`International Journal of Mathematics and Mathematical SciencesVolume 2003 (2003), Issue 52, Pages 3327-3343doi:10.1155/S0161171203106163`

# I. A. Eltayeb1 and M. H. A. Hassan2

1Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, Al-Khodh, Muscat 123, Oman
2Third World Academy of Sciences, International Centre for Theoretical Physics, P.O. Box 586, Miramare 11, Trieste 34100, Italy

Received 18 June 2001; Revised 21 January 2002

Copyright © 2003 I. A. Eltayeb and M. H. A. Hassan. 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

A uniform source situated at a fixed location starts to emit dust at a certain time, t=0, and maintains the same action for t>0. The subsequent spread of the dust into space is governed by an initial boundary value problem of the atmospheric diffusion equation. The equation has been solved when the wind speed is uniform and diffusion is present both along the vertical and the horizontal for a general source. The solution is obtained in a closed form. The behaviour of the solution is illustrated by means of two examples, one of which is relevant to industrial pollution and the other to the environment. The solution is represented in graphic form. It is found that the spread of dust into space depends mainly on the type of source and on the horizontal component of diffusion. For weak diffusion, the dust travels horizontally with a vertical front at the uniform speed of the flow. In the presence of horizontal diffusion, dust diffuses vertically and horizontally. For a point source, the distribution of dust possesses a line of extensive pollution. For a finite-line source, the dust concentration possesses a point of accumulation that moves both horizontally and vertically with time.