One–Dimensional Solute Transport for an Input against the Flow in a Homogeneous Finite Porous Media

Abstract

A theoretical model comprising advection-dispersion equation with temporal seepage velocity, dispersion coefficient and time dependent pulse type input of uniform nature applied against the flow is studied in a finite porous domain. Input concentration is any continuous smooth function of time acts up to some finite time and then eliminated. Concentration gradient at other boundary is proportional to concentration. Dispersion is proportional to seepage velocity. Interpolation method is applied to reduce the input function into a polynomial. Certain transformations are utilized to reduce the variable coefficient advectiondispersion equation into constant coefficient. The Laplace Transform Technique is applied to get the solution of advection dispersion equation. Two different functions of input are discussed to understand the utility of the present study. Obtained result is demonstrated graphically with the help of numerical example.