# Thread: Curious what this differential equation/solution would be

1. ## Curious what this differential equation/solution would be

I've noticed that when a candle burns, the region of melted wax around it is a perfect circle and its radius and hence area is directly proportional to the size of the flame.

Is there a differential equation already out there for this? Because if not I would be interested in finding it myself.

2. ## Re: Curious what this differential equation/solution would be

EDIT: And its solution.

3. ## Re: Curious what this differential equation/solution would be

this is essentially the heat equation, one of the more studied problems in physics.

https://en.wikipedia.org/wiki/Heat_equation

4. ## Re: Curious what this differential equation/solution would be

The heat equation; . The source is heavy on PDE'S. I know the basics from Uni', but their methods didn't come close to mine. Too much to get through in so little time (I don't skip chapters in books; I start at page one and do the whole car wash from front-to-back). I've still got a couple of books on ODE'S I want finished before I progress to PDE'S, that's how I work.

Anyway, I find this thread interesting for myself and I look forward to getting it done. Another thing I've noticed about these candles of mine is that when they burn out there's about 2/3 wax left over. I'd love to minimize their waste and show them how much they could save.

PDE'S is my next goal, thank you.