Love some early morning calcs. Overall heat transfer coefficient with pipesize in this application is estimated at:
22mm : 1105 W/m2/°C
15mm : 1492 W/m2/°C
10mm : 1726 W/m2/°C
However as you can see these are per unit of surface area and smaller pipes have less area per meter of pipe length. Assuming a 30 degree average temperature difference from hot side to cold side (ie coil at 70°C and hot tub at 40°C) the heat input per meter of pipe works out at:
22mm : 2.2kw
15mm : 2.1kw
10mm : 1.6kw
The original 3m of 22mm would equate to 6.6kw of heat input, to achieve this same heat input you would need 3.3m of 15mm pipe and 4.3m of 10mm pipe. The two caveats for 10mm pipe are:
- At 4.3m of length you could struggle with flowrate through the pipe, and you would be better with to 2.15mm lengths in parallel rather than one long lenth
- 10mm pipe has little structural strength and you would need to protect this from someone leaning on it etc!
A coil of 22mm pipe will also look pretty cool, IMHO, so there is the aesthetics to consider.