Richard, I am amazed at this. You are usually SO good at the science, but this is just flat-out wrong. It SEEMS to make sense that the water needs to heat up, and if it goes too fast it won't, but it's still wrong. It simply violates the laws of themodynamics. It's all about fluids.
Think about it: If your statement is true, then on a windy day, the BEST way to stay warm would be to open your coat...the air whistling past you wouldn't have time to get warm from your body and bleed off that heat.
You are right that more heat will transfer from your fixed body to a moving fluid (air) if the fluid is moving faster (and is at lower temperature). However, the effect in a solar panel is not the same as with your body because the heat removed from the solar panel by the moving water lowers the panel's temperature, which lowers the amount of this increase of heat transfer (more flow DOES give more heat transfer, but this increase is less and less as you go to higher flow rates -- i.e. diminishing returns). This is why the efficiency chart in this link is the shape that it is (essentially a log curve). Your body is different because it attempts to maintain its temperature by speeding up metabolism, but if your body's temperature dropped to the same as the wind temperature, then all the wind in the world won't lower your temperature any more.
But obviously, that is NOT true--the faster the wind moves past you, the more heat it sucks out--it's called "Wind Chill Factor" and you freeze your ka-loonies. This is JUST as true of the fluid in your solar panels--the faster it moves through the system the more heat it sucks out. Ideally, your panels on a hot, hot summer day should not be any hotter than your pool water.
Refer to this chart showing the Wind Chill Factor. This shows the point you are making that higher wind transfers heat at a faster rate. Again, this is true IF the temperature of the object you are getting heat from does not change. This is not true with a solar panel. The faster water movement transfers heat faster which lowers the temperature of the panel so that limits the improvement of heat transfer. The net effect is the log curve that never quite gets to 100%. So while it is true that pumping more water will get more heat out of the panel, the amount of incremental increase quickly becomes small and increasingly smaller at higher flow rates. At 4 GPM you already get 80% of the total amount of possible heat you could get. At 8 GPM you get around 90% (not shown on the graph, but extrapolated). It would take an infinite flow rate to achieve 100% efficiency, but who cares? You can't get more energy out of the panel than is being given to it by the sun. If you get 90% of it at 8 GPM, then that is plenty. It's not worth all the problems of higher flow rates with their extra losses in friction through the pipes and cost of electricity for pumps to try and get much more than that.
Remember: Your solar panels are mechanically IDENTICAL to a car's radiator. In fact, if your pool is too hot, you run the panels at night to cool it. In a radiator, if you are idling in a traffic jam on a hot summer's day, your car overheats. You get moving, it cools down. The MORE fluid (air) passes accross the radiator, the more it cools down--faster is better. Do not mistake temperature for BTUs. It's BTU quantity that heats your pool. The more BTUs you can get into the water in a given amount of time, the faster the water heats up!
Faster is better, but the returns are diminishing. At some point, going faster doesn't cool that much faster because the water in the radiator can't get cooled lower than the air temperature. Or put another way, if the air temperature were the same as your engine, then all the wind in the world isn't going to cool your car.
Why? Well a British Thermal Unit is the amount of heat energy necessary to heat one pound of water one degree farenheit. That's the WHOLE secret to why more flow is better. More heat energy, not more temperature. I'd MUCH rather have 10 gallons/minute of water 1 degree warmer than my pool than 1 gallon every 10 minutes that's 10 degrees warmer--my pool will heat up 10 times faster because it's moving 10x the BTUs.
Again, you are talking about the efficiency curve and yes it is much better to have faster flow, especially initially since it increases the heat transfer rate so quickly. But again, the returns are diminishing as you approach 100% efficiency. At 4 GPM you are already extracting out 80% of the heat that there is to extract (i.e. the sun's energy that hits the panel) and at 8 GPM you are extracting out 90%. I don't disagree that 16 GPM through the panel might extract an extra 5%, but the pressure required to do so would exceed the recommendation for the panel (you mention that below) and be more costly throughout the system.
So I split the system into 2 halves of 15 panels each. You can see the Tee in the picture. Each 15 panel half can flow FAR more water than the 30 panel whole because its resistance is half of what it was. And, with two halves, that higher flow is DOUBLED for the same 30 panels (now 15 and 15 in parallel to each other). The result? The last two seasons my pool heats up far, far faster than it used to.
Most solar systems are plumbed to be in parallel, not in series. This is consistent with what you are saying in terms of optimizing water flow. With a solar panel that has a maximum of 8 GPM, you clearly must go in parallel to get to higher overall flow rates (for the system, not per panel). Why is your solar system in series at all? Why aren't ALL of the panels in parallel? Well, maybe not all because then you would need 30x4=120 GPM in your system, but MOST of the panels should be in parallel -- two banks of 15 where the 15 are in parallel and the two banks are in series (60 GPM for system, 4 GPM per panel). To equalize flow (in a bank of parallel panels), you have to make the path length for the water equal for all panels, but that is easy to do by routing connecting all panel bottoms and tops to each other (i.e. everything is in parallel), and then have the input go into the first panel and take the water coming out of the panels from the very last panel (which has a long pipe run to get back to where the first panel is placed).
Here's a diagram to show you what I mean (and similar to how my solar system is hooked up, except the roof isn't so straight). You can see how the total path length for water going through any of the panels is the same (this makes the flow rate equal in all panels). All water comes from the lower left and moves to the right, then goes up one of the panels, then continues to move right to the end, then turns around and comes all the way back.
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Of course, since each 15 panel half has half the surface area it's maximum BTU capability is half. But I've doubled the flow rate for the same surface area and the result is my pool heats up far faster. 3 or 4 degrees a day is now 6 to 8 degrees. I'm getting more BTUs into my water.
I agree that you want more flow rate through each panel, but again, the returns are diminishing. If your panels were truly in series, then the flow rate could have been so slow that you were in the lower left area of the efficiency curve so it's not surprising that your efficiency went way up splitting into two.
The efficiency ratings of solar panels require a little different analysis--the loss of efficiency is due to back-pressure (friction), not the water moving "too fast to heat up".
No, it's the exact opposite. If you look at the link for the FAFCO panels, you will notice the expected increase in pressure loss at higher GPM (it varies as the square of the GPM), but higher GPM results in higher efficiency. If you are saying that the slowdown in efficiency is due to this back-pressure, that is only partially true. Even if there were no friction at all, you would still end up with an efficiency curve that looked similar because faster and faster speeds simply cannot pull more heat from the sun than the sun is delivering to the panel. Again, though the percentage efficiency increases, the returns are diminishing so that in absolute terms of amount of heat gained through faster flow, it's vanishingly small at higher rates.