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International Heat Transfer Conference 15

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)

Relaxation Phenomena in Reaction-Diffusion Processes

Juan I. Ramos
Escuela de Ingenierias Industriales, Universidad de Malaga, Dr. Ortiz Ramos, s/n 29071 Malaga, Spain

DOI: 10.1615/IHTC15.cmb.009830
pages 1226-1240


KEY WORDS: Computational methods, Combustion, relaxation phenomena, reaction-diffusion equations, exponential methods

Abstract

The effects of the relaxation times of both the temperature and concentration and their fluxes on convective–reactive–diffusive systems is analyzed both analytically and numerically by first considering a single linear equation and studying its spatial stability by means of Fourier analysis, and then numerically by means of two finite difference methods. The first numerical procedure is based on the analytical integration of the constitutive equations for the heat and mass fluxes, time–linearization and approximate factorization, whereas the second one is based on fourth–order accurate spatial discretizations and time integration by means of a Runge–Kutta procedure. In one–dimensional systems, it has been found that, in the absence of convection, the solution is characterized by planar propagating fronts of constant amplitude and frequency for the temperature and concentration and that the amplitude and frequency of these fronts depend strongly on the relaxation times of the temperature and concentration, while, in the presence of convection, the fronts make a transition from a planar to a slanted shape whose slope coincides with that of the characteristics of the first–order advection operator. The duration of this transition and the amplitude and frequency of the temperature and concentration fronts that emanate from it depends on the four relaxation times, the characteristic reaction and diffusion times, and the magnitude and direction of the velocity field.

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