I live in a part of Mexico that can get really hot in the summer. I've got an un-airconditioned bedroom on the other side of a wall from a room cooled by a powerful Mirage mini-split AC.
The problem is that the only communication between the two rooms currently is the bedroom doorway which opens from a shared hallway. This is insufficient because of the dead air volume above the doorway (the ceiling is inclined similarly to that over the AC unit). Please see pictures for reference.
My idea is to bore two holes 8-10 inches in diameter through the wall as shown in the detail shot. The purpose would be to establish a convection loop, where the hot air from top of the bedroom would flow out into the area of the AC unit (and be entrained in the cool air flow from it). To compensate for the reduction in pressure, cold air would replace the ventilated hot air by flowing in through the hallway and into the bedroom doorway. I understand that this scheme, if it works, will probably put an additional load on the AC. That's acceptable.
I haven't done any math on this idea (indeed, I'm not sure what math to do), but am just guessing at the size of the holes. Intuitively, it seems feasible.
Any thoughts on whether this would be effective before I get out my chisel and hammer?
Overview shot to demonstrate problem:
Detail shot, with proposed holes:
First, many thanks to all who responded, and particularly for the exhaustive analysis provided by Olin. The hole is being cut now, and the design has changed due to some unforeseen realities in the masonry. It will now be a rectangular opening about 12" x 20", with the top corner about 6" from the ceiling and wall. I'll report back on the outcome, and whether a fan is necessary.