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You're missing a big point in all your analyses. The science of convection is almost all empirical. Predicting heat transfer in a fluid over complex shapes is not something that can have a general solution in all but the most simplified and idealized cases. Complex heat transfer problems are pretty much always solved by numerical modeling. In the end, in a perfectly insulated system, only the initial temp and mass of the ice and whiskey matter, but there's no such thing. The swirling, in particular, is going to vastly accelerate heat loss to the surroundings.The same Techies did a a similar study with stones, steel, and an iced glass. Empirical once again.