A generalized two‐dimensional analytical solution for hydrodynamic dispersion in bounded media with the first‐type boundary condition at the source

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Abstract
A generalized two‐dimensional analytical solution is developed for hydrodynamic dispersion in a unidirectional‐bounded surface and subsurface media flow field from time‐ and space‐dependent sources with the first‐type boundary condition at the source. Longitudinal and transverse dispersion, radioactive decay, and linear adsorption are considered. In the mathematical analysis, Laplace transform and Fourier analysis techniques are used simultaneously, and a general equation, in infinite series form, for the unsteady state concentration distribution has been obtained. Solution for a single‐strip source is obtained as a special case from the general solution. The equations for convective‐dispersive flux components are also derived. The solution of Bruch and Street [1967] for a symmetrically located strip source is shown to be a special case of the solution. Expressions for concentration distribution and convective‐dispersive flux components for the steady state solute transport case are also presented. The results are compared with two different finite element codes with a good agreement. The results of this model may be used for solute transport in a unidirectional porous media flow field as well as in rivers and canals with some additional assumptions. The solutions can also be used for numerical model validation.

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