Hi Johnstra,
Uh oh, now you've asked for it, literally!
I'm actually designing an alcove for my future stove, and have some tweaky, geeky thoughts, for others to sanity check for me.
My quick answer is I think an alcove need not be a problem and, if it is designed well can actually offer some advantages.
"Absurd!" you say? Let me explain.
As I see it, as long as one maintains minimum clearances, etc, there are two main issues, and an option:
1. Not losing heat in the alcove.
2. Getting heat out of the alcove.
3. Optionally, smoothing temperature swings.
1. Not losing the heat: A radiant stove in particular, will heat up the alcove itself, so it seems important that the alcove be well-insulated if it is on an outside wall. Temperature loss through a barrier is directly proportional to the temperature *difference* across that barrier, so a hot wall/alcove of a given R-value will lose a lot more heat to the outside than cooler walls around it with the same R-value.
In particular, backing a stove or insert into an uninsulated masonry fireplace on an external wall will lose more heat to the outside than the same fireplace moved out into the room. So the upshot is, if the alcove is on an outside wall, it should be well-insulated--better than the surrounding walls if their insulation is only fair.
2. Getting the heat out. It seems to me that the trick is simply moving air over the hot surfaces of the alcove to heat the air and get the heat out. This seems fairly simple, and could be a ceiling fan that moves air through the alcove, or a box fan blowing cool air towards the alcove, or a fan behind the stove.
Geometry helps too--an alcove with an angled ceiling would tend to pour air out into the room through natural convection, with less trapped than under a flat ceiling.
Of course convection stoves lessen both of these problems, by heating the air more and the surrounding surfaces less--but usually, if using a blower, at the expense of some noise from the relatively small fans in the blowers. In general, the smaller a fan, the more noise it makes to move a given amount of air.
3. Do you want to smooth out temperature swings? Soapstone, cast iron, and thermostats smooth these swings, but if you have a manual steel stove, you might want thermal mass to suck up bursts of heat, and re-radiate them gradually. An alcove with thick stone walls could do that, though, from #1, outside walls should be well insulated.
In my case, I'm planning on a stove with fairly constant heat, so I'm not concerned about smoothing out temperatures, but just moving heat out into the room. So I'm planning on a well-insulated alcove, with side walls angled to reflect heat out into the rooms, with a 1" airspace under a covering of corrugated sheet metal (on ceramic spacers). Such a covering of spaced sheet metal is usually used as a heat shield to keep the walls from burning, but I'm planning to use the covering mainly to *intercept* the heat, reflecting it out into the room and changing radiant into convection heating by heating the air flowing over it. That air flow will come from natural convection, and will be augmented with a ceiling fan, which will be quieter than most stove blowers.
This setup would have the added advantage of working well in power outages. The reflectivity of the sheet metal, and natural convection over it should transport heat out into the room even without a fan.
That's my plan anyway.
Of course a radiant stove placed centrally in a room avoids all these issues, but that would be too easy. (And in my case, I want the extra space.)
There are my thoughts--I hope they are useful, and that other folks check my reasoning. Happy heating!