Re: [amsat-bb] Peltier element in space ?

[Phil Karn <karn@xxxxxxxx>]

MERRETT, David wrote:

> These have been used before in space, by using a nuclear source to generate
> the heat, and cooling the other side by radiating heat away.

And most of those applications are in the outer solar system where 
sunlight is just too weak to be a practical energy source, and where you 
can just barely overcome the protests of the doomsaying loonies who 
think a launch failure would wipe out the human race. E.g., Jupiter is 
~5AU from the sun, so the solar flux is 1/(5^2) = 1/25 = 4% of what it 
is at Earth. Nuclear power is the only way to go out there.

Peltier devices, operated as generators, are heat engines. As such, the 
Carnot limit applies. The second law of thermodynamics requires that you 
provide not only a source of heat but also a place to discharge most (or 
at least much) of that applied heat at a lower temperature. The fact 
that heat is usually supplied to a heat engine by burning expensive 
nonrenewable fuels tends to obscure for many people the fact that the 
cold sink is just as important, more vital even, than the heat source. 
Otherwise we could just build big power plants that would work off the 
enormous heat energy stored in the oceans. In 1881, a clown by the name 
of John Gamgee managed to talk the US Navy to invest a lot of money in a 
ship engine that would do just this. It never worked, and it never could 
have. The idea was to use ocean heat to boil ammonia to drive a turbine. 
The flaw was that without a cold sink, there was no way to condense the 
ammonia gas back into a liquid for reuse in the boiler.

Even today there are a few (many, actually) crackpots who insist they 
have found a way around this basic physical law. None have ever 
succeeded, but I know a lot who say they're just two weeks away from a 
working prototype, and *then* the world will stand up and take notice...

(There is something called "solar ocean thermal energy conversion", but 
it exploits the temperature *difference* between the surface and deep 
layers in the ocean. Collecting the warm water at the surface is the 
easy part; the hard part is running the pumps and deep pipes required to 
get at the cold water down below.)

In space, you need not only a source of heat (which the sun readily 
provides, at least at earth distance) but also a way to radiate much of 
that heat *at a much lower temperature than your collector*. It's fairly 
easy in the vacuum of space to make a surface very cold -- you just 
paint it with a highly emissive paint and you point it away from both 
the sun and the earth. If it sees only cold sky, it will eventually 
reach an equilibrium with the temperature of the cold sky. Since much of 
the celestial sphere (out of low earth orbit, anyway) is not much above 
the cosmic background of 3K, you can easily get some pretty cold 
temperatures in this way.

But that's only if you don't dump any heat into it. If you do -- and our 
heat engine requires that you must -- you'll increase its temperature 
toward that of your heat source. And the smaller this temperature 
difference, the less efficient your heat engine will be in both theory 
and practice. That means even *more* of your input heat will have to get 
dumped in the radiator, and it will get even hotter, and...

So you must not only make a good radiator that you shield from both the 
sun and the earth, but you must also make it *big*. The bigger it is, 
the more watts of heat it can radiate without exceeding a certain 
temperature.

The problem is, cold objects just aren't very efficient radiators. The 
power any "black body" (the most efficient radiator possible) will 
radiate to deep space is proportional to its surface area and to the 
*fourth power* of its absolute temperature -- and we want to keep that 
temperature very low! So you need a pretty damn big radiator.

Check out the artist's conception of the nuclear-powered Jupiter Icy 
Moons Orbiter at http://www.jpl.nasa.gov/jimo/. Note that really big 
array of black fins down the length of the probe. That's the radiator 
for the nuclear-powered heat engine that powers the spacecraft, 
including its electrically-powered ion engine. That radiator must dump 
most of the heat energy produced by the reactor, and it must do it at a 
temperature well below that of the reactor. This is actually a fairly 
easy task with a reactor since it can run at a fairly high temperature, 
and since it's the temperature difference that counts, so can the 
radiator. If you have to make use of a lower temperature heat source, 
such as that provided by a passive solar collector, then your radiator 
has to operate at an even lower temperature and must be even more 
massive per watt of power to yield an acceptable thermal conversion 
efficiency.

I'm sure a lot of people have looked at that massive Jovian atmosphere, 
made almost entirely of hydrogen, and fantasized about using it as a 
chemical fuel on Earth. But I wouldn't be surprised if Jupiter and its 
icy moons -- which (except for Io) are pretty cold in their outer layers 
-- actually wouldn't have an even bigger theoretical energy potential as 
a *cold sink* for heat engines driven by the heat energy of the earth's 
oceans (which is in turn supplied by the sun). Of course, even *that* is 
far, far too small to justify the actual mining of Jupiter's atmosphere 
with present technology, even if it could somehow be kept cold for the 
return trip...

So the bottom line is that while solar powered heat engines have always 
been intriguing, the fact is that solar cells (which are not heat 
engines) have always been far more practical, in space as well as on the 
ground, and this is even more so with the development of more and more 
efficient solar cells.

Phil



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