Three-dimensional analytical models for time-dependent coefficients through uniform and varying plane input source in semi-infinite adsorbing porous media.

Document Type : Original Research Paper


Department of Mathematics and Astronomy, Lucknow University, Lucknow-226007, India


In the present study, analytical solutions are developed for three-dimensional advection-dispersion equation (ADE) in semi-infinite adsorbing saturated homogeneous porous medium with time dependent dispersion coefficient. It means porosity of the medium is filled with single fluid(water). Dispersion coefficient is considered proportional to seepage velocity while adsorption coefficient inversely proportional to dispersion coefficient. Solutions are derived for both uniform and varying plane input source. The source geometry, including shape and orientation, broadly act major role for the concentration profile through the entire transport procedure. Initially the porous domain is not solute free. It means domain is throughout uniformly polluted. With help of certain transformation advection-dispersion equation is reduced into constant coefficient. The governing advection-dispersion equation, initial and boundary condition is solved by applying Laplace Transform Technique (LTT). The desired closed-form solution for the line source in two-dimensions and point source in one-dimension of uniform and varying nature are also evaluated as particular cases. Effects of parameters and value on the solute transport are demonstrated graphically.


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