Heat Management

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Nothing is perfectly efficient, not even thermal devices that operate on heat, even in ideal cases. The only exceptions are when you are maximizing heat generation or moving heat around (which can actually exceed 100% efficiency). From an engineering perspective, those device inefficiencies result in heat generation. Heat can also come from the external environment, like if you happen to be piloting a subterrene deep down in the depths of the Earth, or less fantastically, when you are being warmed by the sun's rays.

As said in the article about Heat, heat is a flow of entropy with an associated energy, and neither entropy nor energy can be destroyed. Therefore, the heat must be moved somewhere else, or kept in a place where it won't bother you (insulation - though in practice, nothing is a perfect insulator, and so the heat transfer will occur, just on a very slow timescale).

The cause of it all

Most, if not all losses that generate heat, can be traced down to three major things: Friction, electrical resistance, and energy conversion. It's impractical and pretty much nearly impossible to eliminate friction, and unless you have superconductors with zero electrical resistance, we're stuck with plain old copper wiring and semiconductors. As for energy conversion, it turns out that there is only one form of energy conversion which we can make 100% efficient: directly generating heat. We can achieve this with a variety of means, such as with electrical resistors; indeed, your typical home electric heater is a good example of such a perfectly efficient device.

The most famous example of how energy conversion is lossy is Carnot's ideal heat engine . From a thermodynamical perspective, the reason that fundamental inefficiencies and waste heat exist, comes down to the impossibility of absolute zero. Thanks so much, Heisenberg!

Heat transport

We can't destroy heat, so the only thing left to do is move it from where you don't want it to be. The simplest solution to this problem, is that as heat is here considered to be a property of any object - it stands to reason therefore, we can move the object itself around, to move the heat. In fluids, this process is known as advection.

But advection isn't the only way that we can move heat around. The mechanics for heat transport depends on the state of matter in the system we're considering, and while the two are largely coextensive, also the density of matter.

Let's see how heat manifests at the subatomic level. Here, like in the classical picture, heat also takes the form of random oscillations and motion. However, since protons and electrons possess an electromagnetic charge - they generate their own electric fields. Moving electric fields generate moving magnetic fields. These fields intermingle and couple to each other, resulting in the generation of electromagnetic waves - photons. The electron, or proton, loses energy to the photon flying off.

When our system is dominated by a vacuum, like with a gas - these photons can propagate freely. Heat transport here is thus dominated by what we call the mode of "radiation". However, when the density is higher, it's way easier for a photon to hit other objects, such as other atoms and molecules in the system - and these get reabsorbed, transferring heat to the object that was hit. Like the original object that emitted the photon, these atoms and molecules are too, excited, and will reemit another photon. Heat radiation is always present everywhere.

However, as the density of matter increases, so too does the opportunity for atoms to bond increase, and molecules to molecules as well. Two different modes of heat transport exist - heat conduction, and heat convection. In the process of conduction, the manifestation of heat as random particle motion and oscillations, bump into their respective neighbors. In this way, heat is transferred through these collisions, in liquids, gases and solids. However, while in gases and liquids the conduction is dominated by this kind of unorganized mess - solids also transfer heat through collisions of free electrons and the propagation of phonons. Phonons can be thought as quantized soundwaves, just as photons are quanta of light.

Through conduction, systems in thermal disequilibrium (such as if one end is hot, and the other is cold) will equalize as heat spontaneously flows and diffuses from these collisions.

Convection is the combined process of conduction and advection. A typical example is the currents of water in the Earth's oceans. Here, since hotter water is less dense than colder water - it floats on top. As water cools towards the Poles, it sinks downward. The current is then a clockwise (for the Northern Hemisphere) flow, beginning at the Equator - going northward to the Pole, and finally returning back where it started.

A similar process also occurs deep in the Earth, with heat travelling in great and immense loops from the core to the upper mantle - a process which is responsible for volcanism, plate tectonics, hydrothermal vents and so many other phenomena.

Heat pumps

Generally speaking, a heat pump is any device that makes use of work to transfer heat from a cool space, to a hot space. Heat always moves from hot to cold, allowing the system to reach thermal equilibrium - this is the second law of thermodynamics - but we can keep it from reaching equilibrium so long we provide a continuous supply of work.

If we have for example, a spaceship with an engine generating tons of waste heat. We want to reject this heat out into space obviously, but let's say due to our design requirements that the radiator has to run hotter than the engine. Because of the second law of thermodynamics, we can only do this by pumping heat from the engine to the radiator.

With heat generation, we can only achieve a maximum efficiency of 100%. If we measure their, and heat pumps' performance by the ratio of useful heating or cooling provided to work (energy) required - a "Coefficient of Performance" (CoP) - 100% efficiency is represented by a CoP of 1. It turns out that heat pumps are far more efficient than such heat generators, with everyday air conditioners achieving CoPs of 2.5 to 3 (roughly corresponding to 250% or 300% efficiency). This is because heat pumps can bring in additional heat from other sources, rather than just converting work to heat as with say, an electrical resistor.

Thermodynamically, heat pumps are modelled using what's known as "heat pump cycles", or refrigeration cycles. There are many such different ones:

Heat rejection

Heat rejection can refer to the entire system of moving heat around from the heat source to the desired location. However, in the purview of this article - it refers to the teleological end: the terminal part of the entire system. That is, it is which moves heat to the surroundings of the system (a machine). To use more reified (concrete) language, suppose that you have a car - the primary source of heat is the engine, and while heat rejection can refer to the combined system of the car's coolant lines, so on and the radiator, we ultimately want to talk about the terminal part of the system i.e. the radiator.

In fluids

E.g. the ocean, or the atmosphere.

Convective cooling

Convective cooling makes use of aritifically induced (forced) convection as the primary form of heat transport. The easiest and most common way of doing this in any fluid is through pumps, or propellers.

Evaporative cooling

Evaporative cooling makes use of a fluid's enthalpy of vaporization (roughly, the amount of heat energy needed to vaporize some unit of fluid). This can be significantly more energy-efficient than refrigeration. A common example of evaporative cooling in action is human sweat: on average, we reject 2257 kilojoules of heat for every liter of sweat vaporized (at 35 degrees Celsius).

However, evaporative cooling only works within an atmosphere - particularly a dry atmosphere. This is because only gaseous atmospheres can provide the right combination of temperature and pressure to allow vapor to exist. Traditional evaporative cooling fails when the relative humidity is too high (the ratio of the current partial pressure of vapor in a given volume of air to this volume's maximum capacity (saturation vapor pressure)).

Still, it is possible to make use of evaporative cooling even there, through indirect cycles. The best working fluid for evaporative coolers is water, as it has an incredibly high enthalpy of vaporization.

In vacuum

Outer space, baby!

Only two out of the four ways of heat transfer are present in vacuum: radiation, and advection. This is because vacuum is literally the lack of material - and without such to serve as a medium in which to conduct heat, both conduction and convection are not possible at all.

Radiators (classical)

First of all, why radiators? As you might suspect, we're going to a lot of trouble with how long the section ends up - and for what? Mass is at a premium for spacecraft. So, it's easy to see why radiators can be so attractive: we don't need to bring any extra mass that we would have to for advective cooling.

The design of radiators revolves around the emission of heat as light. To emit as much light as possible per unit mass, and also per unit volume, we must maximize the surface area of the radiator. Naturally, fractals seem like the best option. However, when considering fractal shapes (such as a Menger sponge) it turns out not only are they expensive to perfect from an engineering perspective, light emitted will be reabsorbed in many places. This is because they are surrounded by other surfaces of the radiator. Obviously, this is bad for the radiator's own efficiency.

With these two principles in mind (maximization of surface area, and avoidance of self-reflection, or self-illumination) we find that the best shape for a radiator is a flat polygon. Further extending the principle of avoidance of self-illumination from the individual radiator to radiators as many, we find that it is desirable to place radiators in locations where their emitted light will not reach other radiators. Likewise, considering the entire spacecraft as a whole, it's also desirable that the radiator will not shine too much of its light on the spacecraft's body.

This is why many spacecraft designs have just two or three big radiators placed radially on one of the spacecraft's axes of symmetry.

The Stefan-Boltzmann Law, discovered in the 1880s - describes the dynamics of radiation here:

$\phi _{e}=A_{d}\cdot \epsilon \cdot \sigma _{sb}\cdot T^{4}$

• where $\phi _{e}$ is the radiant power - i.e. amount of heat energy rejected per unit time.
• where $A_{d}$ is the radiating surface area.
• where $\epsilon$ is the emissivity of the radiator's material.
• where $\sigma _{sb}$ is the Stefan-Boltzmann constant of proportionality.
• where $T$ is the temperature of the radiator.

Technically, this equation is a derived form of the Stefan Boltzmann Law - instead breaking up intensity into power and surface area. Put simply, the Stefan Boltzmann Law is the relationship of a matter's own temperature to the intensity of thermal radiation it emits (amount of energy per unit area per unit time emitted).

The best radiator would be what's known as an ideal black body - something which absorbs 100% of all light. Since physics is reversible, it also means that this ideal black body has a perfect emissivity - i.e. it emits 100% of its own thermal energy as light. Emissivity is just how close a given material is to being this ideal blackbody - the ratio of the measured radiance to the blackbody's theoretical radiance. Nothing in the real world can be an ideal blackbody. Stars and other astrophysical phenomena, do however, very closely approximate one.

It turns out that increasing the temperature of the radiator will increase the radiant emittance (intensity), all other things equal. This allows us to decrease the surface area of the radiator, which has some very good engineering benefits: the mass of the radiator (since mass is at such a premium for rockets) goes down, and for a combat spacecraft the radiator is a much smaller target. We also want as high of an emissivity we can get, so blacker materials are more preferable. Nevertheless, it's important to note that by blacker it's meant that the material is "black" over the entire electromagnetic spectrum; so materials which appear highly reflective (like ice) in the visible spectrum, a silver of the entire EM spectrum in of itself, may actually have very high emissivities (0.97-0.99)!

Classic radiator designs, are made of solid materials and are evenly hot. We can make it evenly hot just by pumping heat around in a crisscross lattice of channels throughout the radiator.

However, biggaton spacecraft require biggatons of engine, generating biggawatts of heat. As a result, to keep the radiator from getting absurdly large (and they do get absurdly large fast) we must increase the temperature. However, the required temperature (for a target surface area) can quite easily reach well into the thousands of kelvin. At such temperatures, things do quite easily cease to become solid, therefore - we want to look into designs where the radiator doesn't need to be solid.

A comprehensive table of emissivities is given here:

Open cycle (advective) cooling

Oh, what a bother! All that radiation, so much work!

We simply do it like God intended: throw the heat out. Open cycle cooling systems (advectors) can make use of the engine's exhaust itself. However, this only works when the engine has enough thrust (propellant flow) to sustain the required amount of heat rejection: to keep open cycle cooling going when that is no longer possible, one can simply vent hot fluid out into space using internal reserves of some coolant fluid.

As mentioned above, open cycle cooling is far more wasteful when it comes to mass than radiators, hence why they're not as common of as a heat rejection system for spacecraft (where again, mass is at a premium). We want to be very efficient with our open cycle cooling. We must squeeze as much heat we can into every kilogram we throw out. It turns out that water once again, is the best kind of working fluid for this: it has a very high specific heat capacity (amount of heat energy needed to raise an unit mass by one degree of temperature). We can also make use of phase transitions (such as its enthalpy of fusion (melting) and enthalpy of vaporization).

Open cycle cooling is very attractive for combat spacecraft, where huge radiators are a huge liability. In fact, open cycle cooling reduces the heat rejection apparatus down to a mere hole, or perhaps a nozzle - where the hot gas is expelled. You can't shoot hot gas and make it stop working, can you?!

Because of this, combat spacecraft likely make use of a mix of both radiators and open cycle cooling: when they enter combat, they fold in their radiators or however so, and switch to open cycle cooling for the duration of their combat. Likewise, they can also use heat sinks.

Heat sinks

A heat sink is fundamentally a delaying action in the war against heat. You dump all of your heat into it during a period of intense usage, and then plan to radiate / throw it away later. This is especially useful for applications that emanate very large pulses of heat, where radiators and advectors would struggle to keep up - like a laser weapons system, or a spacecraft during a particularly intense combat.

As mentioned above in the section about advection, heat sinks and advectors can be described using heat capacity. Given that the unit of specific heat capacity is heat energy divided by mass divided by temperature, one can devise equations to solve for the mass of the heat sink / amount of material to advect, or the amount of heat energy that the sink/advector can absorb, and so on. Heat sinks will be limited by your design considerations: do you want a solid heat sink, or are you willing to let it melt? At which point does the heat sink pose a liability to the spaceship itself?

It's important to note that specific heat capacity also changes with the state of matter, and even with temperature. Furthermore, for absorbing intense pulses very fast, the heat sink should also have a good thermal conductivity. A slight wrench in this consideration however, is since that the heat sink will be surrounded by other parts and machinery of the spacecraft - it will also be dissipating heat to these parts. This can be solved with judicious application of insulation and design.

Advectors, of course, have looser constraints - if you, oops, end up with plasma - you can simply throw it out.

Material tables

Some potential suggestions for heat sink / advector materials:

Note: If temperature/phase is not specified, assume that it is at standard temperature and pressure conditions. All values are given at constant pressure (isobaric). If a material is not covered on here, and you cannot find the material's specific / volumetric enthalpies or capacities, one can calculate it by dividing the molar enthalpy/capacity by the molar volume/mass of the material.

Material	Specific Heat Capacity (kJ/kg⋅K)	Volumetric Heat Capacity (MJ/m3⋅K)	Specific Enthalpy of Fusion/Sublimation (kJ/kg⋅K)	Specific Enthalpy of Vaporization (kJ/kg⋅K)	Specific Ionization Energy (MJ/kg)
Hydrogen gas	14.3	0.5	58.04	222.9	1302.88
Helium gas	5.1932	0.5	3.448	21.11	592.779
Water (25 °C)	4.1813	4.1796	333.55		67.589
Water, ice (-10 °C)	2.05	1.938	333.55		67.589
Water, steam (100 °C)	2.08	0.00125	333.55		67.589
Lithium, liquid (181 °C)	4.379	2.26	432.3
Lithium	3.58	1.912	432.3
Beryllium	1.82	3.367	1354
Sodium	1.23	1.191	113.1		21.567
Air	1.012	0.00121
Aluminium	0.897	2.422	396.94
Graphite	0.71	1.534	59700 (Ent. of Sublim.)
Diamond	0.5091	1.782	59530 (Ent. of Sublim.)
Steel (stainless)	0.466	3.756	267776	7406000	45.523
Copper	0.385	3.45	206

Calculated Figures:

An important consideration is that the specific ionization energy refers primarily to the first ionization energy (i.e. the energy needed to strip the first electron off the atom.) Second, third, and other ionization energies are not given.

For when the heat comes from outside, not within

Heat Shields

Heat Shields

Credit

Authors: Qalqulserut, Rocketman1999