Basically you concentrate the heat into a high emissivity high temperature material that’s facing deep space and is shaded. Radiators get dramatically smaller as temperature goes up because radiation scales as T⁴ (Stefan–Boltzmann). There are many cases in space where you need to radiate heat - see Kerbal Space Program
"High emissivity, high temperature" sounds good on paper, but to create that temperature gradient within your spacecraft the way you want costs a lot of energy. What you actually do is add a shit load of surface area to your spacecraft, give that whole thing a coating that improves its emissivity, and try your hardest to minimize the thermal gradient from the heat source (the hot part) throughout the radiator. Emissivity isn't going past 1 in that equation, and you're going to have a very hard time getting your radiator to be hotter than your heat source.
Note that KSP is a game that fictionalizes a lot of things, and sizes of solar panels and radiators are one of those things.
I’m not sure I understand why creating the gradient is hard - use a phase transitioning heat pump to a high surface area radiator. The radiator doesn’t have to be hotter than the heat source the radiator just has to be hot, but given the fact we are talking about a space data center, you can certainly use the heat pump to make the radiator much hotter than any single GPU, and even use the energy from the heat cycle to power the pumps, but I imagine such a data center the power draw of the heat pump would be tiny compared to the GPUs.
To be clear I’m not advocating KSP as a reality simulator, or that data centers in space isn’t totally bonkers. However the reality is the hotter the radiator the smaller the surface area for pure radiance dissipation of heat.
I am referring to the "using a heat pump to make the radiator hotter than the GPU" as "creating a thermal gradient." No matter the technology, moving heat like this is always pretty expensive in power terms, and the price goes way up if you want the radiator hotter that the thing it's cooling.
Can you point to a terrestrial system similar to what you are proposing? Liquid cooling and phase change cooling in computers always has a radiator that is cooler than the component it is chilling.
You can do this in theory, but it takes so much power you are better off with some heat pumping to much bigger passive radiators that are cooler than your silicon (like everything else in space).
Yah but the key is that it’s not the power draw that’s the issue is the dissipation of thermal energy through pure radiation. The heat of the radiator is really important because it reduces the required surface area immensely as it scales up.
However the radiators you’re discussing are not pure radiance radiators. They transfer most heat to some other material like forced air. This is why they are cooler - they aren’t relying on the heat of the material to radiate rapidly enough.
I would note an obvious terrestrial example though is a home heat pump. The typical radiator is actually hotter than the home itself, and especially the heads and material being circulated. Another is any adiabatic refrigerator where the coils are much hotter than the refrigerated space. Peltier coolers even more so where you can freeze the nitrogen in the air with a peltier tower but the hot surface is intensely hot and unless you can move the heat from it rapidly the peltier effect collapses. (I went through a period of trying to freeze air at home for fun so there you go)
For radiation of heat the equation is
P = \varepsilon \sigma A T^4
P = radiated power
• A = surface area
• T = absolute temperature (Kelvin)
• \varepsilon = emissivity
• \sigma = Stefan–Boltzmann constant
This means the temperature of the material increases radiation by the fourth power of its value. This is a dramatic amount of variance at it scales. If you can expend the power to double the heat it emits 16x the heat. You can use a much lower mass and surface area.
This is why space based nuclear reactors are invariably high temperature radiators. The idea radiators are effectively carbon radiators in that they have nearly perfect emissivity and extraordinarily high temperature tolerances and even get harder at very high temperatures. They’re just delicate and hard to manufacture. This is very different than conduction based radiators where metals are ideal.
Making your radiator hotter than the thing you're pulling heat out of is very, very expensive in energy terms. This is why home AC is so expensive and why nobody uses systems like this to cool computers. All that energy has to come from a solar panel you fly, too, so you're not saving mass by doing this. You're just shifting it from cooling to power. If you need 200W to cool 100W of compute, you're tripling the amount of power you need to do that work.
Also, peltiers are less energy-efficient than compressors. That is why no home AC uses a peltier.
Stupid question: Why not transfer the heat to some kind of material and then jettison that out to space? Maybe something that can burn itself out and leave little material behind?
Consider your own computer... how often does it get hot under a regular load and the fans kick on? That "fans kick on" is transferring the heat to air and jettisoning it into the room... and you're dealing with 100 watts there. Scale that up to kilowatts that are always running.
There is a lot of energy that is being consumed for computation and being converted into heat.
The other part if that is... its a lot easier to do that transfer heat into some other material and jettison it on earth, without having to ship the rack into space and also deal with the additional mechanics of getting rid of hot things. You've got advantages of things like "cold things sink in gravity" and "you can push heat around and sink it into other things (like phase change of water)" and "you don't need to be sitting on top of a power plant in order to use the power."
