IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

S-shaped curves occur widely in the modelling of chemical reactors and these give rise to multiple steady-states 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 calcualted 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. © 1989.

Department Of Chemical Engineering

Department Of Physics

Chemical Engineering Science

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

Uniqueness conditions for steady solutions in the case of m -th order reactions—non-isothermal pellets with variable transport coefficients

Comparison theorems for exothermally reacting solids in conjugate solid-fluid systems are given. The solids are assumed to be of arbitrary shape and the fluid assumed to be well mixed and in continuous flow. In general the concentration and thermal profiles in the solid are intimately connected with those variables in the fluid leading to integral boundary conditions.The comparison theorems for a zeroth-order reaction show the existence and dependence of basic solutions on system parameters and geometry or domain size. Similar results are also obtained for the ignition point during critical conditions. We have not performed any physical or numerical experiments; only analytical perturbation methods, monotone iteration and the Reynolds transport theorem are used. Comparison with numerical calculations of earlier workers is given for some of our results. Our theorems have been made possible because an unusual inner product has rendered the eigenvalue problem of ignition (nonlinear in the eigenvalue parameter) self-adjoint. We should like to point out that the domain-dependence proof will allow us to consider simpler one-dimensional problems instead of complex three-dimensional problems. © 1988 Oxford University Press.