How to get rid of all the heat in my spaceship?

Question

Spaceships are a peculiar thing. We've got them in all forms, sizes & colours. They run on nuclear fusion, creating loads of power driving all sorts of shenanigans... but they still generate lots of heat that has to be gotten rid of somehow.

Assuming we have mastered the challenges of creating stable fusion reactors and can build spaceships that are more than fireworks with people strapped on top:

Q: What current-day or near-future materials/technologies can be used to (most efficiently) get rid of these massive amounts of heat in my spaceship?

Answer 1

Without numbers for "massive amounts of heat" or more specifics on the size and other details of your ship, I think the best to hope for is an overview of the basics.

Heat flows from higher concentrations to lower concentration. If using refrigeration to move heat from low to high it is never 100% efficient and will produce more total heat. Heat transfer has 3 main methods to move heat around.

Conduction

Heat travels between materials in contact with one another.

ΔQ̇ = -k A ΔT/ΔX

Rate of heat transfer ΔQ̇ is dependent on k the material thermal conductance, A area in contact, ΔT temperature difference between the materials and ΔX how far apart are the temperature reference points.

This is employed internally in the ship moving heat around, but in space with a vacuum outside there is no contact with other materials so no help on cooling the ship as a whole here.

Convection

A special case of Conduction where heat transfers to a fluid (liquid or gas) in contact with your heat source (think atmospheres or underwater) this is a lot more complicated as the fluid is often moving and if not the heat will cause movement transferring more heat than simple conduction.

Again not applicable outside the ship in space as there is no fluid to contact.

Radiation

This is the one most applicable in space applications. If something is hot it emits thermal radiation, sometimes this is visible if the objects are hot enough, but it occurs in the non visible spectrum as well.

Q = εσT⁴

ε is the emissivity of the material with a maximum value of 1, this can be improved by material selection and the use of coatings (i.e. paint)

σ is the Stefan–Boltzmann constant

and T is the temperature.

The main way this is practically used in space craft is to use refrigeration techniques to move heat around concentrating it and making certain parts of your vessel hot to increase the amount of heat emitted as radiation (heat emitted goes up with the 4th power so hotter equals a lot more heat transferred). The radiator heat sources need to be placed so that the surface area is directed away from the ship so the radiation leaving the hot area is not absorbed by other parts of the ship. This is usually done with large external radiator fins (often mistaken for solar panels in actual space vehicles). So your ship is going to be spiky with large cooling fins on the exterior.

Alternate Methods

• A passive cooling method using radiation is to reduce the incoming heat from the Sun's radiation by using shading or reflection (most space ships are white to reflect heat). This won't help with heat generated in the craft but reduces the total heat present.
• Mass Transfer - Again using internal heat transfer systems and refrigeration to selectively heat certain areas or items and then jettison that mass from your ship. The heat loss is Q = m C T; m, mass, C, specific heat, and T temperature. And don't forget to get the energy out of phase changes, so molten iron or steam are good candidates here. It is not a long term strategy as you are losing mass from a limited system and will eventually run out of material to eject.
• Heat storage. Using internal storage locations to heat up under load or alternately having precooled heat sink material present to absorb the heat generated. These do not provide any net source of heat dissipation, but could provide a temporary buffer storage of excess heat to later be expelled using radiators or exchanged at the local trading post or mother ship.
• An interesting semi-future technology with application in the area is Thermal superconductors (currently only exhibited by liquid helium at very low temperatures), they transfer heat through themselves very fast. Apply heat to one end and the whole thing heats up not just the end near the heat. It would allow for some improved designs in internal heat management.
• The most important thing is the effective use of thermal insulators and ship design to prevent heat going where you don't want it. Your fusion reactor and other ship systems might be fine operating at several hundred degrees, but people or other critical systems might not do well under those conditions. The vacuum of space is good at insulating, as we've seen, putting the crew compartment physically separated from the high energy fusion reactor is likely a must.

Answer 2

Thermodynamic basics

The fundamental laws of thermodynamics say:

• The total energy in any isolated system is constant.
• Bound thermal energy (Enthropy) will increase in isolated systems
• Thermal energy cna be seen as the movement of particles and is thus can be seen as the average kinetic energy of particles in a fluid (that is a medium in liquid or gas state)
• Temperature flow follows always the same direction as the temperature gradient between two objects: $\Delta \Delta \text T = \nabla \text T$
  • because of this, it flows only from hot to cold and the driving force of any temperature exchange is the temperature difference, $\Delta \text T$.
  • Heat energy is calculated with $\text Q = \text {mc} \Delta \text T$, Q is the energy, m the mass of the object, c a material constant and $\Delta \text T$ is either the temperature we raised the objects temperature (then Q is the energy we have "given" to it), or the difference to absolute 0 (then Q is the total heat energy).
• Force can create a temperature difference by either:
  • application of friction on a part of the system or
  • transport of a medium with a temperature from one point of the total system to another
  • fluids can change their state, density, volume and temperature, for the question of a gas, this is governed by the gas formula: $\text {p V} = \text {n R T}$ - pressure, times Volume is number of gas molecules times gas constant R times Temperature

Partial solution: Redistribution inside the ship

Inside the ship we have a few problems that we are used to on earth: we have an arrangement of heat sources that need cooling (machines, electronics, human bodies), and a gaseous medium between them.

Here a heat pump comes in handy: because of the gas formula above, we can put a specific amount of gas under pressure and increase its temperature, or reduce its pressure to lower it. With this, we can greatly aid in heat transfer from some points to others, especially from inside the station to the outside on radiators, speeding up the achivement of equilibrium. Better yet, the machine can continue to push all the excessive heat to the outside of the station, especially to the radiators - where our problem begins.

Problem analysis: Space

The main problem with cooling is space is, that space is near vacuum. Near vacuum means, that there is little to no material (medium) to engage in heat transfer, at least not without a loss of mass of the ship.

On average, there is a density between 0.1 atom per cubic centimeter to 1000 atoms in the same volume, while cosmic backdrop temperature is about 3 Kelvin. That is good on one hand (large temperature gradient, so possibly large flow), but bad on the other (little to no material which could take the heat away).

Yes, space is cold as hell, and you can deep freeze an object by just shoving it out of the airlock, but it is really really hard to cool your ship down with basic thermal exchange via Convection. Still, there are ways we could go, mainly radiation.

Solution 1: EM radiation / light

Heating objects enough (generally above 798 K = 525 °C = 977 °F), they start to show incandescence and emit thermal radiation. In other words: they glow. In this state, they dissipate heat energy in the form of EM waves (which is light) in addition to the convection before (heating of toughing air particles and giving them some thermal energy).

As convection is very much hindered do to the aforementioned lack of other medium, the ship could use materials with a very high thermal capacity close to materials that have a very good incandescense effect to dissipate much of the heat in the shape of thermal EM radiation to outside of the station. As an (non calculated) example, it could use pipes filled with liquid metal (lithium springs to mind) at a temperature that makes the pipes glow red to yellow. It is by far not the most efficient way, but it is at least some way to get rid of the heat.

Solution 2: Ejection of (heated) mass

But radiation is not the only way to get some thermal energy out of the system. We have established, that we can transport heat inside the station with heat pumps. In an emergency the heat flow might be redirected into some non-essential module to heat that up as much as possible and then just ditch the whole module. This separates the thermal energy that is now stored in that module from the rest of the station. But this would be an extreme way.

Instead of ditching whole, overheated modules, one could better ship in some low-temperature gas (like liquid nitrogen or hydrogen), heat it up with the heat pump cycles, and then just let the gas out of vents into space. It has expended largely due to this process (gas formula, remember?), and will eject from the ports at a high speed: the residual heat in the station can become part of the Reaction Control/Stability Augmentation System to keep the station where it is supposed to be. Or it is used as a pre-stage for the engines of a spaceship, getting rid of some heat energy through the ship's propulsion system as it prepares (preheats) the fuels for it.

While such a system is for sure helpful as an aid in propulsion or emergency heat relief (just vent an overheated section, then readd atmosphere), it can't be the one and only method to keep the ship cool.

Answer 3

I am writing mostly because of that part in a comment: It always seems ironic that cooling is a problem in space...

Other answers have not paid enough attention to the Stefan-Boltzmann law: $$Q=\sigma T^4\text{, }σ = 5.67×10^{−8} W m^{−2} K^{−4}$$ where $T$ is temperature of emitting surface.

What practical effects does this law actually have? For a blackbody emitter at given temperature, heat loss due to radiation will be:

• 6000K - is energy flow 73MW/m² (The Sun's photosphere)
• 2000K - is energy flow 900kW/m²
• 1000K - is energy flow 56.7kW/m²

or more usual temperatures for us:

• 300K - it is 460W/m²
• 250K - it is 221W/m², coolant(Ammonia) on ISS station
• 200K - it is 91W/m², lowest possible for ISS before coolant begins to clog the system

Vaccuum is not a good insulator, but it seems that way because of the temperatures in which we live and work. Vacuum do not have convection and conduction, which are both important heat transfer modes at room temperature. But at high temperature, radiative transfer becomes much more powerful. The 1000K object listed above gives off as much heat per area as a gas barbeque at full power. In the context of high temperature objects and space, where radiative heat transfer is the dominant mode, vacuum is not an insulator at all.

OP's question

Smart design decisions will solve your heat transfer problem, and carbon nanotubes(CNT) is the material of the future that will allow you to solve them.

The problem with "fireworks with people strapped on top" is the incompatibility between temperatures which are acceptable for humans and the temperatures which are acceptable for machines. So separate them. Separate the living volume from the energy generation units (reactor, engines).

By separating them you have 2 different problems to solve - heat dissipation from living volume (where we have all components which can't be separated from humans, or which have similar temperature requirements as humans) where 300K is the norm; and heat dissipation from reactor-engine where 2000K may be a perfectly normal temperature.

Human quarters

Design of this section depends on size of ship, on personal requirements of volume per human, energy consumption per human.

An example of power consumption per human is 50kW; volume per human 1000m³ (equivalent to a 400 m² house or less), surface temperature 300K. With these conditions then up to 90 humans can live in a 54m diameter spherical living volume and not even need a radiator. With 4.5MW energy consumption, the surface of the spherical module is enough to emit all that energy.

The sphere is an efficient form because it has minimum surface area per volume it encloses, which means less construction materials and mass per volume. However, this form in space is not so critical, and it may be borg cube or some more flat shape with higher surface to volume ratio. Design plays there significant role. Requirements also are important.

Engines and reactor

The nice thing about fusion reactors is that they can be also engine and electricity generation unit. So we will only talk about one unit.

It is hard to discuss them as hard-science, even when we have some successes with thermonuclear reactors, Wendelstein 7-X

Pictures to illustrate taken from projectrho.com Magnetic Confinement

(Second picture is pretty realistic design, an overview of a ship composition, and have radiator attached in a way we may benefit too. Nice generic picture of a thermonuclear ship as whole)

Notice that the plasma temperature is high and it emits waste heat at a high rate. We have to solve the heat problem for the solenoids, but they may be capable of working at high temperatures, significantly higher then a human's 300K. If we keep this entire compartment at high temperature, than the radiators can have significantly higher temperature and emit lot of energy for relatively small surface.

CNT, thermal properties

The temperature stability of carbon nanotubes is estimated to be up to 2800 °C in a vacuum and about 750 °C in air.

If this is true, then since we are in a vacuum we can operate at 2000K while emitting 1MW/m² over our radiators.

All nanotubes are expected to be very good thermal conductors along the tube, exhibiting a property known as "ballistic conduction", but good insulators lateral to the tube axis. Measurements show that a SWNT has a room-temperature thermal conductivity along its axis of about 3500 W·m⁻¹·K⁻¹; compare this to copper, a metal well known for its good thermal conductivity, which transmits 385 W·m⁻¹·K⁻¹. A SWNT has a room-temperature thermal conductivity across its axis (in the radial direction) of about 1.52 W·m⁻¹·K⁻¹

This is exactly what we are looking for an insulation in that case, as it is free out of the box if we make the solenoid coils out of CNT. We can get a conductive wire, insulation for that wire, and structural support all out of the same material.

Ed note: you'll need more references to convince me that the same nanotube bundle can do all three

MolbOrg: Valid request. However with given set of factors as: my competence(main reason), difficulties to find information, ongoing researches of CNT(SWNT, MWNT) about their properties and not established data about CNT's because of problems with their production and measuring properties of single tube - single walled or multi-walled nanotubes, amount of information needed to clarify - seems not possible to establish it with some degree of certainty in this answer. Lets call it a fantasy about pure carbon thermonuclear engine, which may or may not to be true. However some notes will be below in note section⁽¹⁾

The second thing to notice is the coils and separation between them, in vacuum we do not need an enclosure for the plasma. On Earth in the gravity field, we need it for structural integrity and to protect against electromagnetic forces and insulate from the atmosphere. In space we do not need most of that, and we definitely do not need it as a surface without gaps. This way most waste heat from plasma will be emitted directly in to space void without having need to use radiators.

3He-D Mirror Cell

There is an electricity generation unit attached, a Magnetohydrodynamic generator (MHD) that converts plasma exhaust and leakage into electricity.

So the engines basically look like mesh made of structural beams and coil rings, with an attached nozzle or power generation unit on either end (or at one of the ends, also possible).

Another step is that this engine does not have to have fixed attachment to living quarters. The same CNT can be used to make robust cables (same as people imagine for Space elevator) to attach engines flexibly and at a significant distance from living quarters, so as not to mess with their heat emitting solutions.

... get rid of these massive amounts of heat in my spaceship?

The answer is, do not have these massive amounts of heat generated inside of your spaceship, and use the excellent heat transfer properties of vacuum as much as possible.

Note

1. Carbon nanotubes as conductor, insulator, structural strength element(aka make beam from a rope)

   • in first place, situation was considered from heat problem standpoint of view, as it is OP's concern. And some properties of CNT's are interesting in this context and worth to note.
   • insulation which will work at that temperature - ceramic is good enough for that, Al₂O₃ as example. There is no need to use just carbon for that, even if it is possible as I think, as a bit more complex structure then just plain SWNT, SWNT/MSNT doped by something.

   • Engine which I'm referring to, or use as model is described here. It is good as idea, but that all for it.
     It is not scientific paper by any means, even if author tries to refer to some tested equipment, and refers to some works from scientific community for that time and field. But it even have some criticism also not scientific one, just amateur likes that kind of stuff.
     Engine is just a concept, with some numbers in its description. However numbers look reasonable, not to make conclusions, but to have some clue about what we may need, and mostly are not unique to that concept only.

   • make beams from ropes - there are option. An example soft bag in shape of a big sausage will act as beam, higher inside pressure, better beam it will be. Same as with fire hose. Strength of CNT's is about 60-100GPa(depends on who and how did measurements, and which kind of CNT they have tested) and that allows to have pretty high pressure with not so much materials. Internal media which is compressed can be cable made from CNT, and pressure is created by prestretchered winding of external shell which creates that bag and pressure around cable. All together it will have properties of solid beam. But simplest to imagine it is inflatable structure which forms rigid shape. There are other option - in winding(in first place), in using composite matrix, electromagnetic interaction, active structures.

All these problems are far beyond OP's question, but we discover uses for carbon nanotubes, and we are far from exploiting everything they offer to us. Is that material of the future - sure. Will I bet it will replace steel and other construction materials almost everywhere, I will. As hard science it is the best material we currently have, there is no doubt. It looks like it even have superconductive properties, around 0.5K, but still - Electrical Properties and Applications of Carbon Nanotube Structures, page 9

So as far as op interested in future materials, it is. It may be same thing as people 100 years ago was thinking that chemistry will do the magic and can solve everything, and it didn't even if it plays significant role today.

Answer 4

A simple solution might be how the Apollo LEM discarded excess heat from its electronic components. They exposed water to the vacuum of space, where it boiled off, sucking the heat out of the heatsink on the outside of the spacecraft that the water was sprayed onto.

Without water, a heatsink can't radiate heat in the vacuum of space... no air to carry the heat away.

Answer 5

Consider using thermoelectric cooling, and you will have a chance to generate some extra power for your spacecraft.

https://en.wikipedia.org/wiki/Thermoelectric_generator

Mount the Seebeck generator in the wall of your spacecraft, and use heatsinks to direct the heat to the generator from the inside. The greater the difference between plates, the more power you will be able to generate out of it.

You won't be able to cool down all excess heat through this process, so you can use radiators to cool down the rest.