Heat a volume with a warm mass. How math?

Post date: 2023-06-01 18:14:51

I think I'm trying to do some kind of thermal mass calculation. But I'm not even sure how to approach the equations.

The hypothetical:
Dig a circular pit 10 meters in diameter and 3 meters deep.
Put a heavily insulated roof on top of this, and (ideally) a thermal equilibrium will be established. An artificial cave, a root cellar that maintains a stable temperature regardless of seasonal variations.

The stable temperature of this round room is, let's say, 10c.
But I would prefer it to be a stable room temperature at 20c.
In order to do that, I place a cylinder in the center of the room, 2 meters in diameter and 3 meters high.

The question(s):
How much heat does this have to give off, in order to make and maintain that ten degree change?
How much heat do I have to put into into it, in order for the tank to radiate the heat above?
There's also some kind of radiation/absorption thermal inertia factor over time?

What I'm trying to accomplish in this mental exercise in this is to figure out if that thermal mass cylinder can be used as a seasonal heat battery. Take a solar thermal water heater, and instead of using it for the shower, run its coils though a stock tank full of gravel. Sand? Adobe? Charge it over the hot months, draw it down through the cold ones.

The end goal being a 20c thermal equilibrium.

How do I math this? Or am I just imagining some perpetual motion silliness?

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