The flue from a corn fed stove will get as hot as any normal furnace flue. I’m not sure I’d want a 200-400 degree flue at ground level or running up the side of the house. You will also run into problems if there is a window or door on the wall. You can’t exhaust a furnace anywhere near a window or door because all the fumes could get sucked into the house and kill your family.
I would most certainly check with the local building inspector to find out what is legal and what isn’t. If it’s illegal there is a very good reason for it.
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