In the preceding chapter we established the mass balance equationMass balance equation for contaminant transport in porous media. In this chapter, our attention focuses towards addressing boundary value problems that govern contaminant transport in one-dimensional porous medium domains. We solve these boundary value problems of varying complexity using the Fourier methodFourier method. While the geometries studied may seem simplistic, these models hold practical value, particularly during the preliminary stages of investigation. They offer reliable estimations of the qualitative implications arising from various parameters and boundary conditions on the transport process. Furthermore, the presented models provide systematic methodology for solving the governing equations analytically and give insight into whether more intricate models can be addressed.