Most heat radiators in space are flat surfaces. In a sense they are single fin radiators. Has anyone studied the used of multi-finned radiators in space (the vacuum of space, not inside a spacecraft)? Any papers on this?
I think it's easy to understand that as the pitch of the fins decreases they become less effective due to radiating into each other. Where are those limits? Where is the trade between adding fins (surface extension) and simply using a larger flat plate?
I'd be interested in any papers or publicly available publications on the subject.
To be clear, this is what I mean by "fins"...
Image from Digikey heatsink page:
Clarification seems warranted. Let me see if I can do a better job of explaining what I think I know.
- You would need a 3 square meter flat radiator to handle the required heat load
- You are only allowed 1 cubic meter of volume for thermal management
- Your starting point is a 1x1 meter radiator
- Creating a flat plate larger than 1x1 meter is not an option
- Every molecule of the radiator is protected from the sun's radiation
- The entire volume occupied by the radiator is protected from the sun by a spacecraft
1 meter x 1 meter flat plate radiator. The arrow shows heat coming from inside the spacecraft. The vectors represent radiation on the space side of the plate. Radiation is not uniform because the magnitude of radiation from a metal is a function of the angle from the normal (chart below from "Radiation Heat Transfer, Augmented Edition 1st Edition").
We must not forget that this is a three dimensional effect:
It's interesting to note just how much of the radiation occurs between, say, 45° and 90°.
Now we add two fins, 1x1 meter each, at the ends of our flat plate:
It is easy to see that a number of photons will not make it out. If I had to guess, maybe only 30% of the total emitted photons can exit.
And yet it's easy to forget this is a 3D problem:
Now it doesn't look so bad. Most of the photons actually do get out.
Forgive me for not trimming the vectors through the fins, I am doing this in SolidWorks and it would be a ton of work to clean up all of that detail as I illustrate the problem.
Do we gain anything? Yes. Here's the 3D on that:
At the very least we've gained two square meters of radiating area on the outside. We are at a factor of 3 with respect to our flat plate. We've also added the portion of the interior faces of the fins that are able to emit photons into space. Hard to quantify this other than to say that in this scenario it likely isn't a trivial gain.
As a note, photons exchanged between fins have no effect. A photon leaving fin A carries away one unit of heat. So does a photon leaving fin B. As they swap photons the net gain is zero. This makes sense given what the limit looks like for this exercise.
As we add fins it is easy to see quite a bit of heat, in the form of photons, can leave the structure:
At limit we reach a solid block 1x1x1 meter in size where each of five surfaces exposed to space is radiating.
This represents a 5x gain in radiating capacity. Of course the increase in mass is seriously off the charts (20x increase in mass for a 5x increase in radiation capacity).
It would be interesting to see the a graph of the actual gains in radiating capacity vs. mass increase and get a sense of where they might intersect. There are also variants that might have fins that are not normal to the surface of the plate and even fins that are taller in the center and shorter towards the ends (or the opposite) in order to allow more photons to escape.
My conclusion is that fins are effective to a point and that optimization requires extensive computational analysis.
My question had to do with whether or not anyone knows of research in this front. Sometimes you don't have the option to use a larger flat surface. This is where fins could become very relevant. My current path is to throw a bunch of FEA analysis at this and see what comes out the other end. It would be fantastic to learn there are papers out there covering the subject.