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I'd guess 1/2inch because there would be less water inside to heat. I'd imagine there wouldn't be TOO big of a difference between the two either. Maybe someone else can give you a more scientific detailed answer.
There are enough trade-offs that there is no practical meaning to the question, especially with such a small difference in size.
If you have a one foot by one foot square of both, side by side, they will have the same insolation and will absorb a similar amount of energy. The mass of water in the larger tubing is greater (imagine a single tube one foot in diameter as a third option for an extreme example). However, as the tubes heat to a balancing point with the surrounding atmosphere, more heat will be re-radiated from the smaller tubing. Additionally, the thickness and insulative qualities of the tubing are not specified. Larger tubing sizes are commonly thicker, and tubing in a particular size may vary in thickness based upon material and pressure requirements. The type of tubing also makes a difference. Black anodized copper has different characteristics than black poly.
For boilers they use a domestic hot water coil that is finned copper tubing. I'd imagine it would be quite applicable here assuming you have enough heat. Couldn't you just use an old car radiator?
Thanks to all who replied. I am a novice at all this. What I was trying decide was which one to use for an inexpensive diy solar water heater for my pool. I used poly tubing 500 ft of 1/2" on my roof. It works good. Yesterday the temp here was 73º and it raised the temp enough to tell a difference from in to out. Ah, but today the temp only got to 46º so i didn't try it.
Although there is a difference of the amount of water in the pipe, there is also a difference in exposed surface of the pipe. There would be negligable difference. More importantly and something many don't consider, is the flow rate of the water in the tube. If it is too fast it will not transfer the heat efficiently. Placing these tubes in an efficient cabinet will increase transfer by many times.
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