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Posted by Morris Dovey on October 14, 2009, 6:47 pm
Robert Scott wrote:


Excellent observation! The behavior will be strongly affected by the
particular geometry used...

A 180 groove (which isn't really a groove at all, but represents one
extreme fairly well) will both reflect and re-radiate a large portion of
the incident energy.

The number of reflections is determined by dividing 180 by the groove's
interior angle, and the only limit on "smallness" of the interior angle
is production technology. For sake of discussion let's consider the
opposite extreme to be 1.

With a 1 interior angle we get 180 reflections, which should result in
some fairly awesome absorption - but look what else happens...

[1] Since re-radiation from the surface is omni-directional, nearly all
of the re-radiated energy will be directed toward the other side of the
groove, and very little will be directed outside the groove.

[2] Although the initial reflections will be distributed more or less
equally across the width of the groove, the subsequent reflections will
take place progressively deeper in the groove, with the largest number
of reflections closest to the "bottom" - and so with the shortest path
to the collection media.

[3] If the collection takes place in an atmospheric environment (as
opposed to vacuum), there should be a maximally "helpful" boundary layer
(actually a /pair/ of overlapping/intersecting layers) to inhibit
convective losses.

I think the interior angle and depth of the groove will determine how
pronounced each of these effects actually is.

For me, the easiest way will be to build two troughs and equip one with
a plain tube and one with a grooved tube - and then take temperature
measurements of the inside of each tube. Once that's done, I'll swap the
tubes and do it again to reconcile reflector differences. It's a "poor
man" solution, but I think it'll do for my purposes.

It's important to keep in mind that only the boundary layer effect is
dependent on groove scale. If length of the conduction path is a
significant factor, it can be dealt with by making the grooves less deep
(consider a surface with grooves only 0.001 mm deep... :) )


I'm hoping to be able to machine 10 grooves to capture (a guesstimated)
95% of a (calculated) 115-sun intensity, so I'd still be looking at 5-6
suns worth of radiation... I think I'd better stick with my cheap little
IR thermometer. :)

This method is (I think) only practical for concentrating collectors.
There is at least one method of achieving the same kind of efficiencies
for air and water flat panel collectors that doesn't involve anywhere
near the same production cost.

Morris Dovey
DeSoto Solar
DeSoto, Iowa USA

Posted by Robert Scott on October 14, 2009, 8:21 pm

If you are using angle of incidence = angle of reflection, then I think you are
talking about a mirror finish.  A typical flat black paint will "reflect" is
just about every direction at once, regardless of the angle of incidence.  Of
course more light will reflect at the "mirror angle", but a significant amount
of light will go straight back at the sun, unless you have a mirrored surface.
So talking about "capturing" all those reflections is a little unrealistic.

Also, there is little advantage to having more than a few "reflections".  If
your surface is nice and black, it will retain at least 80% of the energy on
every reflection.  So after 2 reflections, only 4% of the energy remains as
light.  After 3 reflections, it is down to 0.8%, and after 4 reflections, only
0.16% of the original incident energy is still bouncing around as light.  So why
bother talking about 180 reflections when there is essentially nothing left to
collect after 4 reflections?

So you already realize that this reflection is not mirror-like.

Again, number of reflections means nothing without taking into account how much
is still left.  I think most of heat will be deposited near the peaks - because
they have a clearer view of the sun than those deep valleys.

But grooves only 0.001 mm deep mean that peaks are only 0.0001 mm wide, and the
heat has to travel down those peaks.

I don't know where you get the 5-6 suns.  Through one square meter there is only
1366 watts of solar energy - no matter how you choose to collect it.  Unless the
5-6 suns is the result of concentrators - in which case the effective apperature
of the collector is increased by those concentrators, not by the grooved target.

Robert Scott
Ypsilanti, Michigan

Posted by Morris Dovey on October 14, 2009, 9:36 pm
 Robert Scott wrote:

I agree, which is why I presented it as an extremity.


"Black" would be the result of no reflections or re-radiation
whatsoever. I assumed bare metal with no coatings at all, which (in my
admittedly limited experience) doesn't exhibit that behavior.

Check the second photo at


Why bother to talk about it? Because I wished to choose /some/ boundary
condition, and that was convenient.

I do, and I also understand that even with mirrors there is no perfect
reflecting surface.

Ah, I'm afraid I must not have made clear that this absorber is intended
to be located at the focus of a concentrating collector, and you must
have missed the last drawing on the web page which shows how the problem
you cite doesn't exist. Sorry.

Exactly so, shall we shorten them still more?





Well my trough is 44" wide and focuses the incident light to a region
3/8" wide. Dividing 44 by 3/8 yields a concentration ratio of ~117. The
mirror will eat a small amount of that, so lets say that the intensity
of the light at the absorber is only 115-suns. If the absorber slurps up
the 95% calculated, then 5% of 115-suns is 5.75-suns, which actually
does fall into the 5-6 suns range. :)

If you'd like a look at the trough in question, there're photos at


I'm not discussing the aperture, only the efficiency of the /absorber/.

Morris Dovey
DeSoto Solar
DeSoto, Iowa USA

Posted by Bruce Richmond on October 15, 2009, 4:34 am
Accordint to your calculator program it should get about 85%.  How are
you getting 95%?

Good to see you have come up with a way to make a tube.  If you wanted
to try a finer pitch, like 4 deg included angle, the shop I work at
has wire EDM machines.  The wire is .010" thick and can cut any shape
under CNC control.

The choice of aluminum is good for heat transfer.

Posted by Morris Dovey on October 15, 2009, 10:28 am
 Bruce Richmond wrote:

I used an absorption rate of 15% - I think the actual rate may be as
high as 20% so I split the difference between that and my original
(conservative) program default rate of 10%. The truth of the matter is
that until I can produce some actual test results, I won't really have
anything more than a guesstimate.

[ The 'angle' program allows entering a (percentage) absorption rate as
a command line parameter - and if none is entered it uses a default rate
of 10%. Once an angle has been decided upon, the 'grooves' program will
provide all of the production geometry. ]

Let's talk off-group about what's reasonably possible and about cost. I
need to do some preliminary testing with whatever I can manage myself,
but I'd really like to find out what's possible with real tooling.

Your mention of a 4 included angle has me drooling. As Rob Scott
pointed out, that may be well beyond the point of diminishing returns -
but even so, actual test data could not only confirm that, but allow
accurate performance prediction.

It'd also be good to know about other metals and alloys for applications
involving the higher pressures Axel mentioned.

Let's talk.

Morris Dovey
DeSoto Solar
DeSoto, Iowa USA

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