Hi. Mechanical engineering degree here, with post-grad research in fluid mechanics and 10 years in acoustics (fluid mechanics).

I wouldn't model this with a ten foot pole.

Here are some things you're not considering:

1) You give a shit about steady-state. Steady-state is room temperature. The steady-state form of this experiment is only dependent on the mass of ice and the mass of bourbon.

2) The transitional phase is driven by a shit ton of variables that will require polynomial math. To whit:

- "swirling speed" will have more effect on a fresh (sharp) ice cube than on a not-fresh (round-edged) ice cube.

- Conductive and convective heat transfer will change non-linearly depending on the size of the cube and the size of the sphere.

- Glass shape and swirl method will put the sphere out of round and the cubes out of square in an unpredictable, nonrepeatable way.

- state change heat transfer will change non-linearly depending on the size of the cubes and size of the spehere.

- thermal conductivity of your drink will change as the ethanol/water blend changes. For that matter, results will be different with Wild turkey 80 and Wild Turkey 101. Not enough to overcome your swirling, but "how fast you swirl" is probably your biggest variable anyway.

- Room temperature matters. Room humidity matters. "big sphere half out of bourbon" is going to absorb more heat from the room; small cubes wholly in bourbon" are going to absorb more heat from the glass. By the way - glass? Ceramic? Crystal? Borosilicate? Cylindrical glass? Prismatic? 4 sides? 6? 8? Yeah, you can control for this, but the more you control for it, the more specific (and less generally applicable) your results will be.

That's off the top of my head. The important factors are this:

- How fast you swirl your drink matters.

- How much contact the cubes have with the drink matters.

- How fast you drink matters.

For the record, I'm a long goddamn ways away from being a purist. I put ice cubes in my bourbon, I drink my scotch straight (although blends with a splash of soda water are tasty). I know whiskey stones are a waste (most of the cooling done by ice is done by transition - IE, melting - not by conduction or convection). The original iteration - all $1500 of it - was much more about table flourish than anything else. BUT: the advantages are this:

1) You can use more ice, because most of it is sitting outside your drink.

2) That additional ice provides some thermal inertia, keeping your drink closer to the beginning of that empirical curve you found.

3) You will finish your drink and have most of your ice left.

Balance that with the fact that HOLY FUCK IT'S JUST ICE and it's been hitting you in the face the entire time you've been drinking. Also, you look like you're guzzling snowball juice, you douche.

This is why I drink Ardbeg, Laphroag and Talisker, and only buy MacAllan when the Chinese are making everything else too goddamn expensive. Although Ralph's 30% off six got me a bottle of Hennessy for $18, a bottle of Woodford for $24 and a bottle of Chivas for $16 so fuck pretense.

If you care that much, drink cask strength. A little melted ice brings it back down to earth quite nicely.

* * *

There's a saying: "You know you're an engineer if you've ever modeled a horse as a sphere." The amount of math going on here is formidable, chaotic, difficult to repeat and tedious. Far more efficient - and far more fun - to solve it empirically. If you're serious about it, run a bunch of experiments, graph the results, then find a curve fit. Maybe even write a grant proposal. I'd fuckin' love to see someone using research dollars on booze.