_wire_oak for your ideas and suggestions.

From what I understood, it might be difficult to impossible task for using the existing duct work with number of 90 degree bends.

Our's is a 3 story town home with kitchen located in the second level.
If I don't use the down draft duct work, what options do I have for the duct work for the new under cabinet hood?

Your suggestions are welcome.

Thanks in advance.

-Rama

Post your layout, and the floorplan of your home. Going straight out a wall to the exterior is almost as good as going straight up. Ductwork can be hidden in an upper shelf of a cabinet if need be.