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Related: Finned heatsinks in space

Multi-fin heatsinks are not normally considered good for heat dissipation in space because adjacent fins radiate into each other, and you would be better off with only 3 or 4 radically mounted fin, and 5 or more puts you solidly into the region of asymptotically diminishing returns.

However, it seems somewhat common for radioisotope thermal generators to have multi-finned radiators

Apollo experiment RTG, 8 fins Apollo surface experiment RTG, from NASA 1971

Cassini's RTG, looks like 8 fins Cassini's RTG, from NASA

Why is this done on RTGs?

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    $\begingroup$ Perhaps because the RTG needs to shed waste heat in Earth's atmosphere? Wouldn't be much use if it melted before launch, would it? $\endgroup$ – jamesqf May 24 at 4:41
  • $\begingroup$ that's something I've also considered concerning about RTGs. $\endgroup$ – ikrase May 24 at 4:56
  • $\begingroup$ The Apollo RTG has 8 fins. ;) $\endgroup$ – Lawnmower Man May 24 at 23:07
  • $\begingroup$ Apparently I can't count. Edited. $\endgroup$ – ikrase May 25 at 0:00
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With typical active radiators on spacecraft, heat is transferred away from the sources into the radiators through forced convection - as heated coolant. At that point the only concern remaining is to remove (radiate) it from the radiators (and as little as possible back into the spacecraft or into other radiators). They are big and they face as much into dark space and as little into each other, the spacecraft and the Sun as possible.

With passive radiators of the RTG, the heat is conducted away from the core through the body of the radiators. They can't be very big, and especially can't extend far length-wise from the core both due to space constraints, and because not much heat will be conducted far from the core.

The sideways configuration makes least amount of such radiator to face into the core. Quite a bit faces into other radiators but as long as the heat goes into far edges and not into the "roots" it's not that big of a deal. Using fewer radiators - like 2-3, more heat would be radiated off per radiator but less heat per the entire cooling set. So - the trade-off in efficiency of individual radiators is made to increase their number, and simultaneously the number is still kept low - 6-8 - because with more we'd face diminishing returns as they face more into each other and less into space.

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    $\begingroup$ In addition to the raised concerns, RTGs are mostly used beyond Mars. Incoming solar radiation is not a very big threat at such distances, reducing the need for what is effectively a large flat plate with a thin edge face-on toward the Sun. $\endgroup$ – David Hammen May 23 at 17:36
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    $\begingroup$ @ikrase RTGs are limited by a number of different correlated factors. One of them being 'toughness' of their casing sufficient to survive RUD of he rocket during launch and the resulting crash. They are very rugged. And that limits use of a whole bunch of other solutions that are efficient but mechanically fragile, like heat pipes. $\endgroup$ – SF. May 24 at 7:42
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    $\begingroup$ @DavidHammen "In addition to the raised concerns, RTGs are mostly used beyond Mars." I would rather say they are necessary beyond Mars. Closer in, you can do with solar panels. But the RTGs are used anywhere they are installed: you can't stop them and probes need the energy while traveling on their slow orbits out of the inner solar system. $\endgroup$ – David Tonhofer May 24 at 9:56
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    $\begingroup$ @DavidTonhofer the current Juno Jupiter probe uses solar panels. nasa.gov/mission_pages/juno/main/index.html $\endgroup$ – Organic Marble May 24 at 13:08
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    $\begingroup$ @OrganicMarble Yes it does. But it's at the limit: jpl.nasa.gov/news/news.php?feature=4818 : "Solar power is possible on Juno due to improved solar-cell performance, energy-efficient instruments and spacecraft, a mission design that can avoid Jupiter's shadow, and a polar orbit that minimizes the total radiation." - Probably not a bad thing to not have to jump through the nuclear reg loops, beside the fact that Pu-238 is rare in the U.S. (What's the state on that?) $\endgroup$ – David Tonhofer May 24 at 14:22
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Multi-fin radiators are worse per unit mass.

But for an RTG, it is absolutely vital to provide a very large thermal gradient between the (very small) core and the outer layers. Adding more fins still improves radiation in sum, you just get less radiation per fin.

Since the cooling requirement of an RTG is high and absolute, designers have no other choice than putting up with the mass penalty of more fins.

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    $\begingroup$ I wouldn't say "per unit mass" but "per unit area". Mass doesn't matter, and might be larger in case of a single large fin due to additional stiffness needed. $\endgroup$ – asdfex May 23 at 12:58
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    $\begingroup$ Mass matters. There's sufficient space in space. $\endgroup$ – SE - stop firing the good guys May 23 at 13:27
  • $\begingroup$ Yes, mass matters, but "Multi-fin radiators are worse per unit mass." is wrong. They are worse per unit area. $\endgroup$ – asdfex May 23 at 13:53
  • $\begingroup$ I don't see your point. Worse per unit area directly implies worse per unit mass. $\endgroup$ – SE - stop firing the good guys May 23 at 13:54
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    $\begingroup$ It doesn't, because mass also depends on thickness. One large fin radiates more heat per unit area, but weighs more per unit area because of additional structural material needed to hold it and conduct the heat over a larger distance. At some point a multi-fin setup starts to be lighter for the same amount of radiated heat. $\endgroup$ – asdfex May 23 at 13:56
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Fins are not really bad for radiative heat transfer. They just face an inevitable point of diminishing returns. Those diminishing returns place a limit on how many fins should practically be included. The optimum is greater than zero but less than a dense packing of fins.

Draw a boundary around any isothermal object radiating heat energy into space. The amount if radiation passing through the boundary is always less than or equal to what the boundary would emit if it were a black body having the temperature of the source inside. In particular, if we draw a tight-fitting convex hull of the emitter as our boundary, then the radiant heat transfer is limited to the black-box radiation that could emerge from the area of the hull. We can approach this convex-hull limit in principle in either of two ways:

1) Use a nearly black-box material. In principle, if the material is perfectly black the radiant heat transfer through the convex hull will reach its limiting value.

2) Put in a lot of concavities and increase the surface area. If we could increase the surface area of the emitting body under the convex hull to infinity, we could get black-body radiation through the hull.

The convex hull depends on geometry, so there is an extra way to increase the limit:

3) Within available space, setting up your geometry to allow a convex hull with a larger surface area enables more heat transfer. As we shall see, this plays a major role in the design of finned radiators. Even if you have a perfectly black material and the radiation then no longer depends on the detailed structure of the emitter, changing the convex hull to an increased surface area opens the way for more heat transfer.

Black-body radiators designed to calibrate pyrometters take the second concept nearly to that extreme. The emitter is an isothermal cavity with a small hole from which the radiation emerges. The area of the emitting surface is so much larger than that of the hole (which is serving as the boundary) that even with common industrial materials the hole comes close to achieving bkack-body heat transfer. The pyrometer is then placed so that (within some tolerance) it receives only this nearly black-body radiation from the hole, providing a standard for the calibration.

In the case of finned RTGs we now have materials available that come close to black surfaces (#1 above), so adding more surface area to the emitting surfaces (#2) has little effect. But we do gain an effect from the area of the convex hull itself (#3). Suppose your RTG has a radius of 0.25 m and a height of 2 m, and you place four 0.5-m long fins around it. The convex hull is a square prism, whose surface area is 10.74 square meters. Now try six fins: your convex hull has changed to a hexagonal prism, and its surface area is increased to 11.92 square meters. You've added 10% more heat transfer just from the convex-hull area alone. You eagerly add more fins, only to discover that you don't get as much bang for the buck (or for the kilograms of additional mass): the convex hull never gets bigger than a cylinder whose area is 12.96 square meters.

We got as much additional area for heat transfer with just two additional fins from four to six as we can ever hope to get with infinitely many more than six. Given this sharp dropoff in return, in real life we should expect an optimal design for heat transfer versus weight, ease of fabrication and testing, etc to involve several but not many fins.

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  • $\begingroup$ Wikipedia says that blackbody radiation does not respect shape or structure at all: en.wikipedia.org/wiki/Black-body_radiation. If it did, you could make a heat engine out of one. Take a solid block, and make one side emit more heat using your juju. Now, that side will always be colder than the other side. You now have a "free" hot/cold pool separation. Place heat engine in between sides. $\endgroup$ – Lawnmower Man May 24 at 23:12
  • $\begingroup$ For a perfectly black body (wherevthe radiant heat transfer reaches the convex hull limit) I never say that the shape or structure of the emitter has any impact. Rather it is the shape and structure of the convex hull that has the impact, and in the case of a finned RTG the convex hull changes (to a limited degree) with the number of fins. I will try to edit to make this more clear $\endgroup$ – Oscar Lanzi May 24 at 23:15
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Most RTG's have finned heat dissapators, namely because it increases the surface area exposed to space to dispose of waste heat. They're heat rejection panels to keep the sun from over heating the tubes. If the tubes are heated they'll fail to do their jobs. So the fins are like awnings as well.

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  • $\begingroup$ "to keep the sun from overheating the tubes"? -1 $\endgroup$ – Organic Marble May 27 at 14:22

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