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Advective Diffusive Solute Transport Through Heterogeneous Medium:
Analytical Solutions Of Some Temporally Dependent Problems
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In the present work, one and two dimensional Advection Diffusion Equations(ADEs) with variable coefficients are solved analytically subject to certain initial and boundary conditions using Laplace Integral Transformation Technique.The sources of the solute mass trasporting through the medium are pulse type point sources of uniform and varying nature. The medium is supposed heterogeneous and initially solute free.The velocity is linearly interpolated in terms of space variable in a finite domain under consideration of study of solute transport.It is also considered temporally dependent.The variable coefficients in the ADE are reduced into constant coefficients through certain transformations,introducing new independent variables. In view of the three dispersion theories available in the literature two types of solutions are obtained. In the first, solutions are obtained to describe the solute transport governed by a theory in which the dispersion parameter is proportional to square of the velocity, while in the second, general forms of solutions are obtained, particularly with temporal dependence, from which the solutions supporting all the three thearies may be obtained.
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