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# Solar heating and perceived temperature Answered

We've had an interesting discussion spanning several months on the efficacy of this instructable's approach to heating:

https://www.instructables.com/id/Foil-Solar-Panels-for-Windows-VERY-Easy/

The conversation has gone long and isn't really that appropriate for the comments there so I've moved it here.

Summary: The approach described in the instructable is to create a thin metal panel that hangs inside of one's window, which is heated by the sun's radiant energy. Convection then carries the hot air next to the panel up and circulates it within the room. The question is whether this approach provides a warmer perceived environment than simply letting the light into the room.

As I see it, the question has two components. First, which one nets more heat energy inside the room? For an average room, the light will be scattered many times before a tiny fraction reflects back out the window. A flat foil panel as described in the instructable would have to be extremely absorptive to match this level of energy capture, because it gets only one bounce for its capture and also must capture the heat in an extremely small thermal mass. For this part of the question, not having a panel seems the likely win.

The second part of the the question is more complicated. What is the perceived temperature in the room, given differences between convection heating of the air versus radiative heating of objects and surfaces in the room? On this count I'm unsure, but it seems that radiative heat contributes more to human comfort (see this Wikipedia article: http://en.wikipedia.org/wiki/Mean_radiant_temperature). If that's true, the panels lose again.

Discuss!

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## 16 Replies

Kiteman (author)2011-09-27

Firstly, if you're hanging the panels inside, a single dark panel would be just as effective.

As to the point of your question, more light will be absorbed if the sunlight is allowed to simply shine into the room and strike furniture and carpets, but less will be felt in the room.

The heat will be absorbed by the bulk of the furniture, conducted into the floor etc, plus the floor is not a good shape for transferring heat to the air - a vertical surface will heat the air by conduction, and warmed air moves out of the way by convection, allowing more air to be heated. It's a lot harder to establish a convection current over a flat surface.

The better you transfer the heat to the air, the better it is felt by you.

nagutron (author)2011-09-27

Regarding the panel, it'd have to be really dark is my point. Let's say it captured 90% of the heat energy, while average "stuff" captured 20%. At ten reflections of "stuff" you'd get parity with the one reflection for the panel. If you think of the number of reflections you'd get in a room full of objects, you can easily imagine more than ten. Maybe hundreds.

This would need to be confirmed by experiment, though. I think you could do it by simply having an infrared camera pointed at the window in question, with and without the panel. Sampling from a large number of angles should give you an answer.

As for the second part of the question, I'm making the point that radiative heat can actually be _more_ important to the perception of temperature than the conduction of the heat in air. Meaning that warm couch and floor might actually make you feel warmer even if the air in between is cold. That's how campfires work, after all. I'm not sure, though: check that wikipedia link and tell me what you think.

slysimon (author)2011-09-27

Very interesting. But won't the foil panels, that will get hotter than the walls and the floor, also produce a lot of radiant heat?

:0)

I do like your idea of experimenting with an infrared camera. Good lateral thinking there.

nagutron (author)2011-09-27

Yes, definitely. The question is the proportion of the total energy that is converted to radiant heat coming from all the room's surfaces versus conductive heat in the room's air. At most times, the panel favors the conductive heat (because it is efficient and convecting air across its surface and because it has low thermal mass -- it would get nastily hot otherwise). On the other hand, the plain room will generally favor radiative heat in comparison.

Which one is more important? The wikipedia article I linked to might indicate that the radiative heat is more important, but I'm not sure and Physika makes a good point in a parallel thread that the total amount is probably quite low, so I'm not sure.

slysimon (author)2011-09-27

Yeah, I read the article and thought, radiant heat is more impotant than I thought. I then re-read it and thought, well maybe not.

I stand by my comments on the other thread that this is not simple. I think it could only reasonably be settled with lots of experimentation.

Personally I think the screens could make a percievable positive difference in a small, not well insulated room. I'm not so sure it would be as effective in a large well insulated one.

Physika (author)2011-09-27

I think that by 'simple' trebuchet03 really meant that it is that the principles governing the systems are well understood, and the correct answers can be arrived at by applying these concepts....that we don't have to guess and experiment. I agree with that premise, but think that to do the correct mental simulation of the whole system can be a bit beyond just understanding the basics of heat transfer, which is what makes it fun to discuss.

I read the article too referred to by nagutron (the wiki article on thermal comfort is perhaps even more useful for this discussion). The thermal comfort article states that air temperature and mean radiant temperature are both important factors for the perception of comfort, but does not rank or weight them explicitly. It hints, I think, that some of the underlying studies may do so. Unless we have some info like that, I don't think we can answer the comfort question well. Thanks for that ref, by the way, nagutron.

I suspect that there will be a perceived benefit to the panel because it heats air more locally, which will feel good, and that it deposits the heat more of the heat into the air rather than into solid objects. I also think that this increase in comfort would be more than offset by darkening the window. Since many people in the original instructable discussion forum believe that they are trading the light for all this free heat, they might see it as a worthwhile tradeoff. For those of us who understand a bit about heat transfer physics, we see it as darkening the room for a small and maybe non-existent comfort benefit, with negligible impact on heating costs.

slysimon (author)2011-09-27

I agree that you can estimate the panels affectiveness using 'simple', well understood principles. For trebuchet03 to dismiss the idea out of hand based on his understanding of a few principals without even offering that mathematical estimate for all to see, and doing so as vehimently as he did, especially when it is claimed by the poster of the instructable that a difference is felt and heating bills lowered, I find to be not very scientific and more than a little insulting.
Indeed, to provide an accurate estimate a very complicated model would be needed, as indicated in my other post, even taking into consideration how many times the toilet is flushed. To then work out if exactly where a number of criteria may lie where the panels would cease to be affective would be more complicated still.
I still think experimentation is a valid way to go. The principals of Physics are well understood, but even large manufacturers with huge R&D budgets will often go down the route of experimentation when designing a prototype, using mathematical models as a starting point.

Physika (author)2011-09-28

Yes, estimating a home's net heat consumption to the accuracy you describe would be quite a daunting task! I don't think many people or even corporate labs would attempt to do that. Too much variability in input parameters. And even variability just in weather conditions like wind and humidity. If the wind is blowing more, you will lose a bit more heat out your windows, for instance, because you transfer heat more effectively off the outside surface of the window....and it would affect air infiltration....what a mess......easier to stick to spherical cows.....

I think trebuchet's response was not entirely directed at you as much as the people dismissing the scientific analysis...he was very vocal early on in that discussion trying to convince people that the panels were not generating free heat that would not have been generated with an open window shade. The 'simple' part he was referring to was probably just the baseline question of whether the panel contributes net heat to the house....and you already agreed with that point anyway. Maybe I am just sympathetic because I saw him incur quite a bit of abuse from the folks who wanted to believe that the panel will significantly lower heating bills.

By the way, if you are interested in a fantastic web resource for cool things Do-it-yourself people are up to in solar and other green stuff, check out www.builditsolar.com. I have spent many hours on that site! A lot of links to DIY projects done by people with both good DIY skills and solid engineering background.

slysimon (author)2011-09-28

Okay, my bad. I do tend to play Devils Advocate rather too much. I do think that some of the principals he was stating were incorrect, or maybe just incorrectly stated, but I would agree that scientific principals on the whole should not be dismissed and that the net heat gain will not be increased with the addition of the panels, possibly lessened by a small amount. Whether or not they would work to increase the level of comfort I believe is open to debate.

I'll take a look at the link you kindly posted.

Physika (author)2011-09-27

Thanks for starting this forum, nagutron.

First, minor point I have is that most 'stuff' captures quite a bit more than 20% of the energy...probably in the 50-70% range. As an example, shiny aluminum foil reflects about 88% of the light energy....dull foil 80% (according the the Wiki article I just looked up). You have to work pretty hard to absorb as little as 20%. So you only get a small number of reflections before the energy is almost entirely absorbed. I agree with earlier assessments that more light is reflected out the window with the panel than it is with a fully-opened shade. I have an idea for how to estimate what is reflected out the window, if anyone is interested.

Next point: in the no-panel case, other than the area that is getting direct light incident on it, we are talking about very very small temperature increases, spread over a large area of the room (expecting someone to chime in with T^4 dependence here....). So I don't think there will be any perceptible change due to radiative heat transfer, other than perhaps from the region that is in direct incidence. I would expect that the primary difference in comfort would be just a matter of heating the air more now with the panel, vs depositing more of it into objects for future release.

kelseymh (author)2011-09-27

On your first point, you seem to have confused "reflect" with "absorb," and in fact your quoted numbers exactly support Nagutron's point. A material which reflects 88% is only absorbing 12%, which is less than 20%. Anything which you can see, and which has color, is clearly reflecting most of the light which hits it, not absorbing.

Nagutron is pointing out that light in a room undergoes many reflections, being very slightly absorbed at each one. Eventually, any given bit of light will be fully absorbed somewhere (if you multiply enough numbers less than 1 together, you eventually get to zero). To have a single panel of material reproduce that, it must be almost perfectly (100%) absorbing, and then it has to reradiate all that energy purely as heat (i.e., no visible glow).

Physika (author)2011-09-27

Hi kelseymh,

I didn't confuse 'reflect' and 'absorb'....I just wrote it in a very unclear manner, and realized it after I hit 'post.' I switched from talking about reflectance to absorption in one breadth. Let me try to do it better.

My point was that aluminum foil is a very reflective surface compared to most objects, such as fabric, or even white paint (speculation). If dull foil has an absorption as high as 20%, then most things are going to have an absorption quite a bit higher than that. I think dull foil is still a lot more reflective than most things.

I am actually agreeing with the point that the light is all absorbed after multiple reflections, but emphasizing that it takes very few reflections off ordinary objects to absorb most all of the light. So, yes, I agree, a panel has little chance of competing against that in terms of absorption.

kelseymh (author)2011-09-27

Thanks for the clarification! I think that we all agree :-)

nagutron (author)2011-09-27

Yup, all in violent agreement :) Physika was calling my estimate conservative, which I think he's right about. I wanted to make sure the argument made sense even with those numbers.

Physika, interested to hear what your method for testing reflected light energy would be.

Physika (author)2011-09-27

Yes, I think a bunch of us who already agree came to this forum. We either need to get some people with fresh views in here or dig to another layer nuance until we disagree ;)

I was actually not talking about testing reflected light, but estimating the light reflected back out the window, using some 'reasonable' assumptions. I think a reasonable approximation is to assume that light hitting these rough surfaces is reflected equally in all directions, over a half sphere. If it wasn't, it should look brighter from some angles than it does from others, such as on a polished floor. I am assuming the surface is not a polished floor, though if it is, I think the estimate for light absorbed by the room goes up because less bounces back out the window from the first reflection.

So if we set up a thought experiment with a 2 meter squared window (pretty large), with the center of the incident light beam about 2 meters from the wall (winter day in north-ish part of U.S.), then to first approximation we might just calculate the solid angle of the window as if it were all at a 2 meter radial distance from the light and divide by 2*pi (solid angle of half sphere). This is approximate because I don't want to bother going to the next layer of math to improve the accuracy....in danger of 'assuming a spherical cow' here....but anyway, if we forge ahead, then we say the window takes up about 15% of the solid angle. If the reflectance of the floor is 50%, then we actually have about 7-8% of the light going back out the window from the first reflection. I think the next order of approximation, taking into account that some of the beam is closer to the window, would increase this estimate. So maybe it is not crazy to think that the panel absorbs as much light as one would get with a fully-opened window shade. It makes a big difference just what the nature of the floor surface is, of course...

This is really at a nuance level, though....I only go here because we seem to agree on the main points.

Physika (author)2011-09-28

Here is a good challenge for the technical crowd. If you look through the original discussion, there are a couple of really interesting posts from Spiraling Homesteader, who tried to do an experiment with some measure of control. Here is his post, copied and pasted:

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FWIW - I have an unheated room, attached to my less than optimally insulated house.
I've insulated the unheated room with radiant barrier and fiberglass as much as the structure will allow.
The discussion here about windows already producing their maximum heat energy is similar to the discussion regarding an exterior passive solar device using window screen material.
So - to dispeel some of this argument, I've been conducting an expirement - (with many variables that make it difficult to emulate and duplicate).
The house's thermostat has been set at a steady temp throughout this time period - 72F.
The door to the unheated room has been closed overnight, allowing a constant morning temperature, within 3 degrees (+/- 1.5).
Outdoor temps have ranged from single digits to 20's F.
I have placed the window sreen for just 1 of the windows - (SSE facing) in a manner similar to the exterior passive solar collector). It is about 75% gray, vs black.
Cloudy days see no temperature change in the room (semi vaulted ceiling, from 7' to 10').
Sunny days, even with single digits outside, see a temperature increase of 8 degrees within 90 minutes of the sun striking the window. This is from 50 (+/- 3) to 58 (+/- 2).
I have conducted this experiment for 3 weeks. I live in upstate NY.
I have concluded that, even if the math states it is impossible (which I do NOT feel like arguing here), it works, and am setting up 5 other windows with similar sun exposure to enhance the passive heating throughout the rest of the house.
I hope this helps confirm Savvy Tech's similar conclusions!

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He later adds in another post: