Actually, the exit
should be lower or maybe equal in height with the entrance into the half barrels.You want the hot gases to be able to rise and stratify at the top, so the coldest gases sink and go out the exit.
You can cut a hole in the bottom of the end of the half barrel for entrance and exit. If you want the half barrels to act as one bell (so the tops are all the same temperature), you would cut out all of the mating barrel ends except for a small strip at the bottom, to allow smooth flow between the barrels. You would want to seal these two barrel ends together so gases would not leak out at the joint.
You can use a piece of 8" duct to go from below the vertical barrel to the end of the horizontal barrel. You want to give the hot gases a smooth path from one to the other, using whatever shape of sheetmetal you can get or make to do this. It is important to not have a "kink" or constriction in the flow at the exit (called the "manifold") from the first barrel, but make this transition a bit bigger than the rest of the system for easy flow.