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I will make some 5mm blackened steel letters for a building. Now, in the sunlight in summer, how hot can they get?

EDIT:

i want to place some LEDs on the back of the letters. now the question is if i have to watch out for high temperatures or if i have to use a special glue. There are some people who say that the letters can heat up to 90°C in Summer while others are saying that the Letters will only heat up to the air temperature or a little bit higher.

So, im in europe, not in the desert but i just wanted to clarify who is nearer to the answer. 90°C or about 30°C ... Depending on the answer i will attach the lighting.

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    $\begingroup$ How hot does it get in your area during the day. This is about how hot the metal will get. $\endgroup$
    – Jimmy360
    Commented May 31, 2015 at 7:07
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    $\begingroup$ Radiative transfer contains some hints. ( note that iron -> 7870 kg/m3 , 420 J /Kg.°K , 5 sun hours at 1 kW/m² ) ... and the wind speed ? hard to get a credible order of magnitude with all theses parameters. The best would be to do some measures :) $\endgroup$
    – user46925
    Commented May 31, 2015 at 9:46
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    $\begingroup$ @Jimmy360 That's wrong: measure the air temperature and compare with the surface temperature of a paved parking lot. $\endgroup$
    – Carl Witthoft
    Commented May 31, 2015 at 12:44
  • $\begingroup$ @CarlWitthoft This is why I said about. $\endgroup$
    – Jimmy360
    Commented May 31, 2015 at 21:14
  • $\begingroup$ hi, i edited the question with more Details to why im asking. maybe that helps. Sorry for the unclear question $\endgroup$
    – dichterDichter
    Commented Jun 1, 2015 at 9:42

2 Answers 2

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While the answer for your particular case depends on a lot of factors, you can estimate how hot an object gets that is facing the sun (and whose back side is insulated) using the Stefan-Boltzmann law. Let us assume that the material is perfectly black (emissivity of 1.0) and facing the sun which delivers approximately 1 kW of power per square meter at the surface of the Earth (a bit more at the top of the atmosphere).

The black surface will heat up until it loses that kW as fast as it is coming in. It will do so by a combination of radiation and convection.

We all know that things inside a car can get very hot - this is because the windows reflect more radiation at long wavelengths (the "greenhouse" effect). But for this calculation I will initially ignore this effect although it does play a role.

Stefan-Boltzmann: $$J = \sigma T^4$$

To lose 1 kW over 1 m2 requires a temperature of $$T=\sqrt[4]{\frac{1000}{5.67\cdot 10^{-8}}}\approx 364\ \mathrm{K}$$

This assumes only the surface facing the sun loses heat by radiation: in other words this is only valid for a black surface mounted on a good insulator. It is an upper limit when we ignore convection and greenhouse effect (which are opposite - convection will cause the material to be cooler, and greenhouse effect will make it hotter). It is clearly not enough to melt your lettering.

Incidentally there are some interesting links on the temperature of objects in the sun. I quite liked this one[archived] describing measurements on cars. It shows that things left in the sun can get significantly hotter than the surrounding air (although there are some issues with the method used, the conclusions are mostly valid),

One final note - how hot things are is not the same as how hot they seem to be. Touching a good conductor (metal) will exaggerate the apparent temperature (hot feels hotter and cold feels colder) when compared to touching thermally insulating materials; and using non contact thermometers can lead to errors when comparing surfaces of different colors (emissivity) - but not enough to explain the reading of 160 °F mentioned in the above article.

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  • $\begingroup$ thank you. So as the measurements of the black rooftop show, there are Temperatures max. 150°F which is about 65°C. This would show that the Letters couldnt get to 90° but only about to 60 during a hot summer day or cool down at night to air temperature which shouldnt be less than -30° in europe :-) $\endgroup$
    – dichterDichter
    Commented Jun 1, 2015 at 9:47
  • $\begingroup$ That sounds about right. A lot depends on the angle of the letters to the sun; some of it depends on ambient temperature and wind speed. But yes, it is unlikely they could get to 90C. $\endgroup$
    – Floris
    Commented Jun 1, 2015 at 10:37
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    $\begingroup$ thats a great fact for me. maybe i will attach a thermometer to one of the letters and make a graph over one year. could be an interesting study to see how hot a letter gets and how warm/cold its outside. $\endgroup$
    – dichterDichter
    Commented Jun 1, 2015 at 11:14
  • $\begingroup$ @dichterDichter yes that would be interesting. I am betting it depends a lot on the angle to the sun so it should make an interesting graph (both daily variation and over the course of a year). $\endgroup$
    – Floris
    Commented Jun 1, 2015 at 11:53
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    $\begingroup$ @bukwyrm the emission part of the equation doesn’t depend on the temperature of “everything the surface is facing” - that only affects the total power received. By saying that is “roughly 1 kW per square meter” I have implicitly assumed the radiation received from the rest of the atmosphere can be neglected. When you use a single significant digit (“1 kW”) that approximation is justified. I do point out that “greenhouse effect” plays a role. And that is basically “radiation from everything else”. $\endgroup$
    – Floris
    Commented Mar 20, 2019 at 13:43
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If the building is located in Hammerfest, Norway the metal might get warm to the touch. If it's on the sun-facing side in Las Vegas you may find it gets hot enough to cause burns. A definitive answer is not possible.

If people can touch it easily the temperature is a concern. If it's out of reach, don't worry about it. The iron isn't going to melt.

"blackened steel" isn't very descriptive. What kind of steel, and what kind of coating? Mild steel with a chemical treatment will rust out in months. Faster if the place is on the ocean. Stainless is hard to treat. Paint works well (provided it's the right paint), and powder coating is particularly durable. Best to call an outdoor sign shop in the installation's area and ask them what works best in that climate.

Aluminum is very popular for outdoor signage, consider changing materials if you haven't finished already. Anodized aluminum is very durable and available in a wide selection of colours. Watch the fasteners though - you can't use steel screws (not even stainless ones) in aluminum plate.

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