My thoughts on thermoelectric generator + rocket:
1 ) Expect ~4% efficiency. This could be justified if the fuel was going to be burned anyway for heat (aka “CHP”), otherwise it’s probably not efficient enough to be justified.
2 ) If you’re actually going to invest the $2-3/W, you might as well keep it running continuously if possible for the entire heating season.
3 ) RMH don’t burn much fuel. Say 1.5 cords/cold-season. Really not much thermal power to work with, especially at ~4% efficiency. To me this implies that all (or nearly all) of the heat should pass through the TEG. This is non-trivial to design, given the small area of the TEG device and the max temperature limitations. Not saying it can’t be done, just non-trivial.
4 ) For max efficiency (already rather low), and max power, it should be run near the max temperature of the device.
5 ) Given these assumptions (moderately high temperature and constant temperature, continuously, I then look to the RMH properties and operation. Fluctuating temperatures and often not a lot of thermal storage at higher temperatures.
This makes me wonder: how could RMH temperature be made more constant?
I was envisioning semi-automatic fuel conveyance. For instance a woodchip system, or perhaps a bundle of few sticks, several feet long, with a weight on top to gravity-feed the J-tube, and refilled once a day.
The batch-box style might work but could require more high-temp thermal storage and additional temperature regulating systems for optimal function.
6 ) From there, them one could think about ways to limit peak temp and heat exchanger design. Due to the high heat-flux requirement, liquid heat transfer on one or both sides of the TEG might well be needed or appropriate, (as mentioned above).
7 ) Much like with solar cells (a very similar semiconductor device), clearly the TEG is enticing for its simplicity, solid-state reliability and low maintenance; that is, if it’s lower efficiency can be justified.
8 ) The niche application would be for cold-climate off-grid use, especially in areas where solar and/or wind aren’t particularly abundant.
9 ) The availability of off-the-shelf TEG components is excellent (especially compared to steam or Stirling heat engines). The safety is probably also considered much better.