On Reaction-Radiation Equilibria in Slab Geometry

Abstract

We consider a slab of absorbing-emitting-reacting medium bounded by two parallel black walls held at constant, equal, temperatures. Taking an Arrhenius law with large activation energy as chemical rate, and a differential equation of radiative transfer, we study analytically the conditions under which the radiant losses, with in-depth absorption included, can balance the heat release due to chemistry.

For slabs of small optical thickness, the criticality conditions corresponding to ignition degenerate to those given by a Semenov-like problem, whereas optically thick slabs lead to results that tend towards the Frank-Kamenetskii problem.