Please Help Me Calculate a Temperature Drop

Factual Questions
1

OK, this sort of thing has never been my strong suit, and I’m getting nowhere with Google (and this is why I studied Biology in school)

I know the temperature experienced from a radiant heat source follows the inverse square law, but I’d like to estimate what that would be for a specific hypothetical:

Given wood stove with 7 inch legs, having a surface temperature of about 500 degrees F, what is the temperature at the floor below the stove?

If anyone cares, this came about because we’re getting one installed and it is rated to be OK above a combustible surface (though ours will be on a hearth) and I just wondered how hot it gets down there. I don’t know what temp the underside of the stove actually gets, especially since there is a pan underneath, so there isn’t direct “exposure” to the firebox; 500F is just a WAG on my part

2

So you are irradiating the floor, and it starts to heat up. ISTM you cannot estimate the equilibrium temperature unless you say what the floor is made of so we can somehow estimate how fast it can conduct heat away.

Anyway the hot stove itself will radiate 2000 to 3000 W/m² (wild guesstimation) which has to go somewhere…

3

Below 1000K (around 1350F) heat transfer by radiation is negligible. Convection through the air layer will dominate. The temperature at the bottom depends on heat it receives and it’s thermal conductivity. You have not given any info on the latter .

4

The floor will be porcelain tiles, about 12x24" each in a bed of mortar, which will sit on 1/2" cement board which will sit on 3/4" OSB

5

As far as convection + heat flow, it seems like you have your iron surface at 260°C, then there will be some heat transfer coefficient to the (relatively still? It’s not like the air rising above a hot stove) air, then an insulating layer of air, then heat transfer to the floor, and finally heat conduction out through the floor to a cool heat sink. So the thermal resistance of the interface + air will dominate that of the floor which will not heat up by that much (10° or something of that order?), getting only fairly warm to the touch. Better run that by an engineer, but I believe them that it won’t combust any surface, definitely not porcelain tiles.