Analytic Solution of The Three Dimensional Unsteady Advection-Dispersion Equation For Non-Conservative Contaminants Transport In Streams
An analytic solution of the unsteady three dimensional advection- dispersion equation is developed. The solution depicts the concentration distribution for a non-conservative contaminant or substance injected as a pulse into a stream by a diffuser installed normal to the stream bank with a certain area. The stream has constant mean velocity and relatively large discharge in comparison to the contaminant source discharge. The solution is developed using FourierSeries and Laplace transforms. The profile of concentration in the stream due to such contaminant disposal is developed in terms of Complementary Error function, Exponential and Trigonometric series. The location variations of the diffuser across the stream are examined. The effects of time period (during and after pulsing) on the concentration profiles across, along and normal to the stream are determined. The paper also represents the effects of decay coefficient as well as many hydraulic and geometric parameters on the variation of mixing patterns.
Keywords- Advective Dispersion equation, three-dimensional dispersion,mixing process