... The problem is that there is no such thing as a thermal superconductor of this kind, and you aren't seeing that it leads to contradictions. The only way it could exist would be if it had NO thermal effect on its surroundings whatever. So it's the ultimate straw-man argument. There is no way it can be legitimately used to demonstrate anything. [Jane Q. Public, 2014-09-01]
Again, we'll have to agree to disagree about thermal superconductors. That's why I've repeatedly pointed out that I've already solved this problem with an aluminum enclosing shell, and it also warms the heated plate (aka Jane's "source") to ~233.8F.
No, they didn't, because it's a different problem, being given a theoretical treatment. You keep doing that, but I'm not buying. Two infinite plates, neither of which is heated, is not even remotely the same situation, and it's also theoretical only. They're not taking into account certain real-world factors pertaining to Spencer's experiment. Latour does. Not that they're doing anything wrong... given the context of their situation: infinite non-heated grey bodies. This is not Spencer's experiment. [Jane Q. Public, 2014-09-01]
No, it's exactly the same problem. The same infinite sum of absorption and reflection. The plates are only "infinite" to avoid having to model fringing field effects around the plate edges. And note that Dr. Latour doesn't model edge effects either, so his plates are either infinite or the passive plate completely encloses the "source". Either way, there would be no edges.
Notice that the first example MIT applies their final equation to is a thermos bottle where the inside wall is heated by hot fluid.
You did not point to a calculation he performed on Spencer's situation and prove it wrong. You took what you incorrectly called an analogous situation and called that wrong. Which has been my whole point here. You keep claiming something else represents Spencer's experiment, but you won't tackle Spencer's actual, original experiment. You have consistently refused, for over 2 years. ... You continue to refuse to actually do what you said you'd done: refute Latour's treatment of Spencer's challenge. [Jane Q. Public, 2014-09-01]
Again, Dr. Spencer's actual, original experiment included the possibility of a fully-enclosing passive plate. And so did Dr. Latour's treatment of it. If you don't agree, please show where Dr. Latour specifies the dimensions of the plates before wrongly concluding that T remains 150.
In fact, as far as I can tell nobody's specified the plate dimensions except for me. Since the argument I'm refuting never specified the plate dimensions, why would the plate dimensions matter?
... I repeat: get the experiment with the two separate plates (actively heated plate and passive plate) right first. Then you can move on to a fully-enclosing plate. You say it's simpler but in a way it's not; you're trying to ride a bicycle when you haven't even managed to ride your tricycle without falling off. ... [Jane Q. Public, 2014-08-29]
... Take Spencer's original experiment, with two separated, non-enclosing plates, and show SPECIFICALLY where Latour was wrong in his calculations. THEN, if you like, you can move on to the enclosed-source situation. ... [Jane Q. Public, 2014-09-01]
Once again, the original experiment included both scenarios: fully-enclosed and not-fully-enclosed. We can agree that one should solve simpler problems before moving on to more complex problems, but we seem to disagree about which of the scenarios in Dr. Spencer's original experiment is simpler.
Again, solving a problem without spherical symmetry means you'll have to solve for equilibrium temperatures which aren't constant across the heated and passive plates. Those equilibrium temperatures wouldn't be simple numbers. They'd be complicated functions that would vary across the plate surfaces. Contrast that with a spherically symmetric enclosing plate, where equilibrium temperatures are just simple numbers.
Are you disputing those facts, or do you really not see which of these problems is more complicated?
I don't have enough time to program a finite element model to account for the fact that a non-fully-enclosing plate would cause plate temperatures to vary across their surfaces. But even if I did, the first thing I'd do after debugging it would be to check the finite element solution in a case where a simple analytic solution can be obtained. Namely, a fully-enclosing passive plate, where the plate temperatures are simple numbers.