FWIW, the second pic is roughly what a Rocket Mass Heater stove uses. Except it doesn’t use a metal woodstove underneath, it uses a masonry firebox to the side with unlimited air supply (ala
masonry heater) and the flue exit passes through a thermal mass of some kind. With a metal woodstove where firebox temps need to be kept under control via air restriction, both of these ideas are stupid.