Solution to Advection–Dispersion Equation for the Heterogeneous Medium Using Duhamel’s Principle

This work dealt with advection–dispersion problem in heterogeneous medium while the medium is initially considered to be polluted as a functional combination of source term and zero-order production term with distance. Further, Dirichlet-type boundary condition is employed to get insight to the realistic situation for achieving practical solution to the problem. Duhamel’s integration technique has been applied to solve the system. Non-dimensional numbers responsible for the domination of advection and dispersion in the transport of solute have been explored through appropriate graphs. Variability of velocity field and dispersion of the solute due to heterogeneity of the medium has also been taken into consideration while solving the system. The comparison has been made between the different outcomes significantly using graphical approach.