Actually, I don't see a code issue with dropping down and over. True that heat rises, but air has mass, and can be pumped down more easily than up. Efficiency will not be affected.
Just exactly how you terminate needs to be worked out. You don't want moist air backfeeding into the basement through that window, or collecting in a poorly ventilated space.
A few errors in physical intuition model here...
*Heat doesn't rise, it moves from hot to cold.
*Less-dense fluids rise as denser fluids fall due to gravity. Hot exhaust gas has lower density than cold exhaust gas (or air), and will rise as the denser gas displaces it due to gravitational forces. (The cloud of less dense gas "floats" in the denser gas, rising.)
*It takes
more energy, not less, to force a lower density gas downward, counter to the gravitational forces on the denser cool gases that it is displacing. (It's "easier" to pump it up, working
with gravity.)
Thought experiment: Take a helium balloon at head height, push it to the floor, what happens? You've forced an equal volume of heavier gas (the air) upward against the force of gravity- that takes energy.
In the dryer vent gas case it's not a huge force if the drop is small, say 3-5', but at 20' you may encounter measurably lower flow (and not just due to duct friction.)
Can't help on the code issue though- no idea.
