Review PaperRemediation of pollution in a river by unsteady aeration with arbitrary initial and boundary conditions

SummaryThe most important parameter controlling the water quality is the dissolved oxygen Y(x, t) because it is very essential for aquatic life. An analytic solution is presented for unsteady equation representing the concentration of the dissolved oxygen Y(x, t) along a river at any time t. The solution is obtained by using Laplace transformation technique. Adjoin solution techniques are used as boundary conditions to solve the equations. The variations of Y(x, t) with time t from t = 0 up to t → ∞ (the steady state case) and with the parameters of the flow are taken into account in our study. It is shown that Y(x, t) increases as t increases, keeping the other parameters constant, but Y(x, t) decreases as the added pollutant rate along the river q increases. The adjoin solution techniques used in this work are effective and accurate for solving the equations representing the concentration of the dissolved oxygen Y(x, t) when arbitrary initial and boundary conditions are given. The details are demonstrated in graphs.