Mathematical Modelling of Convective Transport of
Dispersion in One-Dimensional Flow of Saturated
and Unsaturated Porous Media

T.Ramesh; B.V.Rangaraju; J.Rekha; S.R.Sudheendra

doi:https://doi.org/10.14445/22315373/IJMTT-V67I7P520

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 7 | Year 2021 | Article Id. IJMTT-V67I7P520 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I7P520

Mathematical Modelling of Convective Transport of Dispersion in One-Dimensional Flow of Saturated and Unsaturated Porous Media

T.Ramesh, B.V.Rangaraju, J.Rekha, S.R.Sudheendra

Abstract

The purpose of this paper is to study an analytical first order solution to the one-dimensional advection-dispersion equation with adsorption term C0e-γt to study the transport of pollutant vary exponentially with time using a generalized integral transform method to investigate the transport of sorbing but otherwise non-reacting solutes in hydraulic homogenous but geochemically heterogeneous porous formations. The solution is derived under conditions of steady-state flow and arbitrary initial and inlet boundary conditions. The results obtained by this solution agree well with the results obtained by numerically inverting Laplace transform-generated solutions previously published in the literature. The solution is developed for a third or flux type inlet boundary condition, which is applicable when considering resident solute concentrations and a semi-infinite porous medium.

Keywords

Integral Transforms Method, Mathematical Modelling, One-Dimensional Flow, Porous Media.

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Citation :

T.Ramesh, B.V.Rangaraju, J.Rekha, S.R.Sudheendra, "Mathematical Modelling of Convective Transport of Dispersion in One-Dimensional Flow of Saturated and Unsaturated Porous Media," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 7, pp. 167-177, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I7P520