One-dimensional solute transport, originating from a continuous point source, is studied along unsteady longitudinal flow through a heterogeneous medium of semi-infinite extent. Diffusion 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 adsorption parameter is considered to be inversely proportional to diffusion coefficient. 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 adsorption, heterogeneity and unsteadiness on the solute transport are investigated with various graphs.
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