In this sentence, I'm describing the sides of an underground forge's chimney:
It was an underground cavern with a shoot leading up in the middle.
I would need to find a better substitute for shoot. I'm positive a word exists with the same or similar pronunciation, but I just can't seem to find it anywhere on the internet. I've been thinking about using chute, but that specifically describes a hole in the ground where you put things to transport them somewhere.
I'm looking for the word for the outside walls of the chimney, yes. But with the caveat that said chimney is underground and we cannot see the top of it.
I would accept having to rewrite the sentence if nobody has any suggestions.
[graphic from OP comment, Pinterest]