I found this link the other day
Remember the other day when I talked about using the roof for a solar heater, but doing it with no glazing? Well this article show testing on a small scale. He has small channels for the water to flow through, but it is exposed to the air. He tried to simulate more channels by using the space between the channels and allowing water to flow there. The efficiency went up.
The more surface area the water flows across, the more efficient it becomes. But you also get more evaporation. At 2,200 btu/square foot day, you can get a lot of power. Most collectors are maybe 20 square feet and that means 44,000 btus per day put into the water. So, a 50 gallon tank with about 400 pounds of 60 F water could be raised to 110 F in about half a day. But using 1,000 square feet of roof would raise it to the same temp in about 5 to 10 minutes. My God! And it will do it at a higher efficiency than a evacuated tube would. We are talking 2.2 million BTUs per day possible.
You would probably want a small solar panel to drive two or three cheap pumps in series. That way you would have enough head pressure to get to the roof without having to buy a VERY expensive pump to do it. You don't need much flow, just enough pressure to get it to the roof. With a big insulated 150 - 300 gallon tank acting as your heat exchanger, you would only need to run the system for about 1 or 2 hours every other day. So evaporation won't be that bad. Since you are using the gutters to collect the hot water, you could also make up some water losses via rain collection. A simple diverter on the down spout can give you full control.
But rember, this type of solar collector is more efficient if the ambient air and water temperature are fairly close, like within 50 to 70 degrees different or less. So, if you wanted 140 F water and the air temperature is 70 - 90 F then you are ok. But if it were 50 F outside, then getting the water temperature above 100 - 120 F would be very hard.
I'm just blown away by how much potential energy is available on the average roof. And you don't need a lot of money to throw at the problem. And I know evaporation is an issue, but if you run the system for 1 to 2 hours a day on the sunny days, then you might lose 2 gallons a day or so. That evaporates into the environment and someday soon it will rain and you will collect it back. So it can be sustainable. Even the pump energy would be from the sun.
Also, a good source of small, sometimes free pumps can be dishwashers. They aren't meant to run all day, but they can easily run for 1 to 2 hours and they can pump hot water at 140 F as well.