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Analytical solution of two-dimensional conservative solute transport in a heterogeneous porous medium for varying input point source

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Abstract

In the present study, an analytical solution is obtained for two-dimensional advection–dispersion equation with variable coefficients in a semi-infinite heterogeneous porous medium. Dispersion coefficient and groundwater velocity are assumed to vary temporally as well as spatially while the retardation factor varies spatially only. The first-order decay and zero-order production terms are also considered into account. The variations in parameters along both longitudinal and transverse directions are of exponentially decreasing nature. Initially the geological formation is considered not solute free. The nature of pollutant is considered of conservative and is assumed to be originating from time-dependent varying point source. New time and space variables are introduced to convert the variable coefficients of the advection–dispersion equation into constant coefficients. Analytical solution of the proposed model is obtained by employing Laplace integral transformation technique (LITT). The proposed analytical solution is illustrated graphically to study the effects of various parameters on the solute transport for temporally exponentially decreasing and sinusoidal nature velocities.

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Acknowledgements

We gratefully acknowledgement Prof. Naveen Kumar, Ex-Dean Faculty of Science, B. H. U., Varanasi–India, for his valuable suggestions in improving the article.

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  1. Department of Mathematics & Astronomy, Lucknow University, Lucknow, 226007, U.P, India

    R. R. Yadav & Lav Kush Kumar

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  1. R. R. Yadav
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Correspondence to R. R. Yadav.

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Yadav, R.R., Kumar, L.K. Analytical solution of two-dimensional conservative solute transport in a heterogeneous porous medium for varying input point source. Environ Earth Sci 80, 327 (2021). https://doi.org/10.1007/s12665-021-09584-9

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