The Kirchhoff Transformation and the Fick’s Second Law with Concentration-dependent Diffusion Coefficient-Reference-Cited by-同舟云学术

The Kirchhoff Transformation and the Fick’s Second Law with Concentration-dependent Diffusion Coefficient

Published:2021-07-08 Issue: Volume:16 Page:59-67
ISSN:2224-3461
Container-title:WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER
language:en
Short-container-title:1790-5044

Author:

Gama R. M. S.¹,Gama R. Pazetto S.²

Affiliation:

1. Mechanical Engineering Department, Rio de Janeiro State University, 524 S. F. Xavier st, Rio de janeiro, BRAZIL

2. Department of Informatics, Pontifical Catholic University of Rio de Janeiro, 225 M. S. Vicente st, Rio de janeiro, BRAZIL

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.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

General Physics and Astronomy

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