Enclosing a solar panel that is already at 80-90% efficiency in a "greenhouse" of glass will not improve the efficiency or generate more heat. Essentially, the water flowing through the panel pulls nearly all of the energy hitting it from the sun and the panel as well as the air near it in the "greenhouse" will remain cool. Yes, I know that Carl doesn't think that my FAFCO panels are that efficient and he may be right, but more on that later -- just hang with me on this assuming that the panels are operating efficiently.
There will be a benefit with regard to cutting down heat LOSSES if the air temperature is cooler than the water temperature, especially if there is wind.
The reason that solar hot water heaters are enclosed in the "greenhouse" style of glass is precisely for the reason of preventing heat LOSS, not for capturing more energy. Hot water is hotter than typical air temperatures so it is important to keep the temperature around the panels as hot as the water. Insulated multi-pane glass would ideally allow most of the sun's energy through but would prevent heat loss by keeping the temperature of the air around the panels to be the same as the water flowing in the panels.
[EDIT] It might make sense to use the "greenhouse" style for heating spa water since that is so much hotter than air (usually). I've never heard of solar used for spa heating and the raw panels are only specified to go up to around 90F though I can get my pool to around 92F if I don't tell the thermostat not to do that. I don't see why a hot-water solar "greenhouse" style panel couldn't be used for spa water though multiple panels would likely be needed since the spa has more volume (around 300-600 gallons) than a hot water heater (around 50-100 gallons) [END-EDIT]
Essentially, you need to look at this as if there is a limited amount of energy from the sun hitting a square area on the Earth so the best way to capture more of that energy is to have a larger area of panels. This assumes that you are already at high efficiency (80%-90%), which the flat "tube" panels have if you are at their recommended flow rates of 4-8 GPM. The "floor tile" types of solar heating, like the one that Carl has, are apparently not operating near peak efficiency since increasing flow rates in his system (by his splitting into two parallel systems) increased the heat dramatically (and probably cooled the tiles down as well).
Carl, I agree with you that the panels in my solar system should be cool to the touch even on a blistering hot day. If they are not, then they are not at 80%-90% efficiency. This summer, I'll go up to the roof to see if the panels are cool. They are connected in parallel, not in series, and right now have a flow rate of around 5.5 GPM so theoretically should be above 80% efficiency. I've never seen "steam" or "hot air wigglies" coming from the panels, but I'll go up and feel them on a hot day just to see how efficient they truly are. Though I wouldn't normally trust a manufacturer's specs, I worked with the FAFCO folks when I was getting an MBA in college and they seemed to have integrity, but then again that was over 23 years ago so there may be new players.
By the way, my diagram was supposed to show PARALLEL panels with all bottoms of the panel piped together and all tops piped together. I'm sorry if my drawing didn't make that clear. The water (as if you are sitting on a water molecule) flows through the bottom pipe, up ONE of the panels, then through the top pipe.
Just for the heck of it, let's calculate the maximum amount of possible solar heating capability based on the energy from the sun. The amount of solar radiation reaching the Earth's surface with the sun directly overhead (so noontime summer in northern latitudes) is around 1000 Watts per square meter of area on the Earth which is about 93 Watts per square foot (or 317 BTU/hour per square foot). You simply won't get more energy than that no matter what you do. Interestingly, the FAFCO documentation at this link claims over 1000 BTU per square foot, but that isn't BTU/hour so is equivalent to around 3-4 equivalent "peak" hours (in Florida, by the way) so they are quoting a daily BTU rate. Let's see what happens if we assume the manufacturer FAFCO is right about 80% efficiency at 4 GPM. They essentially are claiming that they are heating my pool water at 800 Watts per square meter. My 12 panels have a mixture of sizes, but the total area is 36.74 square meters (effective area). So in theory, they claim that I am getting, at noontime peak during the summer, 29,400 Watts (almost 30 killowatts) which is about 100,000 BTU/hour (about half of the 200,000 BTU/hour of my gas heater's output) and is also equivalent to 25.3 million calories per hour. 1 calorie raises 1 ml of water 1 degree Celsius. My pool is 16,000 gallons or 60.6 million millilters so that means I should expect a peak temperature increase of 0.4 degrees Celsius per hour or 0.75 degrees Fahrenheit per hour.
I have measured the temperature rise in my pool with the solar on and I would say that APPROXIMATELY this peak temperature rise is about right. It is not, of course, a super-accurate measurement, but I would usually see about a 3 degree increase over 4 hours near noontime in June. The pool loses about 2 degrees overnight in the summer (remember that we try to keep it at 88F and have an opaque cover) and the solar typically clicks on around 10 AM (the pump starts at 9 so the solar turns on when the solar panels are warmer than the pool water) and by 1 PM or 2 PM at the latest, the pool is back to its lovely 88F. So I'm pretty certain that the panels are at least over 50% efficiency if not close to their 80%. My actual flow is more than the 4 GPM (it's closer to 5.5 GPM) so my efficiency should be higher (about 84%), but I've got the piping problem I mentioned in an earlier post that is likely causing "low flow" to three of the panels. And you are right that I should shoot for 8 GPM and 90% efficiency if I want to heat my pool a little faster -- I just need to balance that with the tradeoff of pump electricity costs.
Richard

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