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My thought would be that putting it in the middle may cause you to lose too much heat straight up and out of the drum causing you to burn through fuel. Most I have seen with exhausts are off to the side.
Not sure but just a guess. I am sure someone has one in the middle that might correct me.
Personally I use a weber kettle lid so it is off to the side, but it works perfect, so on any that I build in the future I would go off to the side. Just my .02 cents.
i put mineeto one side because thats how i saw the ones with the stacks, i figured it was better that way in case it rains it would have less chance to go on meat or coals