One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity

One-dimensional solute transport, originating from a continuous uniform point source, is studied along unsteady longitudinal flow through a heterogeneous medium of semi-infinite extent. Velocity is considered as directly proportional to the linear spatially-dependent function that defines the heterogeneity. It is also assumed temporally dependent. It is expressed in both the independent variables in degenerate form. The dispersion parameter is considered to be proportional to square of the velocity. Certain new independent variables are introduced through separate transformations to reduce the variable coefficients of the advection-diffusion equation to constant coefficients. The Laplace Transformation Technique (LTT) is used to obtain the desired solution. The effects of heterogeneity and unsteadiness on the solute transport are investigated.