Would a through-the-wall fan like this one be OK if it's on the opposite wall from where the stove is? Maybe 8' away? Open kitchen window for return air and it should be fine, yes? Both fan and window would be on same wall. (I'm trying to avoid a hole in the roof if possible)
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Steam and fumes from cooking will rise straight up and stain the wall by the stove and ceiling above it. Not enough velocity/ speed to prevent that with fan that far away. Better to have the exhaust fan over the stove to prevent that.
"Cut it twice and it is still too short".