Analytical Solutions for Solute Transport from two-point Sources along Porous Media Flow with Spatial Dispersity involving Flexible Boundary Inputs, initial Distributions and Zero-order Productions

Document Type : Original Research Paper


1 Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Cameroon

2 Nuclear Technology Section, Energy Research Laboratory, Institute of Geological and Mining Research, Yaounde, Cameroon

3 Higher Teacher Training College, Department of physics, University of Bertoua, P.O. Box 652, Cameroun


This study derives an analytical solution of a one-dimensional (1-D) Advection-Dispersion Equation (ADE) for solute transport with two contaminant sources incorporating the source term. Groundwater velocity is considered as a linear function of space while the dispersion as a nth power of velocity and analytical solutions are obtained for , and . The solution is derived using the Generalized Integral Transform Technique (GITT) with a new regular Sturm-Liouville Problem (SLP). Analytical solutions are compared with numerical solutions obtained in MATLAB pedpe solver and are found to be in good agreement. The obtained solutions are illustrated for linear combination of exponential input distribution and its particular cases. The dispersion coefficient and temporal variation of the source term on the solute distribution are demonstrated graphically for the set of input data based on similar data available in the literature. As an illustration, model predictions are used to estimate the time histories of the radiological doses of uranium at different distances from the sources boundary in order to understand the potential radiological impact on the general public for such problem.


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