Re: Temperature calculation for parabolic solar mirrors


"Efthimios" <eangelopoulos@xxxxxxxxx> wrote in message news:474f3787-6cb7-4439-b947-1a32bec82aad@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Does any of you know how to calculate the temperature that a solar
parabolic mirror can rise at the focal point?

Efthmios

Hi Efthmios

First some background :
A parabolic dish aimed at the sun on a clear day will receive about 1000 W power per m^2.
Focal point of a parabolic dish can be as small as the dish of the sun seen from Earth. So it's actually a focal 'area'.
More accurately, the maximum concentration factor of a well made parabolic dish is about 1/sin(phi) where phi is the half-angle of
the dish of the sun as seen from Earth (about 1/4 of a degree). This makes the maximum solar concentration about 230. That means
that your collector (the focal point) has an area of about 1/230th the area of your mirror.
In other words, a parabolic concentrator focal area will obtain 230 kW/m^2 power.

How hot can this get ?
If you do not drain any energy from the collector, and you eliminate convection (by mounting the collector in a vacuum flask or so)
then a perfectly black collector can theoretically get as hot as the surface of the sun (5 778 K). At that point, the collector
reaches radiation equilibrium : it radiates the same amount of energy that it receives. Installing IR filters has no use there,
since the collector is at the same temp as the sun, so follows the same black-body radiation curve.

For power generation, you do not want that high temperature, since radiation losses are so high. But you don't want it too low
either, since you will hit the Carnot limit badly.
Realistic solar thermal plants therefor are designed for temperatures in the range of 800-1200 K. This puts the collector radiation
peak in Infrared, so that radiation losses can be limited by installing a IR-reflective surface on the collector.

So there you have it. A bird's eye overview of solar concentration and temperatures reached.

Rob


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