Imagine a typical fast-food drink cup, made of some kind of heavy waxy-coated paper, half full of ice with no liquid. It is in a room at (say) 70 degrees F. It naturally starts to melt, gradually changing the ice into water.
The question is: will it melt faster* if left alone, or if the water is removed (say) three times during the melting at roughly equal intervals?
*By “melt faster” I mean complete the process of melting faster, in case that makes a difference to the scenario. In other words, the time starting at point A, all ice, and ending at point B, all water.
It will melt faster if the water is left in the cup.
Water is a much, much better conductor of heat than air, so if you want the ice to melt, you want as much ice in thermal contact with the walls of the container, and the water will do that better than air.
In my sink now are two plastic cups, one with holes in the bottom, both with 3 ice cubes, weighing an identical 66g. It is 2:50pm, I will advise as the experiment progresses.
Dry air is a terrible conductor. In a cup of melting ice the air won’t stay dry long, but it is mostly the water content in the air that is contributing to any melting when the ice is not submerged in water.
At 4:10 I have about a quarter inch of liquid water in the cup without holes. There appears to be more melting in that cup despite the tiny amount of liquid.
This is taking a lot longer than I expected. Must be hard water.
Back before refrigeration, one of the first ways ice cut from lakes was stored was by suspending large blocks of ice below ground level with air surrounding the blocks. You can see an example of the ice barn at about minute 4 of this clip:
The air around the ice was such a good insulator that they could store ice like this for months in the South to be sold over the summer.
The show was about one of the first people to figure out the ice trade. He had tried many ways of storing and shipping ice before figuring out that having air gaps worked to provide good insulation. But I’m sure that as ice was commercialized, they worked out any inefficiencies in the system and would have done things like store it in the North.
Dry air and water vapor aren’t hugely different in their conductivities. Water’s a bit better because it is a lighter gas, but it’s not twice as good. However, a quick look at a psychrometric chart shows saturated air around icewater will only be around half a percent water, so almost all the conductivity will be from the nitrogen and oxygen. The water vapor will make a difference that would be hard to detect even with nice expensive instruments.