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In this setting materials science is decades ahead, so answers should be limited by technology that isn't too speculative and don't presume anything supernatural beyond what I describe in this question.

Resources can be assumed to be very abundant. A lack of cultural value placed on precious metals combined with greater abundance and better exploitation also makes precious metals a way cheaper. This is way wealthier than any modern society.

People in this world have the means to create magical darkness through magical enchantments: This darkness absorbs all radiation except non-relativistic atoms without producing any corresponding heat, but it does not otherwise interact with matter physically and only consumes heat via absorbing photons. Some of the darkness is used up when absorbing radiation, so absorbing too much mass or energy worth of radiation will require a prohibitively expensive enchantment (though this shouldn't be an issue except when dealing with supercritical events, or trying to absorb a significant mass of plasma).

The other relevant things the magical darkness can be used for is short range teleportation (entirely within the magical darkness), and physically separating non-solid atomic matter by desired qualities. It can easily physically separate the components of a gas or liquid. It can also replenish nuclear fuel rods while in use with teleportation, or sort objects according to simple rules. Using magical darkness for teleportation is costly however and so you wouldn't want a radiator/heatsink design that regularly had components teleporting around.

Importantly the magical darkness is physically intangible, but it can only co-occupy with gas or any material transparent to visible light.

So it would seem like using water would be the be an obvious choice due to its heat capacity, thermal conductivity, and transparency. However, with nearly any desired isotope being affordable surely you could do better by using heavier isotopes for the water right? Plus there's plenty of materials like molten glass that would work as they are technically transparent even if you can't tell because of their glow. There's also the consideration of what kind of radiator setup to flow the clear liquid through (maybe a highly thermally conductive aerogel?) to maximize cooling, since normal radiators don't have the liberty of just deleting heat.

Though I might be totally wrong about the most efficient general design and maybe it's better to use something else to carry the magical darkness like:

  • Supercritical CO2: It could allow for way more surface area to be in contact with the magical darkness, plus you could make really tiny channels for it to flow through within the device being cooled maybe?

  • Solid diamond: Very thermally conductive and clear, could also be pair with a transparent liquid.

  • Water vapor: Might have more surface area to emit IR?, or does that not apply if the whole bulk of material can shed IR? to carry the magical darkness.

How effectively could a heatsink designed around radiating IR into magical darkness be compared to a normal heatsink in terms of quickly pulling heat from a given volume/mass, and what would it be designed like broadly speaking?

Your answers should particularly focus on compact heat sinks that do not mess up the aerodynamics of what they're attached to like normal radiators would.

I strongly suspect that getting a massive surface area heatsink to shed IR into darkness would let you get orders of magnitude better performance in terms of heat moved per second per volume/mass than just using normal radiators shedding heat into the adjacent environment. After all these shadow-radiators wouldn't be limited by transfer of heat to the surroundings, but by surface area, which seems like something that could be exploited to a way greater degree given we can create things like microchips that are absurdly finely detailed.

I included the hard science tag because I realized this heatsink will play a crucial role in my setting and I need citations and/or math so I can actually know how well I could use it various applications. Extremely compact and effective heatsinks are of great importance for my setting as people want to use small nuclear reactors or Project Pluto style engines for as many things as possible and with good radiation shielding, heat management becomes the biggest obstacle to that (their technology and magic make fallout a non issue, and the environment is already barren of nearly any life such that fallout will increase the biomass). Plus conflict occurring in an Antarctic environment means that thermal imaging is particular effective and it would be profoundly useful to be able to actually hide from IR.

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    $\begingroup$ "Get orders of magnitude better performance": Performance of what? For example, you cannot get "orders of magnitude" better performance of a diesel engine, because it already has an efficiency of about 45% to 55%, so that at best you could make it twice as efficient. You cannot get "orders of magnitude" better performance of a permanent magnet electric motor, because it already is over 90% efficient. $\endgroup$
    – AlexP
    Commented May 17, 2023 at 22:33
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    $\begingroup$ If the darkness can occupy the same space as the coolant, surely surface area is irrelevant, as all heat radiated from that coolant (presumably water) is absorbed? Also, just how transparent does a material need to be for darkness to be able to occupy the same space as it? $\endgroup$
    – M S
    Commented May 17, 2023 at 23:01
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    $\begingroup$ A radiator cannot dissipate more heat than what is produced by the engine (or whatever process) which needs to dissipate heat; and all well-designed radiators dissipate 100% of the heat which needs dissipating. You can make the radiator smaller, great; but in the grand scheme of things, miniaturizing the radiator won't buy you much. Let's say that you replace the radiator of a car with a tiny magical device; that would make the car maybe 15 inches shorter and its engine maybe twice as efficient. That's good, but not world-changing. $\endgroup$
    – AlexP
    Commented May 17, 2023 at 23:06
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    $\begingroup$ @MS: It is indeed a major engineering consideration, but it is in the end just an engineering consideration. We know how to design radiators. What fraction of the mass of the ISS are its radiators? $\endgroup$
    – AlexP
    Commented May 17, 2023 at 23:27
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    $\begingroup$ @gs Of course they're not. OP has in detail described the functionality of all the relevant magic, the rest operates as in the real world. It's honestly bizarre how obtuse some people on this site are. "Well is magic so anything goes". You know this is the worldbuilding stackexchange, right? $\endgroup$
    – M S
    Commented May 18, 2023 at 8:08

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Purely radiative heatsinks are somewhat inconvenient. Heat transfer into a convecting fluid (eg. air or water on a planet) is pretty effective... that's why heating elements in kettles are bar heaters can be fairly compact. The radiator that the internal combustion engines that drive vehicles takes up a pretty small portion of the weight and volume of the vehicle, at least in part because air can be forced through it when the vehicle is in motion which carries away lots of heat.

Conversely, we can insulate things by encapsulating them in a vacuum in the form of Dewar/thermos flasks. Spacecraft don't have the advantage of sitting in a load of convecting fluid, and as such can only lose heat by radiation. There's been quite a lot of thought put into spacecraft radiators, and you can use them as a starting point for your magical heat sinks. I recommend Project Rho's page on heatsinks as a good place to do research... there's a lot of interesting stuff there you can work from. Your heatsinks don't need to worry about self-heating, because heat released from their surfaces in the form of EM radiation will be captured by the magical effect before it can be re-absorbed by anything else, which means you can use existing work on radiators to calculate the area of your heatsink, and then roll it up tightly to keep its overall dimensions under control. Note that this relies on the heat-magic effect remaining present... if anything happens to turn it off, the coiled heatsink will rapidly cook itself, or the thing it is connected to, or both.

Lets imagine a combustion engine with an efficiency of 30%, that's producing a total power output of 20kW. It produces 6kW of useful mechanical oomph, and 14kW of heat. Vehicle engines often use water as coolant, so you won't be getting a radiator temperature greater than 100 degrees C unless you're doing fancy phase-changing things. Using the Stephan-Boltzmann law, you can see that a radiator at that temperature radiates about 1.1kW per square meter of its surface, so you need a total radiator surface area of ~13m2m. Using the Space Shuttle's life support radiators as a model, you end up needing a system that weighs about 40 kilos.

That's big! Pure radiative cooling is always going to be bigger and heavier than convective cooling. That means your magical heatsinks are useful for very specific things, but are not general purpose devices. The fact that you can run your magical effect in any transparent medium does not help you, because you're ultimately relying on radiative heat loss, and radiation just isn't as good as using a convecting fluid.

Your magic will be useful for situations like:

  • air (or water) temperature simliar (or hotter) than the thing you're trying to cool. Think "human in desert" sort of thing. Wrap yourself in something insulating to keep the heat out, and use a magic heatsink to keep yourself cool. Keep your space probes on Mercury, Venus and IO working for longer.
  • lack of convenient convective medium. Spacecraft is the obvious, but equipment buried underground might also benefit here.
  • fitting very hot equipment into places where installing conventional cooling systems is impractical. A magic heatsink might be cheaper and more compact than running a load of air ducts or coolant pipes into an existing industrial facility, or fancy historic building you can't make major modifications to.
  • using hot equipment in places where you don't want to be detected. Big heat plumes and hotspots are easy to spot with thermal cameras. Running something like a clandestine hydroponic garden without arousing suspicion might be easier if your house was not obviously hotter than your neighbours. There are obvious military benefits here, too.
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This technology is incredibly useful as is, and the radiative-only limitation can be completely worked around using transparent aerogels

The Stefan-Boltzmann equation gives P = AeoT^4, where P = power (W), A = area (m^2), e = black body constant (0 to 1), o = 5.7*10^-8 (Wm^-2K-4), and T = temperature (K).

For a 1 metre square blackish object (e = 0.9), at 25 deg C, that gives you 405 W of heatsink. Not bad.

How about at 80 deg C? Now you've got 800 W. At 140 deg C, you get 1640W.

That's with only 1 m^2. Perfectly achievable using conventional methods, especially because it doubtless works even when the vanes of a radiator are only very finely separated.

Now, I don't know how finely this magical darkness can be divided, but if it's perfectly divisible, then things get interesting.

Aerogel has a surface area of up to 3000 m^2 gram, and is transparent. It's hard to heat, but you could make it with a network of holes through it and exhaust hot air straight into it. This heats the aerogel, which immediately radiates it into the magical darkness, thus achieving a workaround of the radiation only rule.

This wouldn't normally work because the aerogel would be radiating into itself 99.99% of its radation and only the exterior surface area would count, but that is not the case here, hence why it works so well.

At 1000 m^2 per gram, and a density of 0.1 g/cm^3, a 5 centimetre cube could have 1250 m^2, giving an amazing 500 kW heatsink capacity at 25 deg C, in a 5 centimetre cube.

Furthermore, it can cool anything down to extremely low temperatures, asymptotically approaching absolute zero. The refrigeration possibilities are endless.

I don't even play games any more and I hate gaudy gaming PCs with their ghastly LEDs, but I would go straight out and buy one just to use my cool heatsink. (Just kidding, I'd be heading down to talk to heat pump companies and the like).

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  • $\begingroup$ This answer was really useful, do you know of any way to figure out how many IR photons (in W) are emitted from a material in total? Since I wonder what the effective surface area would be of a transparent material, given every IR photon emitted from any atom is instantly absorbed if darkness has permeated a given material. So I am curious whether the effective surface area according to the S.B. equation would be astronomically large. $\endgroup$ Commented May 19, 2023 at 17:14
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    $\begingroup$ @VakusDrake That's exactly how it would be. With porous materials in real life, you adsorb nitrogen onto them to figure out the total surface area, which is how we get the figures for porous materials; your magic darkness would function the same way, so total internal surface area can be used, rather than external surface area. I've done surface area characterisation in real life, btw. $\endgroup$
    – user86462
    Commented May 19, 2023 at 21:58
  • $\begingroup$ Thanks for the info! Do you know how I'd figure out what the effective "internal surface area" would be? I suspect that the effective radiative surface area of a material permeated with shadow would be basically the same as if the material were vaporized into a bunch of disconnected atoms spread across a vacuum. Basically I suspect that the IR emission would be equivalent to a single atom of a given material in a vacuum at a given temperature, times the number of total atoms. Would this be the correct approach? And if so how would I calculate it? $\endgroup$ Commented May 19, 2023 at 22:48
  • $\begingroup$ I feel like there must be some equation for a single atoms' emissions in a vacuum and if I had that I could plug in a given atom and temperature and then multiply by the number of atoms to get what I need here. If you can get me that then I think that might be all the info I'd need so I'd also accept your answer for what its worth $\endgroup$ Commented May 19, 2023 at 22:49
  • $\begingroup$ @VakusDrake You can just look up the internal surface area of porous materials. For aerogels, activated carbon, etc, it's one of their main properties. $\endgroup$
    – user86462
    Commented May 20, 2023 at 3:49
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I think the best option would be to have a transparent heat-transfer fluid run through a section of darkness, which would absorb all the heat radiated from every single atom of fluid that runs through it. The real design consideration then would be getting as much heat from the engine into the fluid as possible.

So I guess the optimal fluid would be one that is transparent, highly thermally conductive, and highly emissive.

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First of all, I'm no expert on the equations of heat transfer, but you seem to be talking about two different things. The Wikipedia page on heat transfer mentions 4 main types of heat transfer. You focus on the basic principles of current radiator/heat sink technology, but my understanding of such things is that they run primarily on the methods of "conduction" and "convection". Your magical darkness, as you described it, seems to deal solely with the method of "radiation". There is a mismatch here. Any heat sink maximizing the use of this magic technique will focus mostly on converting as much energy to infrared radiation as possible.

Out of the methods you described, the diamond one shows the most promise. Using conduction to spread heat out across a medium that is transparent to both regular light (which is a requirement listed for your magic) and infrared radiation, which is required to produce the radiation to be absorbed. You could have a solid mass of this filled with magical darkness as a heat sink. Putting fins and liquid coolant into play is only required if you want to employ multiple methods of heat dispersal. Adding conduction-convection cooling to radiation absorption could further increase the cooling ability of the heat sink, but it is not required for your method to work.

Now, as for the math involved... As I said, I'm not nearly an expert. But the easiest to understand equation I can find is the Stefan-Boltzmann law, which governs heat energy naturally converted to infrared (which should equal heat energy lost within magical darkness). This is shown to be P=(Stefan-Boltzmann constant)AT^4 . The 'constant having a value of 1.380 650 5(24)×10−23 J·K−1

The other values being area(A) and absolute temperature (T). The last part is an exponent, which is interesting because it means that the amount of infrared radiation produced will rise exponentially as temperature rises.

Anyway, this is far from a comprehensive answer, but I hope it will give you a clearer idea of what you are trying to accomplish.

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