Ignition and extinction in a model problem with parallel endothermic and exothermic reactions

✍ Scribed by S. Pushpavanam; R. Narayanan

• Book ID: 103007938
• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 775 KB
• Volume: 44
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(89)85205-4

✦ Synopsis

S-shaped curves occur widely in the modelling of chemical reactors and these give rise to multiple steady-slates and hysteresis. At the turning points of an S-shaped curve the behavior of the solutions is catastrophic. The turning points for distributed parameter systems are usually calculated numerically. In this paper we describe, for a model problem, how such catastrophic behavior can be obtained by considering them to be imperfections of systems whose bifurcation diagrams exhibit sub-critical instability. This facilitates approximate calculation of the critical points, i.e. the ignition and extinction points as given by the turning points of the S-shaped curve. The problem, we have considered. is the stability of two zeroth order reactions-one endothermic and the other exothermic. We use a perturbation approach to construct the solutions. Such a calculation helps us divide the parameter space into different regions. The nature of the solutions in each region is explained, wherever possible.