I don't know how people can convince themselves that they can understand these effects.
Unusually effective heat insulation is exactly how they work. (This is tempered by eg radiative losses, so making them thicker doesn't work better.) placing poorer heat (vs electrical) insulators between peltier material is counterproductive, similar to using resistors to improve conduction between copper wires
Don't ask me for a better explanation :)
As to why COP or even Carnot efficiency hasn't been thrown out in favor of temp-difference independent efficiency metrics like exergy.
Indeed, but in practical use (like a mini refrigerator), one will want to insulate the hot and cold sides from each other.
If one makes the walls thick, then they end up with a hole for the Peltier device and somehow sandwich two heatsinks on the device while maintaining insulation around it.
Perhaps easier to deal with in CPU cooling and such since one side is simply smacked into the thing being cooled.
What is exergy? The one time a mechanical engineering colleagues tried to explain it to me, he reached the wrong conclusion on the problem we were working on.
I haven't seen it in any physics thermodynamics book, and only mech eng. seem to know what it is, and then only in the US.
Faires (undergrad MIT Thermo book from the 50s) makes no mention of it as far as I can tell.
But that isn't a mathematical expression. At best, it would appear to be energy * maximum_Carnot_efficiency (for heat engines anyway)
But it seems not to be adding very much, since Carnot efficiency depends on delta_(T). The OPs point that exergy doesn't depend on T is tautological since T has already been accounted for by the Carnot expression.
Unusually effective heat insulation is exactly how they work. (This is tempered by eg radiative losses, so making them thicker doesn't work better.) placing poorer heat (vs electrical) insulators between peltier material is counterproductive, similar to using resistors to improve conduction between copper wires
Don't ask me for a better explanation :)
As to why COP or even Carnot efficiency hasn't been thrown out in favor of temp-difference independent efficiency metrics like exergy.
I can't tell you either