On the mathematical problem that represents the steady state combustion of solid fuels

Abstract

One of the most captivating experiences in childhood is that of contemplating fire. Fire appears as something entirely different from a solid, a liquid or a gas. In particular, this may have leaded the Greeks to choose fire (together with earth, air and water) as one of the elements that constitute all other substances. The fire caused by wood burning is just one instance of a number of phenomena referred to collectively as combustion phenomena. A lighted candle, a Bunsen burner, the explosion of gasoline in an internal combustion engine, a flying rocket, and even iron rusting, are instances of combustion processes. With the exception of iron rusting, it is natural to think that these phenomena are somehow variations of the same idea. It was not until the XVIIIth century that a scientific understanding of what combustion processes essentially are was achieved. In short, a combustion process is an exothermic chemical reaction between a compound (called fuel) and an oxidizer (usually oxygen). Let us consider some examples.