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Analytical solutions for one-dimensional advection–dispersion equation of the pollutant concentration
Ali S Wadi Mourad F Dimian Fayez N Ibrahim
Volume 123 Issue 6 August 2014 pp 1317-1324
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https://www.ias.ac.in/article/fulltext/jess/123/06/1317-1324 -
Keywords
Pollutant ;concentration ;Laplace transformation ;dispersion. -
Abstract
We present simple analytical solutions for the unsteady advection–dispersion equations describing the pollutant concentration $C(x, t)$ in one dimension. The solutions are obtained by using Laplace transformation technique. In this study we divided the river into two regions 𝑥 ≤ 0 and 𝑥 ≥0 and the origin at 𝑥 = 0. The variation of $C(x, t)$ with the time 𝑡 from 𝑡 = 0 up to 𝑡 $\rightarrow \infty $ (the steady state case) is taken into account in our study. The special case for which the dispersion coefficient 𝐷 = 0 is studied in detail. The parameters controlling the pollutant concentration along the river are determined.
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Author Affiliations
Ali S Wadi1 Mourad F Dimian1 Fayez N Ibrahim1
- Department of Mathematics, AinShams University, Cairo 0020, Egypt.
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Dates
- Published
- August 2014
- Manuscript received
- 12 September 2013
- Manuscript revised
- 1 April 2014
- Accepted
- 3 April 2014
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