# Black Body Radiator vs painted surface

1. May 30, 2013

### Overflowing

Recently on an aquarium related forum, I called out someone for making what I considered to be an outlandish claim and I was supported by several others. However I wish to get the opinion and/or facts explained by someone from a purely scientific standpoint.

This has to do with the heat dissipation properties of aluminum used to as an LED heat sink.

The DIY LED fixture in question is simply a piece of aluminum sheet, roughly 4" x 6" and probably a few millimeters thick, with four 3-watt LEDs in a diamond/square pattern. The fixture would be oriented with LEDs down.

So this guys posts "top side should be painted flat or satin black to reduce heat" which I thought was nonsensical.

Someone else caught it and posted "How does painting a heatsink make it work better?"

The response was "It the Black Body Radiator effect." [sic]

My response was literally "Are you serious?"

...and yes, he was.

Now, I'm a EE, PE, in the consulting industry, and I do deal with lighting so I understand at a rather admittedly rudimentary level what a Black Body Radiator is, and my initial reaction was that this guy was crazy to think that painting something black would make it have a greater heat dissipation rate, let alone call it a BBR or related that 'effect' back to it in any way.

A comment was made that even a thin coat of paint would act more as an insulator, but the guy still claimed that painting it black made it a BBR and it was cooler to the touch.

So, the bottom line here is that I would like someone to verify this, right or wrong, as I am mildly satisfied that I am right, but sure would like some scientific backing to go with it.

To get the whole picture, go to the following thread

Then start at post # 5030 and read through to post #5064, where the conversation on that particular topic is pretty much over.

Posts by me are "Floyd R Turbo" and pay particular attention to the posts made by "BeanAnimal" on posts 5046, 5050, and 5058.

"Santa Monica" is the user making the claim...

Bud

2. May 30, 2013

### TheFerruccio

I am going to assume that the amount of black body radiation in the surrounding environment corresponds to a temperature less than that of the heat sink.

I think it would be subtle and relates to conduction, as well as radiation. If you choose black paint that is not has a low coefficient of thermal conductivity, then there would be a much more pronounced gradient across the thickness of the paint, and free space would "see" less heat on the external surface of the paint. From a radiation standpoint, the rate of radiative heat flow Q leaving a body:

$\dot{Q} = \sigma\epsilon A T^4$

Stefan-Boltzmann Constant: σ
Emissivity: ε
Temperature: T
Area: A
[EDIT] forgot area. Surface area also governs this.

So, two things, in this case, govern how much is escaping to the environment. The temperature of the external surface, and the emissivity. Black paint should raise emissivity, but if the black paint isn't that conductive, then the temperature on the outer surface would be lower. You want both a high temperature exposed to the external environment, as well as a high emissivity. If you could raise the emissivity (using black paint) and the black paint was exactly as thermally conductive as aluminum (or better) then it would most likely have a very positive cooling effect to the outside environment. However, if the paint is not that conductive, there would be a lower temperature exposed to the environment, and less cooling.

I have not covered convection, though, and that relates to convective heat transfer coefficients. Having a high conductivity for paint is also important for its ability to transfer heat to the air that brushes by it, and this delves into things such as the Nusselt number, and similar things, but I am not well-versed in this subject.

In short: If the thermal conductivity is crappy, then maybe the paint will be a detriment. If the thermal conductivity is at least as good as the aluminum, then the paint will almost certainly have a positive cooling effect. There are other factors (change in surface area, contact of the paint to the aluminum, orientation of the heat sink, the temperature of the environment) that I didn't cover.

Last edited: May 30, 2013
3. May 30, 2013

### Overflowing

I guess the point here is that no one in the LED heat sink industry physically paints their heat sinks black and then claims they dissipate heat more efficiently. Heck no one even anodizes them. Read those thread posts, one guy makes reference to the fact the people in the car audio industry discuss this also, but their concern is that using paint will cause an insulating effect and reduce the heat dissipation properties of the heat sink.

Let's simplify the issue. Flat piece of aluminum, horizontal, in free air at STP with LEDs on bottom surrounded by an insulating material that does not allow convective heat dissipation. That is, all the heat must be dissipated through the top of the piece of aluminum. Assume that there is no active air convection.

Now, compare and contrast the difference heat dissipative properties of bare aluminum (unpainted, unanodized, etc) to that of the same piece of material which is coated with a thin coat of plain flat or satin black Krylon fusion or similar spray paint.

4. May 30, 2013

### TheFerruccio

Again, it depends. Think about it another way: Suppose you have a warm aluminum sphere object floating in a vacuum in the middle of a larger cold hollow spherical black body. Heat will only be transferred by radiation. Now, add a thick pole of solid silver which touches the aluminum object. Now, you have a strong conduction path. Yes, that part of the sphere is no longer exposed to free space, but heat is rapidly fluxing through that circular surface where the pole is touching, regardless. Heat transfer by radiation is eliminated, but is replaced with *lots* of heat transfer by conduction. Adding paint does not necessarily lower heat transfer to free space, provided the paint is sufficiently heat conductive.

I think the conclusion, then, is the first condition in my "if" statement. Therefore, paint is generally not as conductive as the base metal of the heat sink. That goes down to material properties, and I left that one open.

It depends on a combination of material properties and geometry. I have seen heat sinks which have black anodized layers, silver anodized layers, and other heat sinks which aren't anodized at all. My hard drive has a black anodized aluminum heat sink surrounding it. However, my CPU has non-anodized aluminum fins. My motherboard chipset has a white anodized aluminum heat sink.

4.8 here mentions benefits of painting the surface black under natural convection, but it does not explain why that is.

http://robots.freehostia.com/Heatsinks/Heatsinks.html

5. May 30, 2013

### Overflowing

That is one of the first things I've seen that supports this argument. I would think that 6-8% is not really noticeable to the touch though.

The anodizing method is not really comparable to paint I wouldn't think, because that is an electrolytic coating vs a sprayed on coating.

6. May 30, 2013

### Staff: Mentor

Both points are correct:
1. Painting an object black will improve radiation (if the object is "black" in the wavelengths being radiated). The SR-71 was painted black partly for this reason.
2. Painting an object will insulate it.

So the question really is what the bigger effect is. And the answer, unfortunately, is that it depends. Typically though, the lower the temperature of the object, the smaller the proportion of energy loss is due to radiation, so the less of an improvement in radiation.

Another consideration of course is cost. If it costs more to paint an object black than to provide a slightly larger heat exchanger, you'll be better off using a larger heat exchanger.

7. May 30, 2013

### Overflowing

Can you expand on this point? The part in bold.

8. May 31, 2013

### 256bits

Your common heat sink is designed with forced convection or natural convection as the primary means with which heat is to be transferred from one medium ( metal ) to the next ( air ). At the low temperatures of operation for the finned heat sinks used with power transistors or CPU's, radiation does not play a significant role in heat dissipation and would be neglected in the calculations. You would design for 100% of heat removal by convection.

9. May 31, 2013

### Overflowing

Right. We're talking about a flat sheet of aluminum with (4) deep red (660nm) 3W LEDs on the other side running at 700mA. There's not a ton of heat dissipation required, so it's not like the think is glowing red hot or anything.

So to say that painting it black keeps it cooler by increasing the radiative dissipation properties of the thing, to me, seems silly.

To insist that painting it black actually turns it into a "black body radiator" as he does is borderline preposterous.

Am I wrong?

10. May 31, 2013

### 256bits

Well, as everyone has said here already, it is an "if" situation. Re-read Russ's post, where it is explained quite well. I just added on to his. TheFerruccio explained the outline of the physics of radiation.

I do not think it makes any much of a difference for the situation you describe.
I may add to that later, but have to go for now.

11. May 31, 2013

### MrAnchovy

Yes you are wrong, surface colour does have an effect on radiative emissitivity.

You are wrong to call it borderline preposterous, and he is wrong to say that painting it black turns it into a black body radiator. It was an (imperfect) black body radiator before it was painted black (assuming it wasn't polished), as are most non-reflective opaque objects. Strictly, a black body has an emissivity ε = 1. In practice objects have lower emissivities, and they are sometimes called 'grey bodies' to reflect (oops) this. Painting it black simply increases the emissivity.

The article I linked to has some more information on heat sink design, including some hints as to why heat sinks have different forms depending on their design requirements. Heat sinks designed for high rates of dissipation have forced air circulation (e.g. CPU fans), or are designed to maximise convective dissipation (vertical orientation with fins permitting upward air flow) and radiative dissipation is negligible. Your heat sink is flat and has restricted air circulation so has relatively low potential for convective dissipation: radiative dissipation is therefore important, so painting it black works. There is also less of a disadvantage due to insulation, because all this does is decrease the rate of conductive heat loss, but most heat lost by conduction into the air must then be dissipated via convection anyway.

12. Jun 1, 2013

### bigfooted

Don't confuse an object that is visibly black with a black body. A white colored object and a black colored object can both be black bodies.

Objects have an emissivity and an absorption coefficient. Absorption is about how easy heat gets into the object. Emission is about heat getting out of the object. There is also reflectivity, which is the amount of radiation that is directly reflected without further interaction (like a mirror). And you have transmittance, which is the amount of radiation that passes through the object without further interaction, like glass.
When only radiative heating is involved, these control the equilibrium temperature of the object. All radiation that is not reflected or transmitted, is absorbed. I will focus now on emission and absorption.

The absorption coefficient tells you how well the object absorbs radiation, averaged over the entire (solar) spectrum. So if an object has a high absorption coefficient, it absorbs radiative heat coming from the sun very well.
The emission coefficient tells you how well an objects emits radiation at a certain temperature. If the emissivity at room temperature is very high, it can get rid of radiative heat easily.

Paint usually has a high emissivity, around 0.9. So black as well as white paint are both almost a black body radiator. But the absorption coefficient of white paint is around 0.2-0.4 and the absorption coefficient of black paint is around 0.95. This means that black-paint objects absorb heat very well and emit heat very well, whereas white-paint bodies do not absorb heat very well, and emit heat very well. When they both have the same emissivity, the black paint gets hotter.

Some quick conclusions:
- it doesn't matter in what color you paint your radiator, the emissivity of most paints are the same.
- astronauts have white space suits because of the low absorption coefficient - they don't heat up so much.
- The SR71 is painted with carbon-particle paint because of the high absorption coefficient - incoming radiation from radar is absorbed by the plane.
- aluminum has a very high transmission and a very high reflection coefficient and a very low emission and absorption coefficient. So it heats up slowly and a little, and lets through and reflects almost all radiation. If you want aluminum to heat up, paint it. In any color you like. On the back-side.

13. Jun 1, 2013

### Overflowing

Good info from all.

So given the item in question, the light fixture namely, it would generally be used in such a way that it was in a dark environment, i.e. in a cabinet where a filtration system is located. In this case, there may be little active air movement (no fans) so it would be mainly radiation.

It could also be used in a "reef pond" or in the top of a tank situation, where a light fixture could potentially shine on it.

The first scenario means there is no absorption of radiation, as there is no source from which to absorb.

The second scenario means there is potential absorption of radiation, and from potentially high intensity and close proximity light fixtures, as reef tank light is typically very high K and intense. I had though this as a possibility but was not really focusing on it, seems that painting it black was the wrong move in this instance. I had not considered painting it any other color.

But anyways, I'm seeing some mixed opinions here. Bigfooted, one of your last statements says "if you want aluminum to heat up, paint it" what do you mean here?

Then there is this article that is referenced on the Wiki page that MrAnchovy linked to (#13)

http://ludens.cl/Electron/Thermal.html

under the "heat sink color" header, there is this:

Which seems to support the product developer's claim actually, a non-finned heat sink with no active cooling will gain from being painted matte black.

14. Jun 1, 2013

### Staff: Mentor

Warm/hot objects are not glowing at visible wavelengths so just because it has a high emissivity in the visible doesn't necessarily mean it is high in the infrared.

15. Jun 1, 2013

### Overflowing

The temperature of the aluminum heat sink, on the exact opposite side of the LED, would depend on the thickness of that aluminum, the spacing of the LEDs and the current running through and the efficiency of the LED (cheaper ones are less efficient, i.e. greater heat loss). In this instance, I believe that it is safe to assume that without paint on the back of the heat sink in question, the surface temperature would probably not get hot enough that you would not be able to hold your hand on it without feeling pain.

So yes, the heat sink would not be glowing in the visible spectrum. Now I'm trying to understand your comment on the infrared emissivity?

Also back to the painting point, if painting it would insulate it, wouldn't the aluminum just get hotter, causing a higher temperature gradient and causing more convective loss?

Then, if the other wiki links are right, the black paint, if "looking" into "darkness" would radiate more efficiently as it is a flat (non-finned) surface, should offset this.

I just keep going back and forth, and I'm seeing opinions and evidence in either direction.

16. Jun 2, 2013

### Philip Wood

Had the OP seen the Leslie's cube demonstration he would certainly not regard as 'preposterous' the claim about painting the heat sink black.

The Leslie's cube that I used was a cubical copper tank of about 12 cm3 capacity and wall thickness about 0.7 mm. It was filled with boiling water, which had probably cooled to about 85°C before readings were taken. The outside vertical faces of the cube were polished copper, dull copper, gloss white-painted and dull-black-painted. A thermopile (several thermocouples in series) at the sharp end of a conical guide-tube was used as temperature sensor. It was connected to a 'spot' galvanometer, which was zeroed with the open end of the cone pointing at some arbitrary object in the lab. Then the thermopile was moved to be level with the centre of the polished face of the cube, with the blunt end of the cone 'pointing at' the face, and close enough to the face to collect radiation from the face only.

There was only a very small deflection of the galvanometer's light spot. But with the dull black face of the cube the same distance from the thermopile, the deflection was at least 10 times as much. Interesting it was not a lot less for the gloss-white-painted face, showing that surfaces which are poor emitters of visible light may be good emitters of far infrared. The dull copper surface was a good emitter but not as good as the dull black or white-painted surfaces.

I'm sorry that these results are only semi-quantitative, but the demonstration was a very striking one - once seen never forgotten.

Last edited: Jun 2, 2013
17. Jun 27, 2014

### terryaaa

"bigfooted" makes some good/relative points. Rough white concrete is as close to a black body as asphalt. Both are something like .93. Anodizing is done to improve heat dissipation over painting which impedes heat dissipation. The most common mistake made by people ordering anodization, is that they will achieve the ultimate heat dissipation by ordering black or dark anodizing.(blackbody effect) Anodizers are quick to point out this accomplishes/improves nothing. Considering the low amount of heat dissipation in this case, I don't know how you can make any argument without knowing what the paint is. most paints today are latex or poly something and are good insulators, relative to something like aluminum. Again, the r value of most paints would probably impede the low heat here, over any "blackbody' effect.

18. Jun 27, 2014

### Overflowing

For the record, I obtained one of the LED units in question and was using it for a while to test it out for various purposes in it's intended environment (which was a saltwater aquarium). The paint eventually flaked off almost completely so the claim IMO was totally bogus, and terryaaa just confirmed that for me. While he may have improved the application, it's still an insulator IMO and does not make for a "black body radiator"

19. Apr 16, 2016

### Michael Towell

A company called "Graphtek" makes High-e, High-C coatings for this purpose. (high emissivity, high conduction).
Hold on to your desk when you see the prices.
Yes, a properly coated black heat sink will be much more effective per unit area. But, since the heat sink construction is relatively cheap, increasing the size of the heat sink is usually the most economical alternative unless the space is confined and a very high-e is required, then these specialty coatings may be employed cost effectively.

20. Apr 16, 2016

### Michael Towell

I've erased the word "paint" from any reference in my engineering documents. It can be and usually is misleading.
The more correct term is "coatings" and all coatings have specific properties.