Passively safe solar hot water

Kragen Javier Sitaker, 2012-10-15 (updated 2012-10-16) (6 minutes)

Suppose we want a solar hot-water-heating panel to never heat above 49 degrees under normal circumstances, so that the water it heats never becomes dangerously hot. "Normal circumstances" might involve a temperature of, say, 35 degrees outdoors. One way to do this would be to have a thermal resistance between the panel and the environment that allows a heat flux equivalent to the absorbed sunlight once there's a 14-kelvin difference: given, say, 800 watts per square meter, you need a U-factor of 800 watts/14 kelvin square meters, or an R value of 14 kelvin m²/800 W, or R = 0.018 K m² / W; that's about equivalent to an inch of concrete. However, typical outdoor air film values are around R = 0.03 K m² / W --- on each side, so 0.015 on both sides together.

If that wasn't enough thermal conductance, you could reduce the sunlight by angling the panels or painting them gray or shading them or whatever so that they only collect 400 W/m² or something, and then you should be fine. But there's another problem, which is that that 14-kelvin difference above ambient is still a 14-kelvin difference above ambient when ambient drops to 0 degrees, which will give you 14-degree "hot" water.

That's not really acceptable! To have a passively safe design that still provides adequate heat in winter, you need some kind of more consistent heat sink than the air. Maybe radiating to the sky could work: you use some insulation to keep from losing heat to the nearby air, and radiate your extra heat as infrared into deep space.

For this, you would have enough insulation to permit the difference from ambient air to be up to 50 degrees or so (R = 0.06 K m² / W, which should be achievable with nothing more than some trapped air spaces) while permitting infrared radiation to get to space, in particular around the ten-micron wavelength. Transparent polyethylene film trapping air spaces will apparently work for this (see patent http://www.google.com/patents/US5493126), but it photodegrades rapidly enough that it would need replacement every few months. Acrylic (plexiglass) transmits near infrared; I think it transmits thermal infrared (LWIR) as well, but I haven't tested. FT-IR spectra on the web for polyethylene terephthalate http://deepblue.lib.umich.edu/handle/2027.42/32476 suggest that it, too, transmits LWIR well, and it can survive solar ultraviolet for a long time.

Anyway, then, you just need to angle the panel so that it will be sufficiently coupled to the part of the sky that doesn't have the sun in it to shed the heat it acquires from the sun.

A nice thing about this kind of radiative cooling is that the power transmitted is proportional to the fourth power of the temperature. So if you're transmitting 800 W/m² at 49 degrees (322 K), at 43 degrees (316 K) you'll be transmitting 740 W/m², and at 30 degrees (303 K) you'll only be transmitting 627 W/m² --- you'll have a whole 173 W/m² pushing you toward your target temperature. Unfortunately this is still not enough to be very robust against efficiency losses in picking up the heat. arccos(627/800) is about 38 degrees (of arc!), and arccos(740/800) is only 22 degrees --- so whenever the sun is further than 22 degrees from at right angles to the panel, it won't be able to heat the water above 43 degrees C. Which means, at best, 3 hours a day.

But that's for a flat panel! If the collector isn't flat (for example, if it consists of multiple flat panels at different angles), it will absorb heat from the sun at a more consistent rate throughout the day. That solves the intermittency angle problem. (The requirement that the thermal emission equal the sunlight at the maximum safe temperature can be met, as before, by adjusting the angle of attack to the sunlight.)

The big problem with that approach is its low efficiency. Heating from 0 degrees to 43 degrees, you start off with about 48% efficiency (1-(273/322)^4) but end up with 7% efficiency (1-(316/322)^4). That means you end up with panels covering many times more area, for safety, than you would need simply to gather the appropriate amount of energy, simply because the vast majority of the energy gathered is re-radiated immediately.

There might be a way to avoid this problem: creating a sufficiently selective surface. Blackbody radiation has a fairly sharp cutoff at its top frequency, and absorption bands in plastics also have fairly sharp cutoffs. It might be possible to put together a blend of transparent plastics that block essentially all radiation longer than, say, 8000 nanometers, but have one or two orders of magnitude more transmissivity for shorter wavelengths. A black surface covered with such plastics would have an emissivity that jumped sharply (from, say, 0.001 up to 0.1 or 0.2) upon reaching a target temperature. A sufficiently large radiator of such a surface, backed by sufficiently good heat transport, would maintain a narrow range of temperatures over a wide range of heat flows.

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