Non-local Equations For Concentration Waves In
Reacting Diffusion Systems
Author(s)
A. M. Brener, M. A. Serimbetov & L. M. Musabekova
Abstract
This paper presents the equations modelling concentration waves in reacting
diffusion systems. We show that under the highly general assumptions
concerning the nature of space non-locality of relations between thermodynamic
fluxes and forces the governing transfer equation acts in the form of the modified
Witham’s integro-differential equation. In contradistinction to the known
Witham’s equation the one obtained is heterogeneous under the presence of heat
and mass sources. It is shown that transfer processes with consideration of
dependencies of transfer coefficients on the coordinates and chemical potentials
can also be described by an equation of the same type. In the paper the pre-conditions
and computations leading to the mentioned non-linear equation have
been adduced. The important peculiarity of the equation obtained is the
possibility to describe the propagation of dispersing running waves and moving
wave fronts in media with complex structure. Within the limits of this equation’s
characteristic analysis there proved to be a successful method of the investigation
of the solitary concentration waves by the \“classic way”, i.e. as a result of
interaction between the non-linear phenomena and dispersion.
1 Introduction
It is imperative under calculating heat and mass transfer processes in media with
complex internal structure and various kinds of interaction between medium
elements to account for both the non-linear and the non-local phenomena. The
problem to describe such processes is too complex and far from the complete
solution. In this connection the model approach, which under the successful
choice of the main governing factors and appropriate parameters allows one to
obtain model transfer equations, is relevant.
Keywords
Related Book
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