What is the best colour (inc black or white) to paint a radiator so that its heat output is maximised.
Thx
Heat emitted is:
Q = [symbol]e s[/symbol] T[sup]4[/sup] A t
where Q = heat (J)
[symbol]e[/symbol] = emissivity (dimensionless)
[symbol]s[/symbol] = Stefan-Boltzman constant = 5.67x10[sup]-8[/sup] (J s[sup]-1[/sup]m[sup]-2[/sup]K[sup]-4[/sup])
A = area (m[sup]2[/sup])
t = time (s)
The emissivity is the variable you are asking about. If the radiator were perfectly black, the emissivity would be 1, and heat transfer would be maximised. Any other color will have an emissivity of less than 1.
Left out:
T = temperature (K)
You didn’t specify what kind of radiator, so I’ll try to provide a general overview. Radiators radiate heat by two methods: convection and radiation. You want to maximize the sum of the two. Also you need to minimize heat input from the environment.
Convection doesn’t depend on color, but if you coat the radiator with a thick layer of paint that has low thermal conductivity, convection will be reduced. So you want a thin layer of paint or other surface treatment. Bare metal without any surface treatment would be ideal if you can keep the surface clean.
Radiation is usually in the infrared. The efficiency of a material to emit IR radiation is called emissivity. Darker color material tends to have higher emissivity, but there are exceptions. For example, brushed or polished aluminum has an extremely low emissivity, but if you anodize this surface you can increase the emissivity with very little change in appearance. (At least appearance to our eyes.) Bare metal tends to have very low emissivity.
As for heat input, usually the only significant source, if there is one at all, is sunlight. Most of the energy in sunlight is in the visible wavelength so you can easily tell how much heat a material absorbs - white objects reflect light, black objects absorb light. Sometimes this property is called absorptivity.
So the choice of surface depends on the environment it’s used in. If the radiator is designed primarily for convective cooling (e.g. computer CPU heat sinks and automobile radiators), then you don’t really care about emissivity or absorptivity, you just want a good conductive surface with minimal surface treatment. If the radiator is to be mounted on the dark side of a spacecraft, you find the material with the highest emissivity and use that. If the radiator is in sunlight part of the time (e.g. a spinning satellite), you want a material that has very high emissivity and very low absorptivity. The best choice here is a plastic film with a metal coating on the back surface; the plastic emits IR, but visible light goes right through the plastic and gets reflected by the inner metal coating. Silver coated Teflon is the standard choice for aerospace use, but it’s something like $1000 per square foot. Aluminized polyimide isn’t too bad and significantly cheaper.
Excellent info - Thank you very very much.
From what I’ve seen auto-makers paint them black, I suppose they have a reason.
At first I couldn’t see why color, which has to do with reflected light, should have anything to with radiation due to heat. But I think I have it now.
Color has to do with wavelengths of light reflected. A ideal black body reflects none of the received light. All of it is absorbed, heats the body and then is re-radiated (the mechanism for this is unimportant at the moment). If a body is black, then it means that it easily absorbs EM radiation of any wavelength and turns it into heat energy.
Well, at the microscopic level the individual processes involved are reversible, meaning it can happen one as easily as the reverse. A body that absorbs light of all wavelengths easily will therefore also be a body that easily emits light at all wavelengths easily, and therefore the emissivity will be close to 1.
You got it. Sorry I didn’t explain this more clearly. It’s also possible to think of this in terms of thermodynamics: if something absorbs light very efficiently but doesn’t radiate light at all, it will keep on absorbing heat and get hotter and hotter. If the absorption coefficient is larger than the emission coefficient, the object will get hotter than the light source, which isn’t allowed (heat cannot flow from a hotter to a colder object). To satisfy all the laws of thermodynamics, the two coefficients must be the same.
But keep in mind that the term “color” refers to emission/absorption coefficient in visible light. Unless the radiator is at several thousand degrees most of the emission occurs in the infrared, and the emission coefficient in the infrared (emissivity) is not necessarily the same as in the visible light. So black paint is not necessarily the best choice to put on a radiator.
Don’t paint it. No matter what the color, the paint will add a layer or insulation to the radiator.
We were taught in high school that Black would be the proper color. I don’t have a cite, I’m sorry, but then I was only 14 and we didn’t have the internet then…