How to allow a cylindrical habitat (O'Neill or McKendree) to radiate heat to space?

Question

Background

I am trying to find a design for a cylindrical habitat that would allow the enclosed cylinder to radiate heat out to space as does the Earth without using mirrors and windows.

Problem

In my design, I am not using the mirrors and windows of the classic O'Neill design, my habitat is also tidally locked to the Sun facing it with on of its caps. I'm also assuming that solar panels around the habitat are used to provide the internal living area with the same energy density as the Earth gets from the Sun. In other words, each square meter of the habitat will receive the same power (in the form of electricity that will eventually turn to heat) as each square meter of the Earth. My design looks something like this with the cap always facing the Sun.

The obvious problem now is that there no where for the heat building up inside the habitat to radiate to. For the Earth, the surface and atmosphere is always facing towards empty space, and so the Earth radiates as much as energy as it receives from the Sun creating temperature equilibrium. This is not the case by default in this habitat design.

EDIT: I'm not using windows and I'm unable to use radiators on the outer lateral area of the cylinder because those habitats are part of a Dyson swarm in my design. Therefore, any radiation from this outer lateral area would be absorbed by the other habitats and not radiated to space. The only area possible to radiate directly to empty space would be the end cap not facing the Sun.

Partial solution

To make the habitat achieve the temperature equilibrium at the same temperature as the Earth does, I first thought that the heat will just propagate through the habitat walls and radiate into space, but I then found that conduction is very slow and the interior would be boiling before the outer layer of the habitat wall became hot enough to radiate at the required rate.

This made me think that the solution lies with the atmosphere inside the habitat. I think this can be solved somehow by creating a cycle for the atmosphere to allow it to be outside the habitat for some time to radiate the heat without losing it to space and running this cycle indefinitely. I'm not sure how practical this is and I can't really imagine a design for it.

EDIT #2: I think radiators must be used at the other end cap. The problem now is that the end cap area is 1/20 of the living area inside the habitat. Therefore, I need at least 20 times the area of the end cap to radiate the energy. 20 times the area means 4.5 the radius. If this radiator is rotating, the stresses will most probably break it apart. So, is there a way to use non-rotating radiator with a rotating habitat?

Question

What are some designs for the above mentioned habitat that would allow it to regulate its heat radiation to space to keep it from overheating?

Answer 1

those habitats are part of a Dyson swarm in my design. Therefore, any radiation from this outer lateral area would be absorbed by the other habitats and not radiated to space.

A perfect circle 1AU in radius has a circumference of nearly a billion kilometres. A McKendree cylinder is about 1000km across. If separated from each other by 1000km, you'd be able to fit in ~470000 habitats, giving you a total internal surface area of ~6x10¹²km, which is ~12000 times the surface area of the Earth. Russia is one of the most sparsely populated regions on Earth, with a mere 8.4 people per square kilometre, which you give you plenty of space for fifty trillion people. Each habitat would have an almost entirely clear sky around it, so radiating in all directions would be absolutely fine and only a small fraction of the radiated heat would be re-absorbed.

This is just a single ring around the star... you could have an order of magnitude more habitats spread out in a sphere around the star and they'd be even more widely separated.

I'm not sure what you need your dense swarm for, or how you'd find enough mass to build it, or how you'd be able to fill it with people, for that matter. But anyway, rant over: lets move on.

The only area possible to radiate directly to empty space would be the end cap not facing the Sun.

Behold, the cross-section of a cylinder with modified external geometry to support a) greater external surface area and b) a means of radiating heat without directing any laterally at all. Even if you don't use the sunward-side panels (and they'd be shaded from teh sun by the panel in front of them) you've still got a greater surface area than the cylinder itself.

Note also how you can increase the area of the spaceward endcap substantially, if that's what you felt you had to do.

I think this can be solved somehow by creating a cycle for the atmosphere to allow it to be outside the habitat for some time to radiate the heat without losing it to space and running this cycle indefinitely.

Water is an excellent material for particle radiation shielding, is useful for the occupants of the habitat, and has a very high heat capacity. Circulate it through the outer shell of your habitat to both shield and cool the interior. Pipe it out through external radiators to cool it again.

Ideally you'd use a heat pump system, possibly as a second cooling loop, to chill the water shield and run your external radiators at a higher temperature... the power radiated by a black body is proportional to the fourth power of its temperature, so running your radiators hot is desirable to keep them small. If you're in a dyson swarm, you clearly have power to spare to run such equipment, so the inefficiencies won't be a problem

If this radiator is rotating, the stresses will most probably break it apart. So, is there a way to use non-rotating radiator with a rotating habitat?

Are you sure that you're already at the edge of the envelope for your materials? You haven't specified habitat radius or rotation rate and I'm not about to hazard any guesses, but there's a good chance that a big rotating radiator array is entirely possible.

You could make the radiator non-rotating, and indeed the engineering required to do so is child's play compared to that required to dismantle a solar system and turn it into a dense habitat cloud. It shouldn't be necessary, though.

Answer 2

Heat pipes are the answer:

These were used for the McKenzie Valley pipeline to keep the permafrost cold under the supports.

Thought experiment: Take a 30 foot long steel pipe, and put a few gallons of liquid propane in it. Let it boil, pushing the air out. Cap it. Propane liquifies at -40 under normal atmospheric pressure and temperature, and is a liquid at about 120 psi.

Set the pipe in ground with about 10 feet exposed.

When it's cold out (all winter) propane condenses in the top end, slides down the wall of the pipe, hits the part warmed by the ground, boils. This will happen as along as the top end is colder than the bottom end.

When the top end gets warm, you just have warm propane gas at whatever pressure is in equilibrium with the liquid at the bottom.

This doesn't help your habitat, as you want the inside end to get cold. So you put a material that wicks whatever your working liquid is, and each heat pipe has a pump that pulls liquid from the sump at the space end, and wets the wick in the inboard end.

You want to choose your working liquid to NOT freeze into a solid if a pipe isn't used for a while. (Solids don't pump well) but also to slurp up reasonable amounts of heat to boil. LOX? Liquid nitrogen?

Now for this you a LOT of radiator. One side of your habitat is receiving 1300 W/m2

This calculator https://www.spectralcalc.com/blackbody_calculator/blackbody.php says that at 0 C (273K) a black body radiates 300 W into space. So you need between 4 and 5 square meters of radiator for each square meter of absorber.

However. No windows. For plant growth you don't need anything like full strength sunlight. And at present we don't use close to the full power of sunlight striking the earth.

So calculate your power needs on a per person basis, not on an area basis, paint most of the habitat white.

The sides are covered in dimples to shade the radiators.

Make your cylinder ~5 times as long as it is wide. This gives you a radiation surface of Pi * r* 10r, while the absorbing surface is Pi r^2 The side radiators will only do about 75W (roughly 1/4) of the radiation of a radiator pointed at a hemisphere of empty space.

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Edit: User has a dyson swarm of habitats. Lateral radiation will still work: But the efficiency goes down. What is now required is that radiators are 'beamed' in the sense that each habitat is the tip of a cone of radiation. The cone has to be narrow enough to miss the neighboring habitats. This isn't an onerous requirement at low swarm densities, but becomes increasingly difficult with increasing density.

The nature of a swarm is that it has to be done in 'belts' Orbits by their nature are planar, and are coplanar with the center of mass of the central star. So you can have orbit at 1 A.U. that is 1 habitat wide. Presumably they have some separation, probably by several times their own size. So the radiators that are pointed vaguely at the adjacent habitat aren't effective until they swing by. But if the spacing is say, 10 times the habitat size, then this degrades your radiator system by a percent or so.

Ok. Belt 2 you put in at 1.01 A.U. at, say 60 degrees to the first one. It has an occasional shadow fall across it twice an orbit.

Belt 3 you put in at 1.02 A.U. Also at 60 degrees, but you advance the ascending node by 60 degrees too. It gets 4 chances at a shadow falling on it.

After a while suppose you have 50% of the star's radiation intercepted. The rule still remains: If you take 1300 W/m2 of sunlight in, you need 4.5 square meters of perfect black body at 273 degrees to radiate it out.

Now here's where my thermodynamics falls down. 273K falls into the high microwave/far infrared band. If you can dump your heat as a beam of microwave energy then you can win. But I suspect that this comes in the 'no free lunch' class. That to beam it takes more energy than the system dissipates.

Answer 3

Your Tidal Locking Dilema

You are already pointing tidally locked solar panels at the sun, simply place the panels between the sun and your habitat. This puts your whole living space in their shadow. Then you just need to evenly distribute things inside of your habitat that generate heat (lighting, computer systems etc.) such that they are evenly distributed so that there is no major gradient of origin for heat sources. Then you simply create enough surface area on the outside of the habitat to radiate heat as fast as you make it.

Or if you want to keep your exact design, place things that produce more heat like machine shops, manufacturing, greenhouses, etc. at the back of the station, and lower power infrastructure near the front where it is more passively heated.

Your Swarm Dilema

When building a dyson swarm, there are factors at play that limit how densely your cloud can be built. If you put the habitats, too close together, gravity and tiny tiny little levels of asymmetry will cause a cascade of asymmetry which will result in accretion. (Just like all the dust did that formed the planets) This means you need your habitats really far apart from one another. Sure you can fit thousands, maybe even millions of them around a star, but nowhere near enough to create an even slightly solid shell.

Because of this, they will never be close enough together for lateral radiation to be a problem... unless something has gone terribly wrong in which case the people inside are about to be in for a much worse time than just some heat radiation issues.

Dyson spheres and Ring Worlds overcome this problem through their theoretical structural integrity, but swarms need their distance.

While you could try to overcome this with thrusters, that creates tons of problems as well. First off, you have a massive multi-body problem here. A course adjustment in one would cause a domino effect across the spacing of all stations. This would require ridiculous amounts of calculations and thrust over time to account for. Thrust takes a sacrifice of mass (unless you have a non-newtonian propulsion system); so, your swarm would need to consume a constant influx of matter from other places in the solar system which will lead to all sorts of long-term problems. Lastly, thrust fires highspeed mass out in a linear direction at the thing you are trying to get away from. This means your stations will get close enough to harm each other with maneuvering thrusters long before they get close enough to harm each other with radiant heat.

It is important to remember that heat radiates in spherical waves, not in straight lines; so, even if the structures are really close together as shown below, you'd still have most of the heat radiating out in angles facing deep space. In the graphic below, you'd have about 4/5ths of the radiant heat going off into space, on this axis, and more like 14/15ths along the other axis meaning even bodies this close together will only receive about 1/75th of the other body's radiant heat.

Your End-Cap/Radiator Dilema

I think my last point mostly solves this for you, but in case there is still any doubt: If your end caps have the same population density as your habitat ring, then the heat per area will be less than the rest of the cylinder because they have the extra wall. The exception to this in your current design is your sun-facing end cap which can be shielded if needed with solar panels as I mentioned.

In any case, you also don't need to worry about radiators making your ring less stable, properly designed they will in fact have the opposite effect. Scaffolding is stronger and lighter than a solid surface, and tubes are stronger and lighter than solid bars; so, you just need to build up a scaffold shaped radiator structure out of radiator tubes that has enough surface area to meet the requirements you need at any given area around the circumference of the structure. These shapes will not only radiate heat, but reinforce the station as a whole.

Answer 4

Rearrange, and increase the size of, your solar panels so that they almost completely shade your entire cylinder from the sun. The only openings you need are an entrance to your mirror system for internal lighting.

Arrange any needed radiators on the external hull, which will still be shadowed, allowing for excellent cooling efficiency.

Note that a visibly rotating structure is not the likely appearance of any habitats using rotation to generate "gravity". Any rotating structures will likely be contained withing non-rotating shells.

Answer 5

Metal Iris Umbrella, or Slatted Umbrella

Since your design always points the hub towards the Sun, the primary heat source, it makes designing a light shield really easy. Build a tower directly outward from the hub (it can have an offset if you want landings there). Build a sun-blocking structure that can be fine-tuned. There are many good shapes.

The simplest shape is just two radially-perforated disks, wider than the habitat. When you want it bright, rotate one disk so that the perforations line up and the maximum light comes in. When you want it dark, rotate the disk so that the perforations don't line up. If you can trust your motors and lubricants, merely set them spinning very slowly so that it's on a 24-hour cycle of brightening and darkening.

Your radiator can be at the other hub end. In the shadow of the habitat and its shade, it gives off heat into open space. Heat needs to be pumped into the radiator, perhaps with solid neopentylglycol refrigerants.

The problem with this design is that it doesn't fare well with torque. You need to have a very reliable and responsive and proactive set of thrusters, probably a ring around each hub, in order to keep the hab oriented and in the dark. If ships are docking, small impacts happening, the spin precessing, etc , then the habitat can swing out into the light.

Answer 6

Heat on Earth spreads by convection, conduction and radiation. In space, convection and conduction almost entirely non-existent leaving radiation as the sole method to add or subtract heat.

In your station, anything facing the sun will absorb heat. Anything facing away from the sun will radiate heat. You only need balance the heat being absorbed, the heat required to keep a comfortable habitat and then radiate the remaining heat away from the station on shady surfaces that face away from the sun.