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Generating physical effects with energy generates waste heat. Using a lot of energy, say, by firing a rail gun or a MW laser, generates a lot of heat. A discussion of waste heat issues can be found at Atomic Rockets.

If you are running a star cruiser, and you want to blast a pesky rebel frigate, you might want all your lasers blasting away at once. But that is, again, going to generate a lot of heat.

The simplest way to get rid of waste heat is to build giant radiator units into your space ship, like you might see on top of a CPU. But this gives our space cruiser a 'glass jaw;' simply destroy the (flimsy) radiators and our ship will overheat itself and cook its crew while firing.

I want a method of getting rid of heat during times of high weapon usage. This could be accomplished by getting the heat into some sort of gas, and then venting the gas over the side. What is the most efficient way to vent waste heat into space during a space battle?

In this case, most efficient means the most mass and energy efficient way of getting rid of the waste heat. Keep in mind, the waste heat won't be super high temperature; it is whatever temperature the housing of the laser or mass driver gets up to after a few shots are fired.

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    $\begingroup$ I don't know anything about hvac or spaceship systems, but the word "hydrocoil" came to mind so I looked it up. Turns out they can be used as a method to "dump excess heat". From the Hydroduct hydrofoil applications literature: "NOTE: HEAT SOURCES MAY BE WATER HEATERS OR BOILERS OF VARIOUS TYPES, HEAT PUMPS, OR ANY OTHER DEVICE THAT CAN BE USED TO PROVIDE HEATED WATER. FUEL SOURCES CAN BE, BUT ARE NOT LIMITED TO, ELECTRICITY, GAS, COAL, FUEL OIL, LPG PROPANE, SOLAR, WOOD, GEOTHERMAL, BIO- DIESEL, OR WASTE HEAT FROM ENGINES, GENERA- TORS, ETC." It doesn't exclude spaceship engines. $\endgroup$ – N2ition Sep 19 '18 at 1:22
  • $\begingroup$ Here's the link to the resource I quoted in case the diagrams there are helpful. There's tons of resourceful people that can mod anything to tweak it to a specific application. HYDRO-DUCT™ SERIES HYDRONIC FAN COILS PDFhttps://us.v-cdn.net › uploads › FileUpload $\endgroup$ – N2ition Sep 19 '18 at 1:26
  • $\begingroup$ @N2ition, yeah, it does exclude spaceship engine. The word "fan" is the first clue, unless interplanetary space is full of air. $\endgroup$ – Keith Morrison Sep 19 '18 at 20:23
  • $\begingroup$ @Keith Morrison I was assuming there would be gravitational and air handling systems on board as well due to human passengers. However, now that you point it out, it could be robotic or non air breathing occupants, or remote control ship. Also might be nice if rather than venting the heat out to convert the heat into different energy source internally so as retain use of resources. $\endgroup$ – N2ition Sep 20 '18 at 20:59
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You Won't Need to Do Anything Fancy

More than about 5 AU from a star, interstellar space averages around 2 degrees Kelvin in temperature.

The radiant power equation is:

$ P_{radiant} = A \epsilon \sigma T^4 $

Where $ \sigma $ is Boltzman's constant = $5.67 \times 10^{-8} W \times m^{-2} \times K^{-4}$

Assuming your ship radiators aren't very hot (25 $^0C$ / 300 $^0K$), are pretty good ( $\epsilon$ ~ 1) and you can make use of the entire surface area of your starship to radiate, you get 459 Watts per square meter of heat radiating ability. For, say a 1 GigaWatt laser producing 1% waste heat (10 MegaWatts of waste heat) would need a patch of hull 150 meters (~450 ft) on a side.

Which you can tweak by increasing your ship surface area through techniques like ridges (like a CPU heat sink). Say, an x8 multiplier using carbon nanotube forests to increase surface area brings that down to an 18 meter (55 foot) square of reserved hull space.

The efficiency of this system would drop as you get closer to a star and the average temperature begins to increase.

You could, alternatively, dump all of the heat into some high heat-capacity gas and vent it overboard to save space. Water is a good high heat-sink gas, soaking about 2,257 Joules per gram of water (a Joule is 1 Watt applied for 1 second).

Applied to the same 1 gigawatt space-laser with 1% waste heat lasing for 1 second (just to make the math easier), you'd need to dump 4.43 kilograms of steam overboard per firing. Which is not unreasonable.

But If You Do Decide for Fancy

The absolutely most time, space, and mass efficient way to dispose of waste heat is to recycle it. Fusion reactions past iron on the periodic table are endotropic, meaning it takes a net consumption of energy to make the change from two heavier-than-or-equal-to-iron atoms. And the amount of energy consumed is on par with any other atomic reaction being in around the 0.1% to 10% of the mass-energy involved (roughly 9 Terajoules per gram). Provided some handwavium technology that allows waste heat to be redirected in this manner, you could store a lot of waste heat in this manner.

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    $\begingroup$ You have right, radiant power is enough, but remember that you can't just have 150 meters of the hull to dispatch heat. It must be transferred by some way the heat to all that surface (otherwise only a small part of the hull will be really hot). Maybe steamed water could be used to transport heat to the whole surface. +1 $\endgroup$ – Ender Look Sep 19 '18 at 2:05
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    $\begingroup$ 99% efficiency lasers seems a bit optimistic. For a 50% efficient laser, the calculations look a lot different. I'm looking for an answer that involves venting something. $\endgroup$ – kingledion Sep 19 '18 at 2:15
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    $\begingroup$ I am not sure if it was considered, but you have think about vacuum behaving differently than air. Heat conductivity is also a factor, along with surface area and mass. Metal for example has a higher heat conductivity than wood, meaning even though the temperature is the same, we "feel" as if metal is colder. Vacuum is literally nothing, meaning there is nothing that could absorb heat, which is why it is used to insulate thermos bottles for exchanging heat with anything outside. Passive heat radiation may not be sufficient. $\endgroup$ – Battle Sep 19 '18 at 5:36
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    $\begingroup$ Worth noting that with a ‘forest’ the increase in energy radiated to space is lower than the increase in surface area as the energy gets recaptured by the other radiating towers, so there’s diminishing returns there. $\endgroup$ – Joe Bloggs Sep 19 '18 at 6:38
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    $\begingroup$ The more effective lasers for space combat (EUV or soft X-ray lasers - en.wikipedia.org/wiki/X-ray_laser) are not very efficient at all and you would be lucky to get 10% of the energy input as usable signal, the rest of the energy input is just so much waste heat. $\endgroup$ – GretchenV Sep 19 '18 at 13:20
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I'm going to break my answer up into two sections; first, which gas would be best suited to this task. Second, what process would be the most efficient.

Best Gas
I'll be blunt. Water. But! (I hear you all cry out,) Water isn't a gas! Well, no, it's not. But steam is. The thing that water has going for it is that it has a really high specific heat capacity - 4.18 J/g/C° and water itself is really dense in a liquid form, making it the ideal thermal mass. Based on the specific heat capacity (SHC), it takes around 40 kJ just to heat a litre of water up by 10 C° or so, and its density means that you can store a lot more heat in a much more enclosed space.

This kind of thermal mass property is exactly what's often used to capture waste heat for future use; The capture of waste body heat in a Stockholm train station uses precisely this method to capture and reapply the heat, so this is an approach that's already understood.

In short, your 'cooling gas' is steam.

Best Venting Method
Don't. I mean, sure; you could just vent the steam into space, but the water (even with the heat in it) is still far more useful to your ship and finding another method to disperse the heat means that you don't have to carry water (which is heavy) as a consumable resource. If you use it that way, you're always carrying far more water than you need, and given the high density and mass you're working with, that's not a good thing.

But, water (and steam by extension) is very useful. Don't let it go to waste, but extract the energy back out of it for your own purposes.

The first and most obvious use for it is to drive a turbine. Use your battle's waste energy to power a generator that allows you to run your ship's critical systems off an alternate power source, leaving your main engines for maneuvers and weapons. Also use it to keep critical sections of the ship warm via internal radiators, allowing you to switch off the normal life support system, again conserving your main reactor power.

Finally, when the water is just TOO hot, create a small section inside the hull that is empty and open to space (behind some serious hull shielding of course, preferably between the living areas and the engines, and put your radiators there to dissipate the heat.

Doing all this gives you an unanticipated benefit that makes you truly feared among all the space lanes:

Your ship is a steampunk cruiser.

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  • $\begingroup$ Water is your fuel, the stuff you throw away so that you move $\endgroup$ – Garret Gang Sep 19 '18 at 10:45
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    $\begingroup$ You're not providing any benefit trying to "recycle" the heat because you need to get rid of it in the first place; trying to keep it inside the ship is merely compounding the problem. $\endgroup$ – Keith Morrison Sep 19 '18 at 20:26
  • $\begingroup$ @KeithMorrison What water does in this instance is distribute heat, rather than retain it. Sure, take your steam directly into space via protected radiators if you like, but driving a turbine at least makes use of it during the cycle, and keeping rooms warm against the entropy of space also makes sense on its way to those same radiators. What I'm really saying is that if you can, you should be running your ship on waste heat, not your main reactor (if possible) so that all new energy is prioritised for combat expenditures. $\endgroup$ – Tim B II Sep 22 '18 at 8:28
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Dispatch the heat with the bullets

This isn't exactly an efficient way but I think it's cool and also practical because it takes advantage of something that you already have and use in combat, for combat cooling.

You said "[...] by firing a rail gun [...]" and I've understood that railgun use ammunition to work. You could transfer the heat of your ship to the ammo of the gun, then shoot that ammo to your enemy.
By that way you:

  • Dispatch your heat excess.
  • Overheat your enemy.

To transfer the heat to your ammo you just need to use heat pump, like the AC or freezer of your house, just... bigger.

A heat pump is a device that transfers heat energy from a source of heat to what is called a heat sink. Heat pumps move thermal energy in the opposite direction of spontaneous heat transfer, by absorbing heat from a cold space and releasing it to a warmer one. A heat pump uses a small amount of external power to accomplish the work of transferring energy from the heat source to the heat sink.

It works using the heat pump cycle. In that link, you can find several ways to make a heat pump.

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    $\begingroup$ Railgun bullets are tiny, and the railgun itself requires massive amounts of energy, so this implies incredibly efficient power sources with near-100% efficiency, which is beyond anything we can come up with today, but can work for far-SF. $\endgroup$ – Eth Sep 19 '18 at 16:57
  • $\begingroup$ @Eth, personally I don't think that railgun for spaceships would have so tiny bullets, are you sure? I haven't understood why you said about efficiency... a heat pump is a heat pump, it's already quite efficient moving heat from one place to another. $\endgroup$ – Ender Look Sep 19 '18 at 17:11
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    $\begingroup$ Railgun bullets are necessarily tiny compared to the ship, the same way a shell is necessarily tiny compared to a tank. You need to accelerate at extreme speed, you want to store quite a few of them... Then, the problem with heat pumps is that to move heat around. Basically, if you want to double the temperature (in Kelvin), you will generate several times more heat than you will move, which makes it a loosing battle very fast. $\endgroup$ – Eth Sep 19 '18 at 19:51
  • $\begingroup$ @Eth, but heat pump generates less heat than the amount they move: "In heating mode, heat pumps are three to four times more effective at heating than simple electrical resistance heaters using the same amount of electricity." (Wikipedia) $\endgroup$ – Ender Look Sep 19 '18 at 20:13
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    $\begingroup$ This is when the temperature difference is small (as mesured in Kelvin as a fraction of each-other - so cooling a 300 K (27°C) to 290 °K (17°C) is vastly more efficient than cooling a 600 K (337°C) to 300 K (27°C). And to heat up those bullets enough to dump the whole energy of a non-near-perfect system (let's be extremely generous and say 90% efficiency, we're far beyond any form of heat engine at this point), you would probably need to heat them up to several thousands of °K just to get rid of enough heat, meaning that you just produced dozens of times more of it... $\endgroup$ – Eth Sep 19 '18 at 20:22
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Choice of coolant

Water

As others answers mentioned, the best coolant is water, at the range of temperatures you can expect for your laser. It absorbs heat fast (great thermal conductivity), absorbs a lot of it to raise 1 kg by 1 K (great specific heat), and absorbs even more when melting (great latent heat of fusion) and when evaporating (great latent heat of evaporation). Note that you would store it frozen to get the full benefit of it.

It also makes for a rather good propellant for nuclear-thermal or nuclear-electric drives, so your ship is probably carrying those as propellant, not lugging otherwise-useless tanks of heat sink.

Hydrogen

If your tech needs cryogenic temperatures, liquid hydrogen is by far the superior option. It has the best specific heat ever, and a pretty good latent heat of evaporation.

There is in fact a hypothetical type of spaceship that achieves partial stealth by being a giant tank of liquid or frozen hydrogen and a Vantablack coating, the hull being cooled down by evaporating hydrogen to an extremely hard to detect 14 K. (See details on Atomic Rockets) Whether or not the stealth aspect itself would work is up to debate, but the ship itself, if big enough, could stay out there in the sunlight for years at a time - hydrogen is that good.

On the other hand, hydrogen is absurdly low-density, and armoured warships may want not to have giant fuel tanks. Either they would be exposed to enemy fire or they would require vast quantities of armour. And armour is heavy, which is bad for a spaceship. As you probably read many times on Atomic Rockets, every gram counts.

Similarly to water, those hydrogen tanks are probably your propellant in the first place. Hydrogen is the most efficient thermal propellant by mass, after all.

Sodium

If you need to deal with very high temperatures and don't want to use water - which can be corrosive or even dissociate in hydrogen and oxygen - you may want to go for sodium.

Its specific heat isn't that great compared to the others, but its boiling point is much higher. It is in fact used as coolant liquid in some nuclear reactors.

So while it wouldn't be your propellant, those sodium tanks would instead be your coolant reserve. Again, you would have it anyway, and sacrificial heat sink would be an emergency secondary use.

Radiators

In a spacecraft, anything bigger than a short-range capsule has radiators. The ISS has them (those big accordion panels at an angle with the solar panels), the Space Shuttle had them (lining the inside of the cargo bay doors)...

Future spaceships, especially warships, will have enormous power sources (be it powerplants or even often the drives themselves) that will need enormous radiators to get rid of the waste heat.

Note that varied components will have varied ideal temperatures, for example crew quarters at 300 K and nuclear powerplant at 1400 K. While you may be tempted to use heat pumps to equalise temperature, it adds complexity and is impractical for large temperature differentials, where they become massively inefficient.

Instead, each component with a different temperature will have its own sets of radiators. Probably small ones (like on the ISS) for crew quarters and bigger ones, possibly glowing red, for the powerplant. Some for your cryogenic components (like those water tanks as well) Maybe some more for varied weapons as well.

In general, when designing a component, you want it to have a working temperature as high as possible. That's because the radiator efficiency goes up with the fourth power of the temperature. And you want your radiators to be as small as possible, because not only are they heavy but they also make for great targets.

The upside is that radiators are visually awesome and make your warship look badass. Nothing conveys (quite literally) a sense of power like two giant orange-glowing sails.

Venting heat sinks

So your star cruiser has retracted its radiators to avoid getting them shot. Or some of them have been ripped off by enemy fire. Or its weapons generate so much waste heat that even its full radiator complement can't get rid of it all in combat conditions. Heat sinks are filling up...

Why vent them?

Ideally, you want to keep them around as long as possible. After all, once combat is finished, or even if orbital mechanics temporarily put you out of range, you can then use your (remaining) radiators to cool it back down.

The problem starts when it vaporise. Which is almost immediately with liquid hydrogen. With water, you have some more time, and sodium, as noted above, would only go so hot in case of emergency.

Now, you could keep it under pressure to prevent it from vaporising in the first place, which is probably only practical with sodium. It is easier to harden a coolant system than giant propellant tanks, hot hydrogen tends to escape through walls and hot, supercritical water is one of the most corrosive substances there is.

But if you prevent it from vaporising, you can't make use of its latent heat of vaporisation. In case of emergency, you may simply not have the choice.

So it start vaporising, then. Its volume increases massively - for example, water vapour takes about 1250 times more volume than liquid water. You simply don't have the volume to keep it on board.

You could use it to fill a balloon, but that means you are lugging around a rather massive balloon around just in case (which is very bad - again, every gram counts), and that thin, unprotected balloon will make for a nice big target for the enemy.

So when things get that hot, keeping it on the ship is simply not an option.

Venting it - water or hydrogen

With water and hydrogen, in fact, that's already part of the design. Remember, those are your propellant first and your heat sink second. So to vent it, you send it to your thrusters.

The thermal drives you are probably using right now works by heating up the propellant as much as possible and then letting it expand as much as it wants through the nozzle. Today's chemical rocket drives are a special case where the heat is produced by a chemical reaction between the propellants, and the byproduct of the reaction escapes through the nozzle. Your futuristic drive is probably heating inert propellant through a nuclear reaction (nuclear-thermal) or with electrical power, itself from a nuclear powerplant (nuclear-electric).

In fact, this is already used today, with regenerative cooling: rocket nozzles get so hot that to stop them from melting, still-cold propellant is sent flowing in its walls before going to the reaction chamber.

Here, it's the same thing, except that the propellant is flowing through your coolant system and/or varied component first.

So what it looks like? Your engines are used. If you can't afford to use the engines in the first place (maybe because it would add more heat than you can spare), then it will look like cooler water vapour/hydrogen is flowing from it, which will generate less thrust. You may or may not see some white in the plume as expanding (and thus cooling) water vapour condenses into crystals in that case.

Note that in space, even when working at full thrust, those drives are rather hard to see. The plume may be entirely invisible, and you would see it working only by the ship moving and innermost parts of the nozzle being heated white.

Venting it - sodium

If you can, try and vent sodium vapour through your nozzles as they are firing. This will give you a little bit of extra thrust as the heavier atoms are used as propellant, which is always good to have. This may colour your plume orange, I suspect. If so, this would make for great visuals, as orange plumes show how desperate the fighting warship has become - either because they overheat or because they need every little bit of extra thrust.

But this may not be an option. After all, sodium may condense against the nozzle interior or some component of the chamber, and mess everything up. They may clog something, interfere with nozzle cooling or even fracture it with heat differences. Or your drive may simply not allow it, for example if you use Orion-style external nuclear pulse propulsion (aka pushing a plate with nukes) or other nuclear-detonation-based systems.

So your warship's coolant circuits may have escape valves. Those will probably look like tiny thrusters, and have doors to close them when not in use. When heat or pressure in the circuit is too high, they open and let sodium vapour escape.

They are, essentially, thermal drives, just like your main drives but using sodium instead. Sodium being heavy, it gives good thrust but bad efficiency, and can be seen as such as far as movement goes. They will be shaped like your main drives, for thrust efficiency, but that's because you want the plume to diverge as little as possible (which is the same here). After all, you don't want the plume to hit your ship's hull and condensed sodium and coat everything.

For the same reason, they may optionally extend when in use, so the venting point is as far from the hull as possible - but remember, it will have to be a rigid bar instead of a simple hosepipe, or the thrust will send it flying against the hull.

Given the temperatures, it will probably glow orange at exit point, turning red just a bit further in the plume (at those temperatures, it cools down fast), then as a thin cloud of condensed sodium droplets. Given the energy, it will disperse fast, and disappear pretty much instantly as soon as it stops venting.

Venting itself will probably be done in short bursts, to use only as little as necessary, and to avoid exposing a firing valve as much as possible.

Addendum: why thermal drives?

Thermal drives are much more efficient than chemical drives (though they generally give less thrust), but their mileage is rather awful compared to electric drives like, say, ion engines. So why would the star cruiser use thermal drives instead of those?

That's because for a given energy, you can either have great thrust (chemical drives), great efficiency (electric drives) or a balance (thermal drives). And you can use only so much energy in a drive before it vaporises.

So those electric drives have awful thrust. Which is OK for an interplanetary probe, but your star cruiser will probably need to manoeuvre, for example to avoid incoming enemy projectiles or avoid spending months or even years getting out of deep gravity wells.

The star cruiser may also have a set of electric drives with milligee thrust for slow, interplanetary manoeuvres, when it has time for long-duration thrusts and no giant lasers to eat half the powerplant's output, but it will probably run on thermal drives when fighting.

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How to move heat: convection, conduction, radiation.

Convection; wasteful because you lose gas mass. Conduction - there is no place in space to conduct to. Radiation - that is the option. And you have lasers!

Concentrate your heat and use it to power a laser. Then shoot it at your target also.

You have sweet lasers. Make one that runs on heat. The heat energy then disappears with the coherent electromagnetic radiation that is the laser. This was recently described as a theoretical possibility.

https://phys.org/news/2012-11-powering-lasers.html

In their work, recently published in Physical Review Letters, the two physicists propose the theory that the heating effect in quantum cascade lasers could not only be avoided but, in fact, reversed through a cleverly-devised modification of the thickness of the semiconductor layers. "A crucial part is to spatially separate the cold and warm areas in the laser," explains Kathrin Sandner. "In such a temperature gradient driven laser, electrons are thermally excited in the warm area and then tunnel into the cooler area where photons are emitted." This produces a circuit where light particles are emitted and heat is absorbed from the system simultaneously. "Between the consecutive emissions of light particles a phonon is absorbed and the laser is cooled. When we develop this idea further, we see that the presence of phonons may be sufficient to provide the energy for laser amplification," says Kathrin Sandner. Such a laser could be powered without using electric current.

Read more at: https://phys.org/news/2012-11-powering-lasers.html#jCp

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    $\begingroup$ If you could use waste heat to power things, it wouldn't be waste heat but an energy source. You don't extract energy from heat but from heat flowing through heat gradients - so the heat has to leave at some point, or your heat sinks be filled. Which is exactly the problem here: how to get rid of all this dirty, not-that-high-temperature waste heat before it grips or breaks everything on board from laser to electronics to (optionally) crew. $\endgroup$ – Eth Sep 19 '18 at 16:53
  • $\begingroup$ @Willk, note "...the cold and warm areas of the laser". That means you need to keep part of the laser cool, which means getting rid of its heat, which you can't do with the laser. And moving that heat out of the cool part means using energy, which generates waste heat... $\endgroup$ – Keith Morrison Sep 19 '18 at 20:30
  • $\begingroup$ @Eth: here is the original - journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.193601. They explicitly propose using this kind of laser to dump heat and cool its environs. The waste heat is generated by a different process. It is exactly as king proposes here. $\endgroup$ – Willk Sep 19 '18 at 23:36
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    $\begingroup$ @Willk This isn't using heat as power source - nothing can, in fact. What it is using is heat gradient, that is heat flowing from a hot to a cold place, equalizing the temperatures. So to keep it firing, you need to keep the temperature differential. The hot point is maintained by all the other stuff, but the cold point has to be cooled down by a secondary coolant loop, linked to either radiators or (temporarily) heat sink. Remember, we don't have access to the infinite heat sink of atmosphere there. $\endgroup$ – Eth Sep 20 '18 at 17:08
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    $\begingroup$ @Willk Which also means worse radiator performances: even with less heat to radiate, radiation efficiency vary with the fourth power of temperature. So the resulting radiators will end up being bigger anyway. This can be useful in niche cases, if for some reason you need (probably non-combat) lasers and you can put those without too much of a mass penalty, but they ultimately won't change things much for your heat management system. $\endgroup$ – Eth Sep 20 '18 at 17:12

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