If you have no outside wall or have an opening in that outside wall you will need a Ceiling (island) hung BBQ Rangehood.

Ceiling Rangehoods are secured into a frame built into the ceiling rafters.

Ceiling BBQ Rangehoods need to have an minimum exhaust of 2500m3/hr

They are open on all four sides of the hood.Their overall area that needs to be exhausted of BBQ cooking residue is 25% greater than a wall mounted BBQ rangehood.