rjdudek,
Heck we can even put in a number for h if you like (my old heat transfer text book uses h for convective heat transfer and k for conductive, not that it matters), 3500 W/m2oC for water flowing at 0.5 kg/s in a 2.5cm diameter tube, but that really doesn't help much for this calculation because (I believe anyhow) the overriding problem in my case was/is the resistance to heat transfer accross the plastic tubing I was using when I initially set up my loop.
q =h A (Tw-Tbulk) agreed of course
Tw being the temp of the wall, and T bulk that of the liquid at the centerline of the tubing.
If you assume that the temp of the ground does not change (admittedly not reality, but works to understand things for the moment) then most of the heat transfer resistance is directly proportional to the thickness of the tubing. This fairly well approximates what was happening in my old loop. Water made the entire trip through the loop and did not change temp significantly (q=near zero, therefore Tw nearly equal to Tbulk). Therefore all the resistance to heat transfer was either in the wall of the tubing itself, or in the dirt, or sand just outside the outer wall of the tubing. I'm pretty sure that wet soil or sand is a better conductor of heat than plastic tubing, but I might be wrong on that. In either case it doesn't matter whether that last sentence is true or not since I cannot (or will not) dig up the old line and try to improve it. It's much easier for me just to install a new, better designed line using tubing made of metal that will have a very high thermal conductivity (very low resistance to heat transfer). Then the only question is whether the heat will disperse into the ground around the cooling loop quickly enough.
But admittedly, until I've tested by new system I don't know if it will work much better than the old.
>Also remember the slower the loop velocity the better the thermal exchange is going to be.<
Well...yes and no. The convective heat transfer coefficient (h) can be quite dependent upon the flowrate of liquid through a tube. The faster the flowrate the smaller the boundary layer of water at the surface (this will be also affected by the Reynolds number, as to whether the liquid is in turbulent, or laminar flow). Calculating h can also be quite dependent upon a whole bunch of other parameters, viscosity, density, conductivity of fluid, diameter of pipe, roughness of pipe, etc. etc. As I recall you end up using different calculations with Nusselt, Prantl, and a bunch of other dimentionless numbers raised to different exponents depending upon the flow regimens you are in...
I agree of course that if you flow the water though a loop slow enough you will end up with water coming out of the loop at the same temperature as the medium it's flowing though, but that does not necessarily mean that you will remove the largest amount of heat from your tank operating at the lowest flowrate.
