[terminalshort]

But space isn't actually cold, or at least not space near Earth. It's about 10 C. And that's only about a 10 C less than room temperature, so a human habitable structure in near earth space won't radiate very much heat. But heat radiated is O(Tobject^4 - Tbackground^4), and a computer can operate up to around 90C (I think) so that is actually a very big difference here. Back of the envelope, a data center at 90C will radiate about 10x the heat that a space station at 20C will. With the massive caveat that I don't know what the constant is here, it could actually be easy to keep a datacenter cool even though it is hard to keep a space station cool.

[uplifter]

It's actually only about 3x.

As you intimated, the radiated heat Energy output of an object is described by the Stefan-Boltzmann Law, which is E = [Object Temp ]^4 * [Stefan-Boltzmann Constant]

However, Temp must be in units of an absolute temperature scale, typically Kelvin.

So the relative heat output of a 90C vs 20C objects will be (translating to K):

383^4 / 293^4 = 2.919x

Plugging in the constant (5.67 * 10^-8 W/(m^2*K^4)) The actual values for heat radiation energy output for objects at 90C and 20C objects is 1220 W/m^2 and 417 W/m^2

The incidence of solar flux must also be taken into account, and satellites at LEO and not in the shade will have one side bathing in 1361 W/m^2 of sunlight, which will be absorbed by the satellite with some fractional efficiency -- the article estimates 0.92 -- and that will also need to be dissipated.

The computer's waste heat needs to be shed, for reference[0] a G200 generates up to 700W, but the computer is presumably powered by the incident solar radiation hitting the satellite, so we don't need to add its energy separately, we can just model the satellite as needing to shed 1361 W/m^2 * 0.92 = 1252 W/m^2 for each square meter of its surface facing the sun.

We've already established that objects at 20C and 90C only radiate 1220 W/m^2 and 417 W/m^2, respectively, so to radiate 1252 W per square meter coming in from the sun facing side we'll need 1252/1220 = 1.026 times that area of shaded radiator maintained at a uniform 90C. If we wanted the radiator to run cooler, at 20C, we'd need 2.919x as much as at 90C, or 3.078 square meters of shaded radiator for every square meter of sun facing material.

[0] Nvidia G200 specifications: https://www.nvidia.com/en-us/data-center/h200/

[merman]

You use arbitrary temps to prove at some temps it’s not as efficient. Ok? What about at the actual temps it will be operating in? We’re talking about space here. Why use 20 degC as the temperature for space?

[icegreentea2]

He didn't use 20C as the temperature of space. He used the OP's example of comparing the radiative cooling effectiveness of a heat SOURCE at 90C (chosen to characterize a data center environment) and 20C (chosen to characterize the ISS/human habitable space craft).

[terminalshort]

You forgot about the background. The background temp at Earths distance from the sun is around 283K. Room temperature is around 293K, and a computer can operate at 363K. So for an object at 283K the radiation will be (293^4 - 283^4) = , and a computer will be (363^4 - 283^4)

(293^4 - 283^4) = 9.55e8

(363^4 - 283^4) = 1.09e10

So about 10x

I have no problem with your other numbers which I left out as I was just making a very rough estimate.

[uplifter]

The background temp at Earth's orbit is due to the incidence of solar flux, which I took account of.

I'm assuming the radiators are shaded from that flux by the rest of the satellite, for efficiency reasons, so we don't need to account for solar flux directly heating up the radiators themselves and reducing their efficiency.

In the shade, the radiators emission is relative to the background temp of empty space, which is only 2.7 K[0]. I did neglect to account for that temperature, that's true, but it should be negligible in its effects (for our rough estimate purposes).

[0] https://sciencenotes.org/how-cold-is-space-what-is-its-tempe...

[modeless]

The temperature that you raise to the fourth power is not Celsius, it's Kelvin. Otherwise things at -200 C would radiate more heat than things at 100 C. Also the temperature of space is ~3 K (cosmic microwave background), not 10 C.

[ithkuil]

There is a large region of the upper atmosphere called the thermosphere where there is still a little bit of air. The pressure is extremely low but the few molecules that are there are bombarded by intense radiation and thus reach pretty high temperatures, even 2000 C!

But since there are so few such molecules in any cubic meter, there isn't much energy in them. So if you put an object in such a rarefied atmosphere. It wouldn't get heated up by it despite such a gas formally having such a temperature.

The gas would be cooled down upon contact with the body and the body would be heated up by a negligible amount

[modeless]

These satellites will certainly be above the themosphere. The temperature of the sparse molecules in space is not relevant for cooling because there are too few of them. We're talking about radiative cooling here.

[ithkuil]

indeed. talking about temperature is incomplete without other aspects such as pressure

[terminalshort]

Yeah, if you forget about the giant fucking star nearby

[modeless]

The Sun is also not 10 C. Luckily you have solar arrays which shade your radiators from it, so you can ignore the direct light from it when calculating radiator efficiency. The actual concern in LEO is radiation from the Earth itself.

[ithkuil]

Pressure matters