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Radiating heat into a vacuum is a no-go, so a spaceship that generates any kind of heat is going to be in trouble. I had an idea for a potential solution - dumping your heat into a disposable heat sink component, and then spacing the component. Sort of like the heat-sink clips in Mass Effect 2, but for spacecraft.

Of course, you gotta store these heat sinks somewhere, and they would eventually run out. While this seems like a good way to introduce tension into a travel story, I want to make sure that this is a plausible method.

A typical ship that would want to use this approach is a cargo ship - it has plenty of space, but wants to maximize space for cargo over space for heat sinks. The crew is biological, so it needs some quarters. What would its heat sinks be made out of? How much heatsink stock would you need per day of journey?

Edit: Apparently, radiating heat into space is already a pretty decent method. What conditions would render disposable heat sinks necessary? How much heat would the ship need to generate, and what would require that much energy?

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    $\begingroup$ Why is radiating heat a no-go? All the spacecraft ever built used radiators to dump heat. See two the radiators of the International Space Station. $\endgroup$ – AlexP Jan 9 '17 at 16:11
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    $\begingroup$ Because it's boring. I hope that the answers will also tell me what conditions would lead to this being necessary. $\endgroup$ – SPavel Jan 9 '17 at 16:19
  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – Serban Tanasa Jan 12 '17 at 13:28
  • $\begingroup$ Disposable heat-sinks feature in the video-game Elite:Dangerous $\endgroup$ – RedGrittyBrick Sep 25 '17 at 16:19

15 Answers 15

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TLDR: If you want to dump super heated garbage out the airlock rather than have your ship look like a giant heat sink, go for it.

Heat loss due to radiation (in Watts) is $q = \epsilon \sigma T^4A$.

  • $\epsilon$ is the emissivity of the the object, a ratio from 1 (black body, perfect radiator, to 0).
  • $\sigma$ is the Stefan-Boltzmann constant, about $5.6703 × 10^{-8}$
  • $T$ is the temperature of the body in Kelvins
  • $A$ is the surface area

Let's assume your fantastic space faring folks have perfect radiators ($\epsilon = 1$) made of something that doesn't melt too easy, so it's at 2000 K and is formed into lots of fin shaped vanes (like CPU heat sinks), so it has a high surface area, say 1000 m2. Then the power you can dissipate is 907 MW, or about the size of a small nuclear reactor. That sounds like a lot but this is a space ship. I presume it has cool sci-fi things like big glowy engines, maybe super-luminal drives, laser weapons, shields... lots of stuff that doesn't even work according to our understanding of the laws of physics. It's no stretch to my imagination to say that this ship's reactor outputs 100,000 MW. Maybe it's an antimatter reactor or a hyper dense fusion-black hole hybrid. What in the world are you going to do with all that heat?

Vaporize water and vent it.

Water has a crazy high specific heat, the amount of heat it takes to raise it's temperature 1 deg. According to this table, water at 2000°C and 25 MPa has a enthalpy of about 7 MJ/kg. So to dissipate the heat from your sci-fi 100,000 MW reactor you have to jettison about 14,000 kg of water per second. On the plus side, you might not need anything else for your engines! Compared to my massive 1000 m2 heat sink, you'd need about 130 kg of water per second. In reality we're never going to get that much extra mass into space. In your story, maybe you scoop it up from a super cold gas giant (Neptune?). More plot devices, yay!

Before you ask, I ran the numbers for Tungsten, and at 6200 deg C, past it's point of vaporization, a kg of Tungsten has an enthalpy of ~5 MJ. That's the same order of magnitude as water. So although Tungsten has probably the coolest atomic symbol (W) and a wicked name, it isn't better than water when it comes to dumping heat.

As a plot device I think your idea is great. And as an engineer it does not strain the bounds of my imagination. In fact I think it's more plausible than FTL and a lot of other sci-fi stuff. I've been watching Star Trek the original series and thing that has been bothering me more than any other technical mumble-jumbo is this very issue. The Enterprise with all it's warp drive, transporters and replicators should be turned into a giant ball of plasma by the waste heat alone. If you are telling me that they super heat their garbage and dump it into space I will go back to enjoying the dramatic photography and over the top line delivery.

Thank you.

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    $\begingroup$ I wonder if you could avoid some of the waste heat with room temperature super conductors... No electrical resistance means no wasted electricity and so better efficiency and less waste heat. Also the the electrical lines themselves wouldn't heat up like copper would under heavy loads. $\endgroup$ – AndyD273 Jan 9 '17 at 18:34
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    $\begingroup$ I don't think your CPU heatsink-with-fins analogy really works here. CPU heatsinks work by convection and therefore high surface area (from lots of closely spaced fins) works great. But radiation requires that that the energy be radiated away from your heatsink - which won't be achieved when the surfaces of the fins are amost all facing each other. Only the surfaces which face the outside count towards the radiating area. $\endgroup$ – brhans Jan 9 '17 at 20:02
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    $\begingroup$ @brhans That's a good point. Maybe a 3D fractal/snowflake type design would be more optimal. I wonder if there is some upper limit on radiative surface area per enclosing volume... I feel a nerd snipe coming on. $\endgroup$ – intrepidhero Jan 9 '17 at 20:07
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    $\begingroup$ @intrepidhero No particular 3D geometry will work better for a radiator, all that matters is the 2D projection. I had a similar thought about black body golf balls, do the dimples allow it to radiate more? The answer is no. $\endgroup$ – Samuel Jan 9 '17 at 20:35
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    $\begingroup$ You might want to recheck your tungsten figures. Tungsten is about 5.6 mol/kg, and Heat of Vaoprization alone is about 770,000 J/kg, so I suspect total enthalpy is on the order of 5 MJ, not kJ, and it's right close to water. $\endgroup$ – WhatRoughBeast Jan 9 '17 at 20:41
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Use any ferromagnetic material.

If you want a mix between a consumable based cooling method and engineering feasibility, use a ferromagnetic material, for instance iron.

Using waste heat, melt the metal and spray it into space to dump the heat. The high surface area to volume ratio of the droplets will allow the liquid metal to rapidly cool (radiating your waste heat into space). Now, use an electromagnet to recover a majority of the cooled metal for reuse.

Several advantages here:

  1. The cooling ability isn't quantized by launching discrete bricks of material into space. It's completely adjustable.
  2. You can dial the amount of recovered metal to suit your story or even have your ship engineer modify the recapture on the fly to get them out of a pinch.
  3. It may offer a small amount of protection from micrometers depending on the cloud density.
  4. The magnetic field for cooling material return can double as a radiation shield.
  5. As mentioned by SPavel, additional cooling material can easily be harvested from other ships or (in some cases) harvested from asteroids. Grab the debris and chuck it in the melting pot.
  6. It will look badass. Liquid metal will spew out of your ship and return along magnetic field lines.

enter image description here
Image source

A similar concept was used in the novel Saturn Run. Though they used ribbons of metal that were looped.

Such a method might be required for a spaceship because it simplifies the stowing of high capacity radiators when docking or entering atmosphere. Magnetically suspending your radiator material is a very efficient method for ships that need to sometimes not have huge surface areas.

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    $\begingroup$ The reclaiming idea, plus the military applications, make me wonder if warships couldn't plunder enemy heat sinks as spoils of war. Each side ejects heatsink matter in combat, one side is driven off or defeated, the other resupplies from the debris... $\endgroup$ – SPavel Jan 9 '17 at 22:45
  • $\begingroup$ @SPavel Indeed. It also adds a less-than-lethal option in ship to ship battle. Disrupting an enemy's heatsink field or contaminating their material stream would be an effective method for limiting their ship's operational capacity. At least it would require them to deploy alternative cooling methods. $\endgroup$ – Samuel Jan 9 '17 at 22:54
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    $\begingroup$ There's a name and Wikipedia article for this idea: liquid droplet radiator $\endgroup$ – kwc Jan 10 '17 at 8:01
  • $\begingroup$ Did you make the image yourself? Else, could you add a source link? $\endgroup$ – RudolfJelin Jan 10 '17 at 15:55
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    $\begingroup$ @kwc It's certainly close. Thanks for the link. In a slightly more practical fashion the LDR sprays a liquid onto a collecting sheet. This sci-fi method sprays the liquid onto a magnetic field. $\endgroup$ – Samuel Jan 10 '17 at 17:11
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You would want to avoid using radiators when you are under fire, radiators are pretty delicate and would be destroyed. So this would probably be more of a military application rather than a commercial one.

The reason why heat sinks are not ejected is because that is losing mass, mass that presumably cost a ton of money to bring up out of a gravity well! But you might get away with ejecting a stream of superheated fluid (steam, some other gas, molten metal perhaps) but then you have a secondary thrust rocket on your ship!

But this won't solve your underlying problem, your power plant or whatever is still generating heat that has to go somewhere, so an "ablative heat sink" concept puts a firm time limit on operations. It is probably easier to insulate and isolate a "maxed out" heat sink in order to cool and reuse it later on than to dump it and have to replace it.

Other than combat about the only time I could see this being valuable would be in an environment that doesn't allow for radiative cooling, like operating in/near a star or high radiation environment. Normally you could probably create a shield against the energy source, allowing you to radiate excess heat away into the shadow of the shield (kind of like what they did in the film "Sunshine", IIRC) but if this wasn't possible then you could probably have a totally insulated ship that had to eject superheated waste mass in order to get rid of it. This would work until they ran out of coolant mass, then they would be toast unless they got to a protected area to begin radiative cooling and restock on coolant material.

Additionally, from an in-universe perspective, there may be good reasons why government/military organizations PREVENT commercial ships from having non-radiator based coolant systems. Having exposed radiators will dramatically limit the combat utility of a commercial spaceship and make it easy to track through space (if the radiators are spaced around the ship). Plus it would make it easy to disable and shut down. Other than small back-up emergency heat sinks, it would be pretty reassuring to governments that commercial ships can't suddenly become a rebel navy!

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  • $\begingroup$ Other than Military: Rogue/Mercenary cargo ship that deals in illicit, highly sought-after or otherwise 'dangerous' goods that are likely to draw the attention (and fire) of enemy ships, and thus needs the ability to vent heat in a less-delicate manner than radiators or don't want to glow like a small star on enemy ship's sensors. $\endgroup$ – Robotnik Jan 10 '17 at 4:00
  • $\begingroup$ "or don't want to glow like a small star on enemy ship's sensors." -- compacting all the heat into a small amout of disposable matter will be more visable than a large amount of gently glowing heatsink $\endgroup$ – Andrew Hill Jan 12 '17 at 1:43
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Good Enough...

As other answers have pointed out, radiation is probably good enough for your ship most of the time, assuming they have something close to a blackbody radiator. For most of your ship's functions having some big fins on the outside dumping heat into space is going to be the default behavior. It is simple and gets the job done. Usually...

Until it Isn't

So what kind of atypical scenarios could cause the heat sink to be ineffective/unusable?

The first one that comes to mind is stealth. Space is big, and the distance between things are such that you are going to have to rely on something better than an old-timey spyglass to find anything you are looking for. Radiation from heat is one of the obvious signs of activity if you are looking for a ship. So if you are trying to hide from other ships, those heat sinks are going to be big, bright flags signalling your location. Replacing them with an internal heat sink could help you avoid detection, and jettisoning one or more "full" heat sinks could act as a sort of decoy system while you make your escape.

Another good time to use those disposable heat sinks is when you have some ship function that requires much more energy than usual. Maybe you have a particularly strong weapon, but firing it would overload your usual heat sinks. Like your Mass Effect reference, disposable sinks could be used as a sort of built-in limiter to that weapon's usage.

Or maybe you have the ability to overclock certain ship components in general but need extra dissipation not to damage anything. Give your shields a boost, or run your engine at 125% power, or turn a regular laser into one of the above super shooters. I would actually consider this the best reason to have/need disposable heat sinks, because then their management becomes much more important. Having a couple on hand could get you out of several different hair situations, and running out at a critical moment provides good opportunities for drama.

Reusable vs Disposable

Another thing to keep in mind is that depending on exactly how the extra heat sinks are used, they don't have to be strictly disposable. If they are used normally you could have them build up a material-safe level of heat, then when you have the time set them out into space to cool off. Maybe drag them behind you on a sort of tether.

Conversely, you can use them past that material-safe temperature if you are desperate, which could end up slagging them and making them useless in the future. Again, you could see how that sort of tension could lead to good drama in a story. Do you burn through your last spare heat sink to super charge something, or try to get by with less power so that you can reuse it later?

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    $\begingroup$ Real skyscrapers use water as reusable heat-sinks. At night when electrical load is low, and thus electrical power is cheaper, they freeze ice. Then during the day they melt the ice for air conditioning. Water, being cheap, nonreactive, and having a high latent heat, works well for this application. $\endgroup$ – Phil Frost Jan 11 '17 at 21:26
  • $\begingroup$ @PhilFrost That is a really amusing idea. The ships could basically use space as a giant freezer, and then use the massive ice cubes it makes as the heat sinks. That would make jettisoning them much less of a painful choice, since you can probably find more water on planets or asteroids $\endgroup$ – D.Spetz Jan 12 '17 at 14:11
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Radiating heat into space is done through the age old mechanism of radiators. The Space shuttle had a pair of radiator panels built into the cargo bay doors (hence the doors were always open once in orbit) and the ISS has some pretty impressive sized radiators (although much smaller than the rather spectacular solar array)

enter image description here

ISS showing deployed solar arrays and radiators

For ordinary spacecraft, cargo ships and even military vessels on a normal cruise, this will suffice. Calculating how much radiator area you need can are done using formulas provided in the ever helpful Atomic Rockets site here. There is no sort of general answer, since radiator area will have to be calculated on the basis of things like what sorts of systems are being used, how large is your crew and so on.

The reason for using heat sinks rather than radiators would come from non standard situations. Military spaceships deploying for battle might prefer to pull in their radiators to prevent them from being shot off the ship. At the same time, they are also ramping up high energy equipment like lasers, which will generate a lot of waste heat (once again, vary depending on the type of laser being used). All this heat needs to go somewhere, so heat sinks are the way to go. For civilian spaceships, aerobraking at interplanetary speeds will put a lot of stress on the heat shields, but once again, the conditions don't allow for a deployed radiator to be used while aerobraking, so a heat sink would be appropriate for these kinds of ships as well.

Once again, there is no "one size fits all" equation, since you need to know how much heat needs to be absorbed, what time frame you have (both to absorb heat and if required, eject it through the redeployed radiators) and even what materials you are using in your heat sink. A very low efficiency, low tech heat sink could be made simply by piling rocks in a large cavity and pumping hot coolant inside (some old solar thermal home heating systems did exactly that), while other materials like phase change salts or even large tanks of water or hydrogen could also be used, with vastly different efficiency levels.

One thing which you should consider is that for most spacecraft in a plausible mid future, the "Tyranny or the Rocket equation" will control spacecraft design. While the equations are relatively easy to do, the consequences can be summarized in the expression "every gram counts". Extra mass devoted to heat sinks means either the performance of the ship takes a hit, or you must build an even large ship, in an escalating spiral. Ejectable heat sinks have a certain 'flair", but the extra mass of coolant piping, couplers, valves, quick disconnects and the shaft(s) to eject the heat sink itself will have a very negative effect on ships performance.

What you really want to do is be able to repurpose existing systems to help you out. Fortunately, you can do this!

If your ship is powered by a nuclear or fusion reactor, then in addition to the nuclear fuel there will be a lot of reaction mass. Hydrogen is the best in terms of performance, but ships may choose to use water since it is cheap and easily available throughout the solar system. Since the water needs to be liquid, there will already be a system of heat pipes running through the water tanks, and the tanks have all the associated plumbing needed to fill and drain them. During a space battle, the heat is being shunted into the water tank, and the water is gradually absorbing the heat. You can keep adding more heat until the water starts to boil (and if you are willing to absorb the mass hit, you could make the tanks capable of being pressurized to allow the boiling point to be artificially raised above 100 C). At some point, however, you are dealing with a potential bomb, so the Captain will order "vent steam", and the excess heat leaves the ship in a stream of superheated water vapour. This could even be through the main engine bell, providing a bit of combat thrust as well.

The downside of this scheme is you are now short however much reaction mass was vented, and of course superheated steam could cause corrosion or damage to engine parts when it is vented (if you choose to vent through the engine nozzle. if you use a dedcated port remember there will be off axis thrust being applied to the ship).

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    $\begingroup$ The thing that would really help this answer is some hand drawn arrows pointing out the radiators in your picture. $\endgroup$ – Erik Jan 9 '17 at 21:34
  • $\begingroup$ @Erik: The radiators are those whitish long strips perpendicular to the copperish solar panels. $\endgroup$ – AlexP Jan 10 '17 at 0:40
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    $\begingroup$ @Erik No, it must be free hand red circles. $\endgroup$ – jpmc26 Jan 10 '17 at 13:08
  • $\begingroup$ @jpmc26 I stand corrected :) $\endgroup$ – Erik Jan 10 '17 at 14:53
  • $\begingroup$ @Erik Also the pair of white triplets on either side of the module stack in the center. These things are big, btw. One of those white panels is about six feet by eight feet. $\endgroup$ – Tristan Jan 10 '17 at 15:40
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reasons not to use plain ol' radiators

Stealth. You do not want to transform your ship into a infrared flare broadcasting your positions to all and sundry.

Wear and tear. When operating in hostile zones, or even if the space is reasonably "dusty", you don't want to have fragile radiators and cooling tubes possibly full of fluids on the hull.

alternatives

The "disposable heat sink" would require some substance with very high thermal capacity (specific heat by mass), or capable of resisting to very high temperatures. In the first case you can use water, or slightly better, ammonia (even if it's toxic). For solids, you can use lithium, which melts at 450 K; aluminum melts at more than double that, but has a fourth of lithium's thermal capacity. Spraying superheated vapors could double as propulsion.

At the same time, ejecting superheated pellets isn't too stealthy.

Unobtainium-laser cooling. There are substances, such as water, where laser energy can induce a transfer of vibrational energy from the modes that we call "temperature" to more exotic modes. The net result is a decrease in temperature, and a capability to ingest additional heat. What you need is some substance like unobtainium fluoride, which exhibits the same laser-coolness of water, but a lot more so. Then you have your not-necessarily-discardable heat sump. You could do this with water, but you would need a lot of it. Why would you then discard the "full" heat capacitor? Well, because after some time, those exotic vibrational modes decay, the heat reappears, and the heat capacitor explodes. The fluoride compounds are a nightmare to manage, so the capacitors might double up as space mines for the unwary, if you can manage to jettison some on the appropriate trajectory during a stern chase.

But still not very stealthy (well, they are, until and unless you overcharge them past the capacity of the passive radiators, and are forced to jettison).

superradiative cooling. You have one boatload of low-level thermal energy. This will radiate according to Boltzmann's law, at a not-so-great rate. So what you do is pump it to a higher temperature. To do so you need to expend extra energy, so you now have to get rid of one boatload and a half. But doubling the temperature, emission rate gets multiplied by sixteen. At four times the original temperature (in kelvin degrees) you get a 256-fold increase in emission. Now a small radiator can get rid of a lot of heat. Also, it can do so directionally. Place the radiator in the focus of a parabola, and you get a heat ray that can be pointed away from most curious eyes... possibly not straight away, or the Gegenschein might still be detectable.

To recap, you can:

  • in relax, radiate through low-cost passive radiators.
  • when wary, you cool the radiators and dispatch the heat through superradiative cooling.
  • when you need stealth - for short periods - you pump the heat internally in heat sumps and hope to be able to dump the heat normally
  • if they get overcharged, stealth goes to hell anyway, and you have a short time before you jettison them; or you can vent ammonia or water to get rid of the heat and do an "emergency discharge".

I remember some sort of "laser cooler" using a X-ray laser propulsion system being used in David Brin's Sundiver.

Also I remember a story possibly in Poul Anderson's Polesotechnic League where a ship was trying to mask its heat, but got betrayed by the heat that it had released hours before - traveling at the speed of light, it caused a detectable excitation effect [it would have required handwavium CCDs, I suspect] in a solar system's dust. You can get an idea of what that would have looked like by watching V838 Monocerotis's nova echoes (they appear as material expelled from the star, but NASA says they're not).

(Unfortunately, in space no one can hear you scream, but it appears that everybody can see you take a heat dump. And with planetary distances in play, light speed effects need to be considered).

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  • $\begingroup$ Haha, "take a heat dump." I guess ships wouldn't want to be seen dumping their heat in polite company! $\endgroup$ – SPavel Jan 10 '17 at 12:56
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Use the vacuum to help cool the ship. Specifically, have several enclosed/mostly enclosed spaces that are transparent to IR and that is pumped to a vacuum. Use water to absorb the heat, and then spray the water into this vacuum chamber.

Because water boils at a very low temperature (-67 C) in vacuum, it will flash into vapor, and then crystalize into ice as the heat radiates off into space, before sticking to the chamber walls. When the chamber is no longer at sufficient vacuum then the water is diverted to the next chamber. Then the ice is collected and the chamber is pumped back into a vacuum state for the next round.

You could do this pretty easily by venting it to space once the majority of the atmosphere is pulled out. There would be some losses, and the ship may need to eat a comet once in a while.

For the dramatic tension you could have an accident vent a large amount of water to space, and so a source of water needs to be found quickly before things start to overheat.
This can be prolonged a bit by turning off non essential systems.

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    $\begingroup$ Unfortunately that's not how that works. The vacuum of space has a thermal capacity of zero, because there's nothing to have a thermal capacity. It's not hot or cold - temperature is meaningless because there's nothing to have a temperature. All you'd accomplish by doing this is spraying a room with warm water vapor. Any heat radiated away would be instantly re-captured by the walls. This is why sinking heat in a spaceship is so difficult - The only way to get rid of it is to dump it overboard with infra-red radiation, because there's no material to carry the heat away by conduction. $\endgroup$ – UIDAlexD Jan 10 '17 at 19:21
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    $\begingroup$ @UIDAlexD Except that as it turns into vapor it would have a high surface area to volume ratio, which will allow the liquid to rapidly cool, radiating the waste heat into space through the IR transparent walls. If you do a little research you'll find that when astronauts urinate on a shuttle the liquid is vented to space. The liquid instantly boils, then freezes, then desublimates into urine ice crystals. You'd probably want some kind of a wiper to scrape the desublimating ice off the walls to keep it from blocking the IR radiation from escaping. This is a radiator, but with more surface area. $\endgroup$ – AndyD273 Jan 10 '17 at 20:22
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    $\begingroup$ My apologies, I completely missed the IR Transparent bit. Guess the morning coffee is wearing off. That said, how does this make them different from a regular radiator, aside from the phase-change? $\endgroup$ – UIDAlexD Jan 10 '17 at 20:26
  • $\begingroup$ @UIDAlexD No problem. I think it needs to be a mostly closed system, because anything you throw away has to be replaced from somewhere, and space has a lot of empty space with few resources. As is you'd need to replenish water and oxygen semi regularly. You'd want to design systems to produce as little waste heat as possible. $\endgroup$ – AndyD273 Jan 10 '17 at 20:32
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Heat sinks are only feasible for dumping a limited amount of heat, their capacity is limited by material and achievable temperature.

We don't use heat sinks in applications that need continous operation, except in cases where the heat sink can be continously replenished (e.g. river water cooling for power plants).

The main problem with using a heat sink for spaceships is that spaceships presumable use a lot of energy, and in turn generate a lot of heat to be dumped. This doesn't combine well with the fact that whatever you'll be using as a heatsink will add weight to the ship, in turn increasing the energy output needed.

Some gases, water and plasma have a high energy per mass unit for heating (called https://en.wikipedia.org/wiki/Heat_capacity#Specific_heat_capacity), but the gases have the drawback of increasing pressure with temperature and plasmas are already hot to begin with and thus, hard to contain in bulk. That leaves solids and liquids as usable materials, and these are generally limited to around their boiling point or the point where they chemically decompose (either way they do become gases at some point).

If you look at water, for example, it has a notably exceptional specific heat capacity. But still, to dump really large amounts of heat (talking at least gigawatts here, probably more) you need a lot of water.

That makes heatsinks not a good choice for getting rid of heat that is continously produced, radiators are the way to go.

However reclaimable heatsinks are an excellent way to buffer short peaks in heat production, so heat sinks would possibly be employed to cool systems that produce huge amounts of heat in very short bursts (e.g. weapons). The heat sink takes on the majority of the heat, then a cooling system radiates away the heat stored in the sink over time and the system is ready to go again.

So, in spaceships heat sinks are more likely to be employed in a buffering function, not as primary method of heat disposal.

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For the heatsinks you'd want substances with the highest heat capacity (the amount of heat it needs to go up in temperate, pretty self-explaining name).

Currently they are... Water, and ammonia. Ammonia is what the ISS uses to transport heat to its radiators: https://www.nasa.gov/mission_pages/station/structure/elements/radiators.html#.WHO_gFPJyHs

There is a series of tubes that are routed throughout the radiators, and ammonia is circulated through the tubes.

So you could plug your heatsinks directly into your radiators. Convenient! Specially given that radiators work better the hotter they are (see Steffan-Boltzmann law).

Now, when would your heatsinks need to be ejected? Depends.

The heatsink concept has to face a truth: Heat flies away from where it's hot.

You have to push heat into a heatsink, and that costs energy. And producing that energy usually comes with waste heat (depends on your energy source, and you are in the sci-fi range here). Eventually, you'll be producing as much heat as you are pushing. At that point you should just stop pushing and let the heatsink be for a while until it cools down.

But maybe your heatsinks (which would likely be essentially pressurized gas tanks) would go boom before reaching that equilibrium point. Then your space captain has to take into account the possibility of ejecting the heatsink.

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Combat would be the primary reason I would expect to eject mass to dispose of heat.

Assume you have energy based weapons. Inverse square law dictates they are a lot more effective at close range. So you absorb the energy from your opponet firing (and use it to superheat water) The ejected water acts as a maneuvering jet to accelerate more rapidly. So you absorb the energy of an attack and use it to accelerate to a position where your weapons do considerably more damage.

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Let's break this down a bit.

What conditions would render disposable heat sinks necessary?

As has been noted already: combat and stealth. Radiators can be damaged, and will give your ship a nice big heat signature that'll stand out against the vacuum of space (assuming your ship's thrusters don't already do that). Dump that heat in an internal heat sink instead and you'll be much harder to spot.

So to use your original idea, a cargo ship could use disposable heat sinks to avoid detection by space pirates or, if it's illegal cargo, the authorities. As for combat, small/medium ships could use them to avoid detection by enemies, and larger ships... I'll get onto that later.

How much heat would the ship need to generate, and what would require that much energy?

Again, as has been stated, sustained laser fire will very quickly build up a lot of excess heat that would ideally have to be dumped in heat sinks. During normal flight, the heat sinks might not need to absorb too much energy, or even any at all if your ship also has radiators - but that's a good thing, as you don't want to be ejecting and replacing heat sinks every five minutes.

What would its heat sinks be made out of?

Whatever it is, it needs to be able to store as much heat as possible, so a substance with the highest melting point or thermal capacity you can get. The obvious answer is some kind of unobtainium, but failing that you could go for tungsten or lithium, as has been suggested, or just plain old H2O.

[Just having radiators is] boring.

Honestly, I feel like just ejecting the spent heat sinks is kinda boring too. Let's weaponize them. Instead of one big heat sink, have loads of smaller ones all over the ship - they'd be easier to fit into the design, easier to dispose of and replace, and easier to use for what I have in mind here.

Taking all the above into account, the heat sinks would probably get the most use during combat scenarios. Put a futuristic railgun on your warship and you can then either eject the spent heat sinks (if it has nothing to fire them at, or to act as decoys like @D Spetz suggested), or load 'em up and fire them at enemy ships. A big chunk of metal heated to several thousand degrees Celsius and travelling at God-knows-what-velocity is gonna do a fair amount of damage.

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    $\begingroup$ +1 for "Let's weaponize them." Transfer your cooling problem to your enemy. Now I want to play "Elite:Heat wars" $\endgroup$ – Gavin Lock Jan 10 '17 at 14:43
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Heatsinking material makes sense in some applications. Before I go on to those, we need to clear something up first.

You can never, ever have stealth in space.

You are a material object in a sea of nothing. Any and every active and passive sensor will be able to detect you, from RADAR to LIDAR to a simple Telescope. Worse yet, you're literally glowing in the IR spectrum because of your waste heat. So why don't you just paint your ship black, make it RADAR stealthed, and cool the hull to a few K above absolute zero?

Because you can't. Even if you get your internal systems to run on just a few watts of power at 99.99% efficiency, you're probably going to be flying near a Stellar-scale fusion reactor called the Sun, which is constantly bathing you in infra-red and visible-light radiation. That's a lot of thermal flux to contend with, and in space that means Radiators.

You might say you can dump it all into heatsinks and jettison them, and you're right, but you still don't get anywhere. Jettisoning a heatsink advertises your position with a flare a thousand times hotter than your own signature. Firing up your engines to move away from it creates a superheated plume of exhaust and creates massive amounts of engine-heat for you to sink, eject, and again run away from.

TL;DR, Stealth is a losing game

Here's where expendable heatsinks make sense

Battle

Weapons make heat, and the reactors to power them make more. You can use absolutely titanic radiators to get rid of it, but those are massive and fragile. Instead, use some kind of open-cycle cooling to augment the performance of smaller radiators. Get the idea of thermal clips out of your head, it makes a lot more sense to spray the radiators with water, or pass expendable coolant through a secondary cooling loop that vents to space.

The advantages are twofold: First, you get to re-use your small, light, low-demand radiators. Second - and more interesting - is that you do gain a kind of stealth from this. You are now one heat-signature against a cloud of heated gas. Picking your tiny and cool signature out from that massive, hot cloud is going to be non-trivial

Spike-Demands

Firing Engines. Cranking the reactor to 100%. Using the coffee maker. Anything that makes waste-heat and eats power but isn't on for most of the trip. Same approach as battle: Open cycle cooling by passing high-thermal-capacity liquids over or through your existing radiators and dumping them to space. Advantage of this is that it saves the mass and fragility of a huge radiator that you won't be using 99% of the time. Disadvantage is that your usage of these systems is now limited by how much expendable coolant you can spare.

Emergencies

This is like Spike Demands, but with a twist: Some of the normal radiators are damaged or destroyed. The reactor needs 4 radiators operational or it will melt down, but only two are operable. The solution? Switch the remaining two to open cycle mode, spending your limited coolant to keep it active for a few more hours. Has all the same disadvantages of Spike Demands, but this time they're mission-critical systems. Advantage is that you gain lots of Apollo-13 style dramatic tension, but instead of powering down to save battery life, you've powered down to save coolant so the fusion reactor doesn't go nova.

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Power is energy. Heat is energy. You'd ideally just recycle the waste heat back to re-charge your drive, and save fuel. If you have too much heat in battle, use it to power your shields or weapons -heat up your kinetic ammo and fire it at the enemy or convert the heat to electricity to power your rail guns. In Stargate Atlantis, the Ori used the bombardment of their shield (and the detonation of a gate-buster nuke) to power the growth of the shield itself, until the shield completely enclosed the planet.

In The Mote in God's Eye by Larry Niven (& Jerry Pournell?) the Langston field modified by the Moties expanded as it heated to create a greater radiator surface - thereby extending the life and improving the efficiency of the shield (although as the Motie ships warped into the outer atmosphere of a red-giant, the larger surface area thing was a major disadvantage - but these guys are thinking too small (and Niven dreamed up Ringworld!)

If you really need to radiate lots of heat, just unfurl a gigantic (I mean GIGANTIC!!!) sheet of conducting material behind your ship (like something made of carbon nanotubes like vanta-black). It can be a few molecules thin, will have a massive surface area to mass and can be pulled back in after use. It can have a STUPENDOUS surface area. THOUSANDS of kilometres square if needed. It won't drag your ship as you're in a vacuum. It would show up on your enemy's scope as infra-red, maybe presenting a huge but pointless target. You could equally deploy it around your ship to mask your own heat signature as a stealth tool if it was cooled to the same as local space.

More likely you'd need something that size to harvest solar energy or starlight or as a lightsail. Modern machines are pretty efficient at using their power but you have to get the power from somewhere.

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The PC game Elite:Dangerous uses exactly this mechanism to make the craft harder to detect. I don't know if that's the source of your curiosity or why no one else mentions it. I think it is an unreasonable system to use continuously just because of the mass of the required heat sinks you'll have to carry and then dump. Simply put, even if you heat it up ten times more than your engine/craft would have heated up by the energy you want to get rid of, it'll need to be 10% of your engine/craft's mass. That is quite significant. It could be acceptable for a one-off trick at a key point, or even scaled up to a couple charges, but the number would always remain very limited and its use will have to be very selective and strategic and not be the main means of removing heat over a long journey.

If the reason you want this is indeed stealth, some method of focused radiation seems more appropriate.

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Ejection == propulsion

Anything you eject from your ship will produce an equal and opposite force propelling you in the opposite direction. I would suggest the logical solution therefore is to integrate your heatsink and propulsion technologies. One way of doing this might be to use water and vaporise to provide both heat dissipation and propulsion. There are large stores of water in space which could be mined and directly transferred to your ship in space.

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