Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 827363, 17 pages
doi:10.1155/2010/827363
Research Article

Analysis of Nonlinear Dispersion of a Pollutant Ejected by an External Source into a Channel Flow

T. Chinyoka1 and O. D. Makinde2

1Center for Research in Computational and Applied Mechanics, University of Cape Town, Rondebosch 7701, South Africa
2Faculty of Engineering, Cape Peninsula University of Technology, P.O. Box 1906, Bellville 7535, South Africa

Received 6 December 2009; Accepted 8 March 2010

Academic Editor: Kuppalapalle Vajravelu

Copyright © 2010 T. Chinyoka and O. D. Makinde. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper focuses on the transient analysis of nonlinear dispersion of a pollutant ejected by an external source into a laminar flow of an incompressible fluid in a channel. The influence of density variation with pollutant concentration is approximated according to the Boussinesq approximation, and the nonlinear governing equations of momentum and pollutant concentration are obtained. The problem is solved numerically using a semi-implicit finite difference method. Solutions are presented in graphical form and given in terms of fluid velocity, pollutant concentration, skin friction, and wall mass transfer rate for various parametric values. The model can be a useful tool for understanding the polluting situations of an improper discharge incident and evaluating the effects of decontaminating measures for the water body.