International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 52, Pages 3327-3343
doi:10.1155/S0161171203106163
The evolution of dust emitted by a uniform source above ground level
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.