BTU rating of Earth below frost line

sday

Does anyone know how many BTU's the Earth is capable of transferring per minute or hour per square foot of surface area below the frost line?

thanks
-Steve

mfb

Transfer from what to what, in which way? In addition, nearly any heat transfer will depend on the temperature gradient.
Do you have some specific setup in mind?

sday

Say earth at 55 degrees F with a rectangular cement tank buried. If The concrete if 4" thick and you put 45 degree water or 65 degree water (10 degree difference + or -), how many BTU of transfer would occur per square foot? Is that enough info?

mfb

That looks like a completely different question.
Yes, you can calculate it (assuming the outside remains at constant temperature), if you know the thermal conductivity of cement. It should be straight forward how to do it (just multiply everything together). If you need help there please use SI units, they are much more convenient in physics.

sday

Can I just use H = (A(Th-Tc))/R?

I tried approaching it the same way I calculated two containers full of water separated by a copper barrier using the above formula, but I don't understand how to apply it to Earth. For a relatively small body of water can one just assume Earth is always capable of transferring at the lesser of the material in contact with soil? I have found coefficients for dry and wet soil.

Can I just assume if deep enough, the temperature of the soil will remain stable and just dutifully transfer heat at a given rate?

mfb

If the thermal conductivity of soil is significantly better (compared to cement), this should be a good approximation.

For a cylinder of infinite length or a half-sphere, it is possible to take the soil into account in an analytical way. For finite cylinders, a numerical approach or some approximation might help.

sday

Well after looking at this, it seems like it will be difficult to determine what the transfer will be because the difference from dry soil to solid rock is a huge variable. A 4" cement wall around the container seems as if it will actually act as some what of an insulator unless it is any but dry sand. Some type of a Poly container would allow for much more transfer.

So my current thinking is that the BTU transfer of heat from/to Earth is whatever the maximum transfer ability is of the soil you are in, which has a k value of 0.15 - 7.0. I think I'm on the right track to figuring this out.

Thanks for the feedback.
-Steve