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Some problems concerning the non‐adiabatic tubular reactor a‐priori bounds, qualitative behavior, preliminary uniqueness and stability considerations
Author(s) -
Varma Arvind,
Amundson Neal R.
Publication year - 1972
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450500406
Subject(s) - uniqueness , adiabatic process , steady state (chemistry) , a priori and a posteriori , stability (learning theory) , nonlinear system , differential equation , mathematics , exponential stability , mathematical analysis , thermodynamics , physics , chemistry , computer science , quantum mechanics , machine learning , philosophy , epistemology
An investigation of the non‐adiabatic tubular reactor, in which a single chemical reaction occurs, is presented. The steady state mass and heat balance equations are shown to be a pair of coupled, nonlinear differential equations, and are shown to uncouple into a single functional‐differential equation for the case Le = 1. A‐priori bounds on the steady state concentration and temperature are developed, and some remarks about the shape of the steady state profiles made. Sufficient conditions ensuring uniqueness of steady states and their asymptotic stability are derived.