The Asymptotic Justification of a Nonlocal 1-D Model Arising in Porous Catalyst Theory
✍ Scribed by Francisco J. Mancebo; José M. Vega
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 839 KB
- Volume
- 134
- Category
- Article
- ISSN
- 0022-0396
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✦ Synopsis
An asymptotic model of isothermal catalyst is obtained from a well-known model of porous catalyst for appropriate, realistic limiting values of some nondimensional parameters. In this limit, the original model is a singularly perturbed m-D reaction diffusion system. The asymptotic model consists of an ordinary differential equation coupled with a semilinear parabolic equation on a semi-infinite one-dimensional interval.
1997 Academic Press
1. Introduction
This paper deals with a well-known model of porous catalyst that after suitable nondimensionalization [1, Vol. I] may be written as u t=2u&, 2 f (u, v) in 0, u n=_(1&u) at 0, (1.1)
for t>0, with appropriate initial conditions u=u 0 >0, v=v 0 >0 in 0, at t=0.
(1.3)
Here u>0 and v>0 are the reactant concentration and the temperature respectively, 2 is the Laplacian operator, n is the outward unit normal to the smooth boundary of the bounded domain 0/R m (with m 1) and the parameters , 2 (Damko hler number), L (Lewis number), ; (Prater number), _, and & (material and thermal Biot numbers) are strictly positive. The nonlinearity f accounts for the reaction rate and is usually of one of the following forms, that are associated with the so-called Arrhenius and Langmuir Hinshelwood kinetic laws [1],
article no. DE963210