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.
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