Mathematical modeling of thermal explosion with natural convection: a brief survey

Thermal (or heat) explosion occurs in a reacting medium if the heat production due to an exothermic chemical reaction exceeds the heat loss through the boundary. In the mathematical approximation heat explosion is characterized by an unbounded temperature growth. If the reaction occurs in a liquid or gaseous medium, then a nonuniform temperature distribution can lead to natural convection. The interaction of heat explosion with natural convection can result in various regimes with a bounded temperature distribution (stationary, periodic, chaotic) and to a transition to heat explosion. The latter can be accompanied by a monotonic temperature growth or by temperature oscillations (oscillating heat explosion). This paper presents a review on mathematical modelling of heat explosion with natural convection in a homogeneous fluid and in a porous medium.