At first I thought the fan would quicken the thawing, since it moves more relatively warm room-temperature air onto the bottle.
But then I thought of the condensing liquid on the outside surface evaporating away quicker, which takes away heat.
It would be relatively simple experiment, but I don’t feel like getting another bottle.
Blowing air on something cold will increase the rate of condensation, which gives heat. This should more than compensate for evaporative cooling.
Faster… you’re moving the cold air from the area away from the bottle, so room temperature air can replace it, thus thawing it faster.
Interesting question. It seems to me that the liquid on the outside comes from the condensation of water vapor in the surrounding air. Upon condensation on the bottle this vapor gave up heat to the ice-filled bottle thus warming it. When it re-evaporates it takes that extra heat away so it would seem to be an even game.
At the same time blowing air increases the rate of convective heat transfer so I think blowing air over the bottle would make the ice melt faster.
Any water that condenses and then evaporates is a break-even. On the other hand, water which condenses and then is blown away in small liquid droplets will have a net warming effect. The forced convection will also cause the bottle to more quickly reach equilibrium with its surroundings, and inefficiencies in the fan motor will add heat to the environment.
So we have four effects at work, one of which breaks even and the other three of which would tend to warm the bottle quicker. So the bottle will definitely warm quicker.
Thanks all. Where I went off the beam with one was that I didn’t think of fact that the heat from the water vapor being condensed went to bottle.