Chemically reacting flows and continuous flow stirred tank reactors: The large diffusivity limit
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.
scientific article; zbMATH DE number 1547250