Analytical solutions of the one‐dimensional advection equation and two‐ or three‐dimensional dispersion equation

For many transport problems involving one‐dimensional flow a significant amount of solute might move in the direction transverse to the flow. In this study the advection‐dispersion equation was solved analytically to evaluate transient solute transport in a two‐dimensional semi‐infinite isotropic porous medium (half plane) with a step change in concentration along the inlet during one‐dimensional flow. The solution was obtained with Laplace and Fourier transforms and verified with various numerical and analytical solutions. The same technique was used to obtain analytical solutions for some other concentration distributions at the inlet under conditions of either two‐ or three‐dimensional dispersion.