Analytical solutions to two-dimensional advection–dispersion equation in cylindrical coordinates in finite domain subject to first- and third-type inlet boundary conditions

Abstract

► Analytical solutions for 2-D advection–dispersion equation in cylindrical coordinates in finite domain was derived. ► Significant discrepancy between solutions for first- and third-type conditions. ► Solutions useful for interpreting a column experiment or an infiltration tracer test. This study presents exact analytical solutions to the two-dimensional advection–dispersion equation in cylindrical coordinates in finite domain subject to the first- and third-type inlet boundary conditions. The second kind finite Hankel transform and the generalized integral transform technique are adopted to solve the two-dimensional advection–dispersion equation in cylindrical coordinates and its associated initial and boundary conditions. The developed analytical solutions are compared with the solutions for semi-infinite domain subject to the first- and third-type inlet boundary conditions available in literature to illustrate the impacts of the exit boundary conditions. Results show that significant discrepancies between the breakthrough curves obtained from analytical solutions for the finite domain and infinite domain for small Peclet number. Numerical evaluations of the developed analytical solutions for finite domain are computationally intensive because that the convergences of the series progress slowly for medium Peclet number. The developed solutions should be especially useful for testing numerical model simulated solutions for the finite domain subject to first- and third-type inlet boundary conditions.