Creating a Matryoshka Shell world: temperature regulation

Question

In a galaxy far far away, during a fit of inspiration for a super massive marvel of technology, the Imperator dedicates an astounding 10% of energy and materials from his civilization's dyson sphere and solar materials processing units to attempt an innovative (and possibly insane) plan to create a matryoshka world. By attempting a massive 3d printing of multiple world shells, the leader hopes to create many planetary shells within each other.

So the first problems appear, heat regulation.

If you don't want to bake the inner shells nor freeze the outer shell, how do you process heat (or a lack thereof) upward or downward between different shells?

Is this really as simple as putting a bunch of massive vents or would it require more than that?

Edit: To be more specific about what is Habitable for this civilization there should be no extended periods of heat above 40 degrees C nor below -5 degrees C.

Edit 2: Septerra Core is a good analog for the world I'm creating. It is a video game with a similar world. But it does not have a ton of information on how the heat is regulated within the world shells. In addition, the shells don't fully cover the other shells allowing light (and heat) to go into lower shells and heat to be radiated upwards. In this constructed world there would be no such gaps. Shell 1 receives all the light from the star and radiates all the heat from every other shell below. Assuming that's how that works (I don't do a lot of science).

Edit 3: This created planet is put in a convenient location near the star enough to get energy put into it and in orbit around the star. But to clarify, this question is primarily concerned with how to regulate waste heat production created from within the shells to keep the lower shells and upper shells in a habitable state.

Edit 4: I have dispensed with a majority of backstory to just get the question at hand answered.

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

Answer 1

You do want to freeze the outer shells and bake the inner shells. That is the entire point of a Matryoshka Brain. The entire point is to be able to create a multi-stage Carnot engine with a massive number of stages, and an incredibly high efficiency. This will implicitly call for hot inner shells and cold outer shells.

The one thing you don't do is put massive vents to let the heat out. If you do that, you aren't getting work out of your difference in heat. You pass all the heat through heat engines.

If you want to minimize this effect, keep the layers all in middle-range orbital distances. The sun produces a fixed amount of energy per second. If you have a larger inner radius, that energy is distributed wider, making it easier to manage the heating. Likewise, small outer radii help minimize cooling into space.

However, you'll have to look at how efficient you want to be. The efficiency of a Carnot engine, multi-stage or single-stage, is goverened by the ratio of the temperature of the cold sink to the heat sink. If your inner layer isn't really close to the sun (getting hot), it limits your maximum efficiency.

Answer 2

This has been said in some of the comments to the answers, but no one has stated it outright:

Why does a civilization capable of producing a Dyson Sphere require this boondoggle?

If it's a vanity project, because the Imperator wants to build one, sure, no problem. But the inner (or outer, depending on star type) surface of a Dyson sphere can be arranged to be at a distance from the star that makes it habitable. If it is so arranged, you have a surface area equivalent to five hundred and fifty million Earths.

Population pressure will not be a problem for at least 25 generations, assuming no population control. (Assuming doubling of population per generation, with one earth's worth of people to start.)

It's an impossibly vast space to fill... and, importantly, vs. the elaborate shell-game that is the proposed planet, they've already built one.

Gravity could potentially be a problem if you're living on the inside, or with certain kinds of star, but this could be overcome with sufficient engineering, provided your civilization has access to some remarkable materials (which they would have to have anyway).

Answer 3

Your comments suggest your already aware of Septerra Core, so maybe use it's solutions.

The upper shells are a desert, the top being a polar desert, the second being a warmer windy desert, and the bottom being a warm dark jungle with plants competing for the little light available and the heat coming from the lava on the core itself. There is not much water on shell 7 but the moisture is high because water falling from the higher shells turns to mist and steam on the lower shells.

The plants have to give off their own light to attract insects to pollinate, making the bottom shell glow to people on shell 5 and 6. Shell 3 becomes a temperate zone, located high enough to get sun, but low enough to get extra water from the above 2 shells.

Shell 5 will likely have the most people, as they are able to mine the core rather easily for resources, collect water from upper shells easily, and still collect enough sunlight for farming.

Shell 3 will have less access to resources, but stronger farming. This means shell 4 will probably become a trade hub between shell 5 and 3.

Answer 4

You want to insulate the outside layer and let heat through to the inside layer.

The outside layer is going to have a temperature dominated by the cold of space, at something like -270C. It's really cold. Heat is going to constantly flow through it. You need to make sure that the energy from 1 star can pass through this layer at a rate which preserves the -5C minumum you mention. This will likely involve controlling the conductivity of the outside shell, and possibly even putting insulation on it.

You'll want to do similar for the inside layer. It is going to face the star all day, so it will get much hotter than our environment does today with its transitions between day and night. You'll probably also need to put insulation here, but we may approach that differently.

The real trick is to get the thermal resistance of the inner shells low. Think of it like 7 layers of copper sandwiched in styrofoam. No matter how you heat or chill the outside layers of the stryofoam, the 7 layers conduct heat quickyl from one to ther other, so they are all relatively similar in temperature.

I would choose to do this by erecting giant fresnel lenses over the inner layer which focus a large fraction of the light through relatively small holes in the the layer. If you covered 50% of the area this way, only 50% of the light would fall on the inner layer (the part that was not covered). The remaining light could go through holes, which would cause the inner layer to look like a giant constelation of stars, with each hole providing some of the sun's light to the next layer. This would let you rapidly move heat from one layer to another without wasting large amounts of surface area. It also means you can have natural light on the second and third layers, which is a nice perk.