Introduction

Most of us know that a catalytic converter is a device that is located in our car somewhere between the engine and the tail pipe, and that its basic function is to convert harmful components of the engine exhaust, such as carbon monoxide, to less harmful ones, such as carbon dioxide. It is an important device in pollution mitigation especially in urban areas where there is a large concentration of cars. For most of us the story ends there. However, for a manufacturer of catalytic converters, such as Allied Signal, there is an obvious need to gain a deeper understanding of the behavior of catalytic converters. At the Fifth Workshop on Mathematical Problems in Industry held at RPI in May, 1989, a representative of the research group at Allied Signal presented various mathematical problems related to the dynamic behavior of catalytic converters. The industrial representative had a set of differential equations modelling the behavior of the gas concentrations and temperatures in the device but was finding it difficult to obtain numerical solutions of the equations, due, in part, to the stiffness of the chemical reaction terms which can create rapid changes in the solution. The main goal, then, was to study the set of the equations and, if possible, find reduced models and use analytical methods to predict the solution behavior and give insight into appropriate numerical techniques. Atypical automotive catalytic converter consists of an inert ceramic monolith with many narrow channels running the length of the converter, through which the exhaust gas from the engine flows (see figure 7.1).