The evolution of dust emitted by a uniform source above ground level

I. A. Eltayeb, M. H A Hassan

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)3327-3343
Number of pages17
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume2003
Issue number52
DOIs
Publication statusPublished - 2003

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Horizontal
Pollution
Vertical
Line
Wind Speed
Point Source
Diffusion equation
Initial-boundary-value Problem
Closed-form
Form
Graphics

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

The evolution of dust emitted by a uniform source above ground level. / Eltayeb, I. A.; Hassan, M. H A.

In: International Journal of Mathematics and Mathematical Sciences, Vol. 2003, No. 52, 2003, p. 3327-3343.

Research output: Contribution to journalArticle

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