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Pollutant; concentration; Laplace transformation; dispersion.

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.

Ali S Wadi¹ Mourad F Dimian¹ Fayez N Ibrahim¹

1. Department of Mathematics, AinShams University, Cairo 0020, Egypt.

Published

August 2014

Manuscript received

12 September 2013

Manuscript revised

1 April 2014

Accepted

3 April 2014