Groundwater is part of the hydrological cycle that flows through the saturated zone at rates that are influenced by gravity, pressure, and the characteristics of geologic formations. Groundwater is one of the main sources of water supply for meeting agricultural, domestic, environmental, and industrial demands in many areas. Groundwater flow models solve for the distribution of head or groundwater flow, whereas solute transport models solve for the concentration of solute as affected by advection, dispersion, and chemical reactions, which slow down or transform solutes. Using a generalized integral transform technique, C. W. Liu et al. derived the solution of one-dimensional solute transport equation with Cauchy-type boundary condition in a finite domain. Solute transport in groundwater generally necessitates special attention due to very slow velocity of water and interaction of solute particle with the solid matrix. Groundwater models broadly are divided into two categories: groundwater flow models and solute transport models.