Chemically reacting flows and continuous flow stirred tank reactors: The large diffusivity limit
type: Item
instance of: scholarly article
title: Chemically reacting flows and continuous flow stirred tank reactors: The large diffusivity limit
zbMATH Open document ID: 0973.35155
DOI: 10.1023/A:1009016408577
published in: Journal of Dynamics and Differential Equations
publication date: 2001-12-09T00:00:00Z
review text: The author considers the Navier-Stokes-Boussinesq approximation to chemically reacting flows, which is governed by partial differential equations (PDEs), and shows that, as chemical and thermal diffusivities go to infinity, the solutions of the corresponding PDEs converge to the solutions of two ordinary differential equations which describe the continuous flow stirred reactor. The same is shown to be true also for the corresponding global attractors if one studies the long-time behaviour of the solutions. The main idea of the analysis is to prove that the Laplacian with mixed Robin-Neumann boundary conditions for chemistry and temperature converges to the Laplacian with Neumann boundary conditions as diffusivities go to infinity. This is clear intuitively, but the rigorous proof given in the paper requires a fine spectral analysis of the corresponding linear operators.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76V05
Mathematics Subject Classification ID: 80A25
Mathematics Subject Classification ID: 92E20
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 1547250
zbMATH Keywords: large diffusivity limit
zbMATH Keywords: shadow system
zbMATH Keywords: Arrhenius kinetics
zbMATH Keywords: reaction-diffusion equations
zbMATH Keywords: Navier-Stokes-Boussinesq approximation
zbMATH Keywords: chemically reacting flows
zbMATH Keywords: continuous flow stirred reactor
zbMATH Keywords: global attractors
zbMATH Keywords: Laplacian
zbMATH Keywords: Robin-Neumann boundary conditions
zbMATH Keywords: Neumann boundary conditions
zbMATH Keywords: spectral analysis
zbMATH Keywords: linear operators
author: David E. Norman
MaRDI profile type: Publication
full work available at URL: a:1009016408577
OpenAlex ID: W39532124
description: scientific article; zbMATH DE number 1547250