1. The problem statement, all variables and given/known data In essence, I'm trying to make a model of how the heat from a point source diffuses through air. It should be a function of both distance and time (I'm assuming either a 1/r^2 or an exponential dependence on distance). 2. Relevant equations I found this equation: [tex] \Phi (x,t) = (1/√4πkt) exp(-x^2/4kt) [/tex] I have two issues. First of all, at x,t=0 (initial conditions of the point source) the temperature of the point source should be a constant. I assume it's a Dirac delta function, which makes me think this isn't the correct equation. In addition, the point source is also being heated while the heat is being diffused. This isn't a homework question, just a problem I'm working on for an internship. 3. The attempt at a solution From the above equation and Newton's law of cooling, I have reason to think that the decay is exponential, but have no idea how to quantify this. I considered adding a term to the previous equation, but that still doesn't account for it heating up.