[dunham]

It's not clear to me what they're using for the surface heat transfer coefficient, which I think would be different for a skillet vs sous vide. (Or even, in their case, Side 1 = skillet vs side 2 = air.) But I only have a cursory knowledge of the physics involved.

For the sous vide case, I've tried implementing Douglas Baldwin's model on Observable. It seems to match the "SousVideDash" results, but this is my first foray into solving PDEs, so use with caution.

https://beta.observablehq.com/@dunhamsteve/sous-vide-calcula...

If anyone here does know the physics / math, I'd like more details on the $\beta$ "geometric factor" that Baldwin uses. I couldn't find mention of it in books and wonder if it is something you derive (say transforming coordinate systems) or something determined experimentally.

[btrettel]

Fluid dynamicist here. The $\beta$ notation appears to be a convenient way to write the Laplacian assuming that the temperature is homogeneous in the angular direction. The values are exact for certain coordinate systems.

https://en.wikipedia.org/wiki/Laplace_operator#Three_dimensi...