[UkrainianJew]

Heat keeps leaking out. The amount of stored heat is proportional to the cube of the linear size, the leak rate is proportional to the surface area (square of the linear size). Hence, the bigger the storage, the higher the efficiency.

Same why a flea can jump >10x its height, and a human cannot (square growth of strength, cubic growth of weight).

[GistNoesis]

I'm not sure if the leak is really proportional to the surface area. (It's probably even less due to how the heat equation works).

The equation for the thermal resistance of a cylindrical system is explained in https://youtu.be/6x-jdCGWuHI?t=801

The thermal resistance is the sum of 3 (or more) terms, and while the outer terms are indeed proportional to surface area, I'm not sure if the physical constants of the system aren't designed so that the middle heat conductive terms of resistance R=ln(r2/r1)/(2pikL) is the dominant factor.

[WalterBright]

Thanks for the answer. I suppose the answer is a decent insulation on the box. It only has to last for a few hours.

Of course, some engineering would have to go into optimizing the size of the rocks and the surface area / mass for the expected use.

[lazide]

The other issue is ‘heat quality’ (or temperature deltas). It’s easier to recover a given amount of heat from very hot sources than from only luke warm sources, and smaller heat stores will have a very pronounced difference very quickly, resulting in control issues.

Basically, if you only have a small amount of sand, it’s harder to keep it warm for longer (more surface area for the mass, so more insulation required), and harder to deal with effectively (fan needs to blow much harder when it’s only warm, much less when it’s hot), etc.

[mtrycz2]

So like, sand?