Dunebilly said:
Sorry to jump into this so late, but I think the primary consideration would be the heat conduction rate of the metals involved. Since copper's rate of heat conduction is aproximately 6(six) times that of stainless steel, there is not much of a question. As far as finned conductors, these would make more sense in a water to air system, since most of the conduction is from the edge of the fins, effectively adding very little surface area in a water to water system. I have to agree with Tom, the most economical and practical system is smooth copper tube.
Heat transfer is an astonishingly complex process, and almost any first-approximation mathematical model is wrong - sometimes shockingly wrong. In a fluid-to-fluid heat exchanger, turbulence and convection are both important. Here's a way to look at it. First, a static model of a coil-in-tank system:
Imagine a hot water molecule on the inside of the pipe, at an average distance from the pipe surface - say 1/4". We need to transfer the heat from that water molecule to a cold water molecule that's an average distance from the outside ot the pipe - say 6". There are 5 thermal barriers to deal with:
1) The 1/4" of water between the hot molecule and the pipe wall.
2) The boundary layer between the water and copper (or stainless)
3) The metal of the pipe itself
4) The boundary layer on the outside of the pipe
5) the 6" of water between the outside of the pipe and the average 'cold' water molecule.
Of these, the water itself is by FAR the biggest insulator. My guess is that the boundary layers are next, and the metal pipe is last, whether it's copper or stainless.
There is another factor, of course - how much time you have before the hot molecule is circulated away.
On the outside of the pipe, this model is too simple. Still fluids naturally establish convection currents as heated fluid rises and cool fluid falls. This serves to bring fresh cooler fluid into contact with the heated surface and reduce the average distance between the hot surface and the average cool water molecule. However, there is a maximum convection velocity which is much too slow to accomplish optimum heat transfer. For that reason, anything that increases the amount of external surface area will help dramatically by bringing more cool water in contact with the heat source.
On the inside of the pipe, the static model is also too simple. For the diameters and flows that we're going to have, flow is very turbulent and water molecules are continuously bouncing around from the center to the outside. The only thing that can help here is more surface are and more time. A larger diameter pipe helps in both cases. Because the flow is already turbulent, additional turbulence enhancers probably don't make much difference.
If you wanted to get hard data, what you'd want to do is measure temps at multiple spots and look at the temperature differences:
1) fluid, center of pipe
2) fluid, at pipe wall
3) pipe wall, inside surface
4) pipe wall, outside surface
5) fluid, at outside of pipe wall
6) fluid, short distance above pipe
I suspect that you'd find virtually no difference in the first two, showing that the fluid is turbulent and well mixed. There would be a larger drop between the fluid at the pipe wall and the pipe wall itself (both inside and outside), but virtually none between the inner and outer surfaces of the pipe. The biggest drop would be the fluid at the outside pipe wall vs. fluid an inch or two away.
If I'm right, that argues for the largest diameter pipe that you can do, with fins on the outside if possible.