WSEAS Transactions on Heat and Mass Transfer
Print ISSN: 1790-5044, E-ISSN: 2224-3461
Volume 16, 2021
The Kirchhoff Transformation and the Fick’s Second Law with Concentration-dependent Diffusion Coefficient
Authors: ,
Abstract: 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.
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Keywords: Second Fick’s Law, Concentration-Dependent Diffusion, Kirchhoff Transformation, Nonlinear Differential Equation, Semi Implicit Numerical Scheme, Finite Difference
Pages: 59-67
DOI: 10.37394/232012.2021.16.9