Open AccessThe Kirchhoff Transformation and the Fick’s Second Law with Concentration-dependent Diffusion Coefficient
Author(s) -
Rogério Martins Saldanha da Gama,
Rogério Pazetto Saldanha da Gama
Publication year - 2021
Publication title -
wseas transactions on heat and mass transfer
Language(s) - English
Resource type - Journals
eISSN - 2224-3461
pISSN - 1790-5044
DOI - 10.37394/232012.2021.16.9
Subject(s) - piecewise , diffusion , transformation (genetics) , mathematics , context (archaeology) , mathematical analysis , work (physics) , piecewise linear function , inverse , limit (mathematics) , constant (computer programming) , function (biology) , thermodynamics , physics , geometry , computer science , chemistry , programming language , paleontology , biochemistry , evolutionary biology , biology , gene
In this work it is considered the Fick’s second law in a context in which the diffusion coefficient depends on the concentration. It is employed the Kirchhoff transformation in order to simplify the mathematical structure of the Fick’s second law, giving rise to a more convenient description. In order to provide a general protocol, the diffusion coefficient will be assumed a piecewise constant function of the concentration. Exact formulas are presented for both the Kirchhoff transformation and its inverse, in such a way that there is no limit of accuracy. Some numerical examples are presented with the aid of a semi-implicit procedure associated with a finite difference approximation.