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Would be all for it if I didn't need to cut such a custom shape for mine and not have the tools for it. Needs to be skinnier under the desk and a bit wider outside the desk.
Would be better to know the exact cookie it uses for skips so people could possibly use something to block it.
I Imagine because cold air drops, and hot air rises. If you put it near the top there's chance you won't pass air over all the ice(not sure how much it will truly make a difference). Though I'm sure there are ways you could modify the airflow like a tube that almost hits the bottom and holes near the top of the cooler so air is forced to the bottom and back up.
You could do that, you could even just use frozen water bottles. I believe the reason they used popsicle sticks is the surface area to volume ratio. The biggest key is having a large surface area to pass air over.
Uh...last I checked dry climates are the place to increase humidity, you know, because the air is dry and it's easier to add water to the air than it is to air that's already humid. Humid air also helps with skin, and breathing. I live in a humid climate, and trust me no one here uses swamp coolers. Where as freezing water(in a container) or passing air over something cold will remove moisture from the air, like how a cold water bottle sweats on a hot humid day, and basically how an AC unit works.