Glenn Herbert wrote:It seems you're going for extreme heat loss efficiency, so with the tiny size you could get by with quite a small system. A major issue might be the door - you would lose a noticeable fraction of the room air each time you open it. The RMH is valuable in this because its primary function is not to heat air but to make a warm surface to sit on. I would suggest making the mass in/under the bed so you get maximum benefit from it overnight. Even if you are not sitting on the bed when awake, you will be right next to it most of the time.
In the extreme Arctic-like conditions you describe, I would expect a good amount of gusty weather, so an exit straight out a sidewall is likely to be a problem. You really want the chimney to go straight up inside to keep it warmer for good draft, and to position it where it will get the least gust effects. If it is within a few feet of the top center of the dome, and a few feet higher, it will be as well situated as possible.
Is there any kind of clay available in the vicinity of your build site? If so, you will have a simple job of constructing a mass cavity beneath the bed. If not, you might need to bring in some sheetmetal sections and fabricate a tight box to surround with stones. A 55 gallon barrel cut in half lengthwise and surrounded with stone would be a quick and effective means to do this.
Sizing: In general, a 6" diameter system is the smallest common size; a 4" system can sometimes be made to work well if built just right and tweaked, but it has severely limited output. In a more temperate climate, I might suggest close to 4" for such a small space, but I think you would be safer going with 6". If it generates too much heat for the space, you just need to run it for shorter periods to charge up the mass. You might want to burn a couple of times a day to cook anyway. By the way, how is the wood supply in your location? You can use small stuff, even spruce/fir if that is what grows there, but it will need to be dry. A smaller system is especially sensitive to this.
The exact dimensions of the combustion core will depend in part on your materials. Firebrick is an excellent choice, likely to outlast you. You will need good insulation surrounding a firebrick core, which can be rockwool, ceramic fiber blanket, perlite, or any fireproof material you have available. The feed tube, burn tunnel and heat riser should have similar shapes and sizes, like 5" x 5", 4 1/2" x 6", or whatever works. For the riser and possibly other areas, you can use firebrick splits (4 1/2" x 9" x 1 1/4") to minimize unhelpful mass in the unit and weight carried in. You would want a small steel barrel to go over the riser, any size that gives at least 1" at pinch points around the insulated riser and around 2" average, for good airflow. Remember the recommended ratio of 1:2:4 for feed tube height above burn tunnel floor, burn tunnel total length, and riser height above floor. The actual dimensions will depend on your barrel clearances and brick sizes. The burn tunnel can be as short as possible and still have working clearances.
Have you read the book Rocket Mass Heaters, third edition (or as a digital download from rocketstoves.com) yet? It gives a lot of details for construction in various conditions.