TY - JOUR ID - 68064 TI - Analytical solutions of one-dimensional Advection equation with Dispersion coefficient as function of Space in a semi-infinite porous media JO - Pollution JA - POLL LA - en SN - 2383-451X AU - Yadav, R. R. AU - Kumar, L. K. AD - Department of Mathematics & Astronomy, Lucknow University, Lucknow-226007, U.P, India Y1 - 2018 PY - 2018 VL - 4 IS - 4 SP - 745 EP - 758 KW - Advection KW - dispersion KW - Unit step function KW - Point Source KW - Heterogeneous medium DO - 10.22059/poll.2018.253350.410 N2 - The aim of this study is to develop analytical solutions for one-dimensional advection-dispersion equation in a semi-infinite heterogeneous porous medium. The geological formation is initially not solute free. The nature of pollutants and porous medium are considered non-reactive. Dispersion coefficient is considered squarely proportional to the seepage velocity where as seepage velocity is considered linearly spatially dependent. Varying type input condition for multiple point sources of arbitrary time-dependent emission rate pattern is considered at origin. Concentration gradient is considered zero at infinity. A new space variable is introduced by a transformation to reduce the variable coefficients of the advection-dispersion equation into constant coefficients. Laplace Transform Technique is applied to obtain the analytical solutions of governing transport equation. Obtain results are shown graphically for various parameter and value on the dispersion coefficient and seepage velocity. The developed analytical solutions may help as a useful tool for evaluating the aquifer concentration at any position and time. UR - https://jpoll.ut.ac.ir/article_68064.html L1 - https://jpoll.ut.ac.ir/article_68064_7bab5d83c23cb6fb2d2438e205b8ce18.pdf ER -