Longitudinal dispersion with time-dependent source concentration in semi-infinite aquifer

An analytical solution is obtained to predict the contaminant concentration along unsteady groundwater flow in semi-infinite aquifer. Initially, the aquifer is not supposed to be solute free, i.e., aquifer is not clean. A time-dependent source concentration is considered at the origin of the aquifer and at the other end of the aquifer, it is supposed to be zero. The time-dependent forms of unsteady velocities are considered in which one such form, i.e., sinusoidal form represents the seasonal pattern in a year in tropical regions. The Laplace Transformation Technique (LTT) is used to get an analytical solution and a graphical representation is made through MATLAB.