Generalized analytical solution for advection-dispersion equation in finite spatial domain with arbitrary time-dependent inlet boundary condition

This study presents a generalized analytical solution for one-dimensional solute transport in finite spatial domain subject to arbitrary time-dependent inlet boundary condition. The governing equation includes terms accounting for advection, hydrodynamic dispersion, linear equilibrium sorption, and first order decay processes. The generalized analytical solution is derived by using the Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate. Some special cases are presented and compared to illustrate the robustness of the derived generalized analytical solution. Result shows an excellent agreement between the analytical and numerical solutions. The analytical solutions of the special cases derived in this study have practical applications. Moreover, the derived generalized solution which consists an integral representation is evaluated by the numerical integration to extend its usage. The developed generalized solution offers a convenient tool for further development of analytical solution of specified time-dependent inlet boundary conditions or numerical evaluation of the concentration field for arbitrary time-dependent inlet boundary problem.