A fire in a hearth disperses heat to, I guess, three places:
- the bricks of the chimney
- out the hearth (where the person tending the fire is standing)
- out the chimney, above the house
How would you go about figuring out how much of a fire's heat goes to each of these three places? I assume the specific heat(†) of the bricks plays a role in both capturing and retaining heat from the flames. But what do you need to measure, and what calculations would you do with those measurements, to predict how much heat would go to each of those places?
Just a pointer to the right approach would be helpful.
† (BTW, this seems like a good example of temperature vs heat: if the volume of air in the house is much larger than the volume of flames, then even a hot fire cannot warm a cold house very much.)
Bonus question: I want to contrast colonial homes with one fireplace in the centre, versus homes with several small fireplaces around the edges. I'm thinking of modelling this as a plate with one large central heat source, versus a plate with several small heat sources around the edges. Any reasons why this is wrong would be appreciated.
Best Answer
This is such a complicated question! The worst part is that as heat leaves the chimney, it draws air from the room with it - air that needs to be replaced from outside. This actually makes fires quite good as ventilation systems.
Whether a fire heats a building depends in very large part on the degree to which cool air can flow past parts heated by the fire. This makes a wood stove (metal pot "in the room" with a small pipe leading out) much more efficient than a hearth. But in many cases a fire place might have other mechanisms to improve heat transfer - for example with ducts that run alongside the chimney and that draw in and heat cool air from the room.
Measuring this is quite tricky. I suppose you start with measuring the temperature of the effluent at the point in the chimney still just inside the house (air might cool more when you get further out but that only heats the external chimney and boer the house). You also need the flow rate of the air - this will allow you to estimate "heat going out the chimney" (assume outside temperature for the initial temperature because you are drawing outside air in). Next, for a fireplace that is on the outside wall, measure the temperature of the outside wall (IR non contact thermometer) and make reasonable assumptions about the h factor of air flowing past the wall and the heat transport. I would not worry about bricks of the chimney and their heat capacity - in the steady state that neither gains not loses energy.
Finally measure how much wood you are burning per hour and use this to estimate the net heat going in- this allows you to estimate how much of the heat is making it into the house. You could also measure how warm the house gets with the fire (again use steady state) and see what kind of (electrical) heater you would need for the same effect.
Note that a fireplace is most effective as a radiant heater - you sit/ stand nearby and feel warm, even though the room might be quite chilly.
As I said - this is a really hard problem.