Due to the Isoperimetric inequality the sphere has the minimal surface area compared to ANY other solid. With a greater surface area, the drink probably will cool faster with ice cubes, thus the drink will reach the "steady state" where ice melts slower faster. I would guess that once at the steady state, the rate of melting will be the same for any shape ice. But by the time it's the steady state, won't the cube turn into spheres anyways? Maybe I would rephrase the conditions of the question to adding spheres or cubes to an already cooled drink... But then the answer does not have many practical applications. The easy solution is to buy whiskey stones :p I'm no engineer and i'm pretty curious if anybody can provide a mathematical answer to this question :)
False. Whiskey stones would require more mass just too cool the initial measure. The phase change of ice is a major part of its ability to cool. Assuming you put enough mass of stone in to actually cool the drink to the desired temperature, the boundary conditions would once again be the same, then the drink with the stones in it would rise in temperature, while the drink with ice in it would remain cold. Think of it this way. It takes X Joules to cool a drink from T1 to T2 (70 to 32F, let's say.) Depending on the specific heat of the stones (be they granite, stainless steel, or brass) will determine how much mass are needed, or alternatively how cold they themselves need to be from the start. My freezer only sets to one temp, so figure they start off the same. The same Techies did a a similar study with stones, steel, and an iced glass. Empirical once again. Add more Joules from your hand and the ambient air. Temperature of the system goes up. Remember we swirl, so the drink/ice or drink/stones keep essentially a homogeneous temperature. If you had ice, the temp would stay the same and you'd get more phase change (melting.) To your first point, yes, obviously a spherical shape cools the slowest.
Your second paragraph (guess) is also correct - but that's the part I want proven with math. It could be a double helix vs a sphere, or a "snowflake" (theoretically infinite surface area) vs sphere. My point is that once we're at steady state the amount of surface area between solid and liquid no longer matters, as energy into the system is the same either way. I'm drunk now, either way.
I received a set of whiskey stones for xmas. They are probably okay for keeping something chilled, but they don't chill a drink down as fast as ice. I actually prefer my bourbon and water at room temp anyway.
In fairness, it doesn't overlook that. I'm trying to compare spherical ice vs cubes or whatever. The determination that ice is preferred has already been made by the person adding the ice. The only thing we're trying to figure now is the best shape for the ice.
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.