Hot air duct from the thermal mass

I'm sure it's been covered but I don't see where.  Has anyone done research for burying say a 4" duct in the cob (thermal battery) to deliver heated air to a clothes dryer or perhaps a distant room that doesn't heat well by convection?  A very small ducted fan could be controlled by a thermostat for temperature control.  My questions are along the lines of: how long to run the duct; what diameter, (4", 6"); how fast would it deplete the thermal mass?

I don't think there is any actual research on this. I expect it would work, but how well depends entirely on all the individual details of the build.

I would use a 6" duct in the cob mass, fairly close to the main duct but still several inches clear, as long as reasonable without contortions, and insulate the duct leading to the remote space. It would deplete some of the thermal storage, but you can burn enough longer to make up for that. Experimentation is the only way to give numbers to this question. I hope you try it, and come back with your results and all the sizes and details you can think of.

I don't have enough experience to say if it would be great or just alright, but I would follow the advice of Glenn.  You might try a pebble system so that you can adapt/move the pipe around/closer to your exhaust pipe and experiment with how that works (?).