### 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 language | English |
---|---|

Pages (from-to) | 3327-3343 |

Number of pages | 17 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 2003 |

Issue number | 52 |

DOIs | |

Publication status | Published - 2003 |

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### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

*International Journal of Mathematics and Mathematical Sciences*,

*2003*(52), 3327-3343. https://doi.org/10.1155/S0161171203106163

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

Research output: Contribution to journal › Article

*International Journal of Mathematics and Mathematical Sciences*, vol. 2003, no. 52, pp. 3327-3343. https://doi.org/10.1155/S0161171203106163

}

TY - JOUR

T1 - The evolution of dust emitted by a uniform source above ground level

AU - Eltayeb, I. A.

AU - Hassan, M. H A

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=17844408397&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17844408397&partnerID=8YFLogxK

U2 - 10.1155/S0161171203106163

DO - 10.1155/S0161171203106163

M3 - Article

AN - SCOPUS:17844408397

VL - 2003

SP - 3327

EP - 3343

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

IS - 52

ER -