ISSN:
1572-9222
Keywords:
chemically reacting flow
;
continuous flow stirred tank reactor
;
shadow system
;
large diffusivity
;
Arrhenius kinetics
;
incompressible Navier–Stokes equations
;
reaction–diffusion equations
;
Boussinesq models
;
mixed Neumann and Robin boundary conditions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper we consider the relationship between chemically reacting flows and continuous flow stirred tank reactors (CSTR). In particular, we show that in the limit as the chemical and thermal diffusivities go to infinity, the solutions of the reacting flow PDE approach the solutions to the CSTR ODE. We further show that the global attractors for the reacting flow come arbitrarily close top the CSTR global attractor as the diffusivities go to infinity. An important feature of the reacting flow model we use is Robin–Neumann boundary conditions for the chemistry and temperature, which we use to mimic the CSTR inflow and outflow terms. The key in our analysis is an examination of how the Laplacian with Robin–Neumann boundary conditions converges to the Laplacian with Neumann boundary conditions as the diffusivity goes to infinity.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009016408577
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