Analytical approach of one-dimensional solute transport through inhomogeneous semi-infinite porous domain for unsteady flow: Dispersion being proportional to square of velocity

In this study, we present an analytical solution for solute transport in a semi-infinite inhomogeneous porous domain and a time-varying boundary condition. Dispersion is considered directly proportional to the square of velocity whereas the velocity is time and spatially dependent function. It is expressed in degenerate form. Initially the domain is solute free. The input condition is considered pulse type at the origin and flux type at the other end of the domain. Certain new independent variables are introduced through separate transformation to eliminate the variable coefficients of Advection Diffusion Equation (ADE) into constant coefficient. Laplace transform technique (LTT) is used to get the analytical solution of ADE concentration values are illustrated graphically.