Jane's "interest" in that NAS report evaporated after I showed that Jane had been fooled by "Steven Goddard" once again. So let's return to Jane's confusion about basic thermodynamics.
But net radiative power out of a boundary around the source = "radiative power out" minus "radiative power in", so the equation Jane just described also says:
NO!!!!! As I have explained to you innumerable times now, you can also consider your heat source, by itself, that "sphere". The only NET radiative power out comes from the electrical power in. Further, the cooler walls do not contribute any of that NET power out. That's what net means. [Jane Q. Public, 2014-12-16]
I've already pointed out that Jane's hopelessly confused about the word "net", but that's just one of the mistakes Jane packed into these few sentences.
Jane's also wrong to imply that energy conservation across one choice of boundary could somehow contradict energy conservation across another boundary choice. That's impossible. Many boundary choices are inconvenient but they all have to be consistent. Otherwise, how could we possibly tell which boundary choice was correct?
So Jane can't object to the simple energy conservation equation I derived by claiming that some other boundary choice would somehow contradict my equation. That's completely impossible, and if Jane doesn't understand that point then he should learn about conservation of energy: example (backup), example (backup), example (backup).
As you can tell after reading those introductions, here's how to apply conservation of energy. Draw a boundary around the heat source:
power in = electrical heating power + radiative power in from the chamber walls
power out = radiative power out from the heat source
Since power in = power out through any boundary where nothing inside is changing:
electrical heating power + radiative power in from the chamber walls = radiative power out from the heat source
I put the boundary around the heat source so the boundary is in vacuum. That's because radiation can't travel through opaque solids like the heat source. So the only way to obtain an energy conservation equation with radiative terms is to place the boundary around the heat source.
For example, I calculated the enclosing shell's inner temperature by drawing the boundary within the enclosing shell. This boundary was inside aluminum, so heat transfer through it was by thermal conduction, not radiation. Notice that even this boundary choice leads to a conduction equation where electrical heating power depends on the cooler chamber wall temperature. That's because all boundary choices have to be consistent. They can't contradict each other unless one of them is wrong.
After I asked Jane to explain exactly where his boundary would be drawn, Jane replied:
... You can draw the boundary right around the heat source. Electric power comes in, radiative power goes out. There is no contradiction, and no inconsistency. ... [Jane Q. Public, 2014-09-15]
Nonsense. I've repeatedly explained that my boundary is drawn around the heat source, so it's in vacuum and therefore contains radiative terms both for radiation going out and radiation going in.
Choosing to put the boundary somewhere else, like inside the heat source, leads to an energy conservation equation with conduction rather than radiative terms. But even those conduction equations agree that electrical heating power depends on the cooler chamber wall temperature. They can't contradict each other. Putting the boundary somewhere else might be inconvenient, but it couldn't possibly contradict the fact that electrical heating power depends on the cooler chamber wall temperature.
My energy conservation equation is this: electrical power in = (epsilon * sigma) * T^4 * area = radiant power out [Jane Q. Public, 2014-10-08]
Once again, Jane's wrong. There is literally no choice of boundary which will lead to his absurd equation. Once again, it really sounds like Jane opened a textbook and found "radiative power out per square meter = (e*s)*T^4" and simply assumed that "radiative power out" is just a fancy way of saying "electrical heating power".
At least, that's the most charitable explanation. Once again, I'm trying to rule out less charitable explanations like the disturbing possibility that Jane isn't honestly confused about basic thermodynamics. Maybe Jane/Lonny Eachus has simply betrayed humanity by deliberately spreading civilization-paralyzing misinformation.
Jane/Lonny Eachus could help convince posterity that he was just honestly confused by thinking carefully about conservation of energy, explaining exactly where his boundary lies, and carefully listing all the power going in and out of that boundary.
Or Jane/Lonny Eachus could help convince posterity that he's betrayed humanity by continuing to spread civilization-paralyzing misinformation.