There seem to be a range of choices for stoves for a hut. Ranging from self built rocket stoves through to expensive narrow-boat inspired option's and cooking ranges. What are you choosing for your hut and why is it the right stove for you ?
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Water is at first look a sound choice in and of itself. It is much less about the density and much more about the specific heat capacity. It is cheap, readily available and is often used by some (bottles of water placed around the roots of plants/bushes/trees) etc as frost mitigation. I think some folk may want to experiment with this but be aware of the issues that come with it.
Pulling out a quote:-
"Specific heat capacity often varies with temperature, and is different for each state of matter. Liquid water has one of the highest specific heat capacities among common substances, about 4184 J⋅kg−1⋅K−1 at 20 °C; but that of ice, just below 0 °C, is only 2093 J⋅kg−1⋅K−1. The specific heat capacities of iron, granite, and hydrogen gas are about 449 J⋅kg−1⋅K−1, 790 J⋅kg−1⋅K−1, and 14300 J⋅kg−1⋅K−1, respectively.[3] While the substance is undergoing a phase transition, such as melting or boiling, its specific heat capacity is technically infinite, because the heat goes into changing its state rather than raising its temperature."
Adding other stuff into solution in your water will alter its phase transition temperature (freezing point, boiling point etc) but increasing its density does not help at all.
Water (especially with other stuff in solution) comes with its own maintenance and environmental risks. It is not really a fit and forget option for a low tech hut that is used occasionally and will be prone to some degree of freeze/thaw. I also have a big aversion to contracting legionaries disease. Warming up volumes of water to breeding temperatures for long periods of time is arguably a touch risky. You can of course mitigate this with additives and regular change etc but it is for me a lot of faf and I am on holiday in my hut LOL.
Putting all of this together and finding something fireproof to place directly around a stove (burn guard) was sort of where/how I arrived at the suggestion of granite, magnetite(Iron) or combined concrete blocks. Better still if you don't have to make them but can score enough surplus storage heater blocks. And I guess how the storage heater brick makers arrived at their own decision on materials.
There is however lots of room for experimentation here, real life applications of anything are always a compromise, there is no one size fits all, and a compromise that suits me may not suit anyone else.
BTW just thought if you had the room it may be better to build a recycled storage heater block surround by laying the blocks on their flatter sides. Sort of C shape downwards towards the floor. They would be a lot more stable that way and still have air passages between the room and the stove..