I only became aware of the need to cool the burn tube this morning while reading this thread ---
https://permies.com/t/32099/rocket-stoves/doubling-power-RMH-cooling-feed --- The author has built a metal contraption to draw heat from the tube. He heats water with it. A few seconds later, I thought of this.
My metal working skills are thus --- I can make really nice straight cuts and I can do simple curved cuts. I can sand sharp edges. That's it, my full arsenal. Most of us are familiar with how the aluminum fins on an air cooled engine work. Aluminum is great at moving heat around. It transfers heat many times faster than steel does. The large surface area of the fins allow heat that is drawn from the engine to be given off to the cooler air. The structure of a firebrick feed tube lends itself perfectly to the insertion of plate aluminum fins. It's just a matter of cutting the plate to size, so that a little sticks into the burn tube and several inches protrude beyond the brick, into the cool air near the floor. The plate could be bent at a 90 degree angle so that one surface could rest tight against the inside of the burn tube. Not only will this reduce heat build up in the burn tube, it warms the air near the floor where it could be used as the supply for a secondary burn.
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Plate aluminum under the insulated burn floor will diffuse heat to the much larger hearth. There would still be a little insulation between the aluminum and the wooden floor. Since aluminum allows heat to travel along it's length very easily, any heat that makes it through the insulated burn floor, will be directed laterally. Say we use a 30 inch square plate under a 6 inch system. the whole thing is 900 sq. inches. The part beneath the fire is 36 sq. inches. This large radiant area will easily keep the plate under the fire relatively cool. Pans full of water could be warmed while sitting on the plate.
Plate aluminum is worth less than $1 per pound as scrap metal. I could see using 20 lbs. of it between the fins and the hearth plate.