This section consists of a few points about the role of the above for temperature regulation in space colonies or spaceships.
Any habitat needs light. This may be provided as sunlight or artificial light, but whichever, it will introduce energy, much of which will end up as heat, thus tending to increase the temperature of the habitat. The activities of the inhabitants and their artifacts may add to the heat generated, particularly if they rely on further imported energy (e.g. as food, electricity etc.). In spaceships, the engines would be yet another heat source.
Nothing too remarkable about that, just simple physics. The temperature of the entire habitat would increase until it reached an equilibrium value at which it was losing as much energy by radiation to space as was being put in from whatever source. From the point of view of this section, the thing to be careful of in habitat design is that said equilibrium value should not be so high as to prevent the habitat's functioning. This could be achieved by increasing the rate of radiative heat loss to a point at which the equilibrium temperature was low enough to allow optimum habitat function. Radiators, in this context, are devices for increasing the rate at which heat can be dumped to space.
Shape of Radiators
For efficiency, a radiator needs to be as thin as possible, to maximise surface (from which radiation takes place) to volume (and thus mass) ratio. A radiator that radiates from both faces will be twice as efficient as one that can only radiate from one face, all else being equal. However, if radiating from both surfaces, the radiator must be flat and not curve towards either face, since the concave face would be, in part, radiating onto itself. A one sided radiator can be curved provided that the convex face is the one that is radiating.
Relative to the habitat that is being cooled, a radiator needs to be positioned so that it radiates as little as possible back towards the colony. For a two faced radiator, the can be achieved by placing the radiator as far as is practical from the habitat and perpendicular (edge on) to the habitat. Any deviation from the perpendicular would mean that one face was radiating back towards the habitat more than was necessary. Another way to look at this is that the habitat should 'see' as little as possible of the radiating surface(s) of the radiator. For a one sided radiator the position can be as close as desired to the habitat, provided the habitat is 'behind' the radiator. Such a radiator could be positioned on the outer surface of the habitat.
The next important aspect of radiator position is its orientation with respect to the sun. To avoid the radiator acting, also, as a solar heat collector it is important that it is edge on to the sun. If the habitat involved has a vertical axis of rotation, with respect to the plane of the ecliptic, then keeping the radiator edge on to both the sun and the habitat seems to inevitably involve a rotating connection, with any complications that entails*. If the habitat axis of rotation is perpendicular to the sun, then the radiator could rotate with the colony and stay edge on to both the sun and the habitat. Rotation of the radiator would impose structural stresses and require increased structural strength (and possibly mass). Thus, even though not geometrically necessary, a radiator on a habitat with an axis of rotation perpendicular to the sun may be best if provided with a rotating connection, so that it may itself not have to rotate.
The best type of radiator to rotate with a habitat would probably be a one sided and placed on the outer surface of the habitat (as above). Such an intimate position would allow structure to be intrinsically stronger than for a stand-alone radiator and thus limit any additional structure mass involved in resisting rotation stresses. The efficiency would be lower than for a two sided radiator, but again this may be partly offset by the contribution the radiator itself could make to structural strength and shielding of the habitat. The radiator would be, effectively, under the 'floor' of the habitat (a cylindrical habitat is assumed here) and would obviously require active pumping of the transfer medium, but there would be no need for a rotating connection. As with stand alone radiators, you would not want habitat surface radiators to be 'face-on' to the sun, as they would then be collecting heat rather than dumping it. Thus habitat surface radiators would work for habitats with their axis of rotation perpendicular to the sun, but would be no good for habitats with their axis of rotation vertical with respect to the plane of the ecliptic. Habitat surface radiators would also, obviously, be restricted to a maximum radiating surface area no greater than the surface area of the habitat itself, whereas stand alone radiators could theoretically have surface area as big as required.
If you're going interstellar (or anywhere well away from a star) any direction will be cold for most of the time, so one-sided radiators on external habitat surfaces would work. A further factor to consider in interstellar flight would be erosion by impact with interstellar matter, at the high velocities necessary for interstellar transit (even of an ark-ship), and protection against it. In interstellar flight, any loss of volatiles would be serious and a significant loss could be disastrous, given the virtual impossibility of replenishment until the target system was reached. Radiators would represent the part of the starship most vulnerable to loss of volatiles through being punctured, since their walls would have to be relatively thin to allow them to function effectively. One method by which to limit losses from a puncture would be to subdivide the radiator area into may smaller systems, each isolated from the other, but this could not be taken too far without affecting radiator efficiency. A radiator would need to be edge on to the direction of flight to avoid damage or to minimise the shielding necessary to prevent erosive damage. Probably the one sided radiator on the habitat surface would be excellent in terms of erosion avoidance (again, as above, assuming a cylindrical habitat, since habitat rotation axis would have to be aligned along the direction of travel/acceleration [see Pushing and Big Gyros Figure 6.]), but low aspect ratio 'wings' may also be acceptable. The latter may be of particular value in cooling hot areas like the engine or power reactor, which may not have enough intrinsic surface area to allow one sided surface radiators to provide sufficient cooling. Such parts would probably be non-rotating, which would allow the radiator also to be non-rotating (without any complication of rotating connections) and thus avoid the problems of stresses associated with rotation. It would probably be even better if the two sided radiators were arranged so that they were in the erosion 'shadow' of the main bulk of the ship (the habitat and its shielding) (Figure 1). This would probably be more difficult if the engine were being used for deceleration, since the ship would be the other way around and erosive effects would be coming from the opposite direction. However, when decelerating, the rocket plume from the operation of the engine would make a considerable contribution to destruction or diversion of erosive matter (it would have to, to protect the engine itself from erosion), so if the radiator were also in the erosion shadow from the engine it should be OK.
Partitioning the Problem
In some cases, the problem of dumping waste heat may be reducible by reducing the heat input to the system to be cooled. For example, it might be better if you could 'intercept' the heat (of sunlight, for example) in a non-rotating part of the structure (and thus dump it through a non-rotating radiator) leaving the rest of the light to enter the rotating habitat. This may allow the rotating habitat to get away with one-sided surface heat dumping, where otherwise that wouldn't have been the case. The intercepting could be done by, for example, passing the sunlight (or artificial light, if this was a deep space, interstellar or otherwise artificially lit habitat) through an infra-red absorbing, but otherwise transparent, fluid. Said fluid would then carry the heat away to a non-rotating radiator. An example of such a fluid would be water. This type of thing is done by photographers when trying to adequately illuminate small, but fast moving organisms for filming without cooking said organisms. I think they call it cold light.
As said above, radiators (in the inner solar system at least) should be edge on to the sun to avoid absorbing rather than dumping heat. This restriction may be eased by using a sunshade to cast a shadow on the radiator. For example, if the radiator of a vertical axis colony were shaded, it may be possible that it could be allowed to rotate with the colony, avoiding the complications of a rotating connection (but, of course, imposing rotation stresses on the radiator itself). The nature of the sunshade should be such as to prevent it reflecting heat back to the radiator, or toward the colony. It should also, while stopping the sunlight falling on the radiator, not itself be so heated by that sunlight that it acts as a heat source more local to the radiator (and colony). It would probably be best if it reflected the sunlight as efficiently as possible, and if it was multi-layered so that heat would not be efficiently conducted from the sun side to the dark side. Further, it should not stop sunlight falling on the light collecting mirror for the colony (it might be a good trick if it could be so arranged that it reflected sunlight onto the light collecting mirror for the colony, allowing the latter to be smaller). To keep the shade in the correct position with respect to the colony and radiator it would probably have to be connected to the colony somehow and this connection would obviously have to allow for rotation. The whole idea sounds rather complicated and may not be worth the trouble.
* For example, it is difficult to envisage an efficient heat transfer system through a rotating connection (between static radiator and rotating habitat) that does not involve some sort of fluid-tight rotating seal. This would apply whether the radiator fluid was the habitat atmosphere or another fluid which interacted with the habitat atmosphere via a heat exchanger. Such fluid tight seals obviously exist and work on Earth, but their operation continuously with the hard vacuum of space on the other side of the seal may present some problems, such as the nature of the sealant/lubricant employed.
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