blow the hot air out (from) the top
suck the cool air in from the bottom
is there a carbon filter involved?
leave one end of your hood open, duct the other side to the fan blowing out of the tent (through optional carbon filter)
have passive openings near the bottom of the tent to replace the air the fan sucked out.
this way both the tent and the hood get cooled with 1 fan
this plan will NOT work with a "toy" in-line fan, it needs to have power to suck/blow through all that duct/hood (filter) etc
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