Analytical Solutions for Unsteady Transport Dispersion of Nonconservative Pollutant with Time-Dependent Periodic Waste Discharge Concentration

Analytical solutions have been obtained by the Fourier transform method for the case of unsteady transport dispersion of nonconservative pollutant/biochemical oxygen demand with first-order decay under each of the sine and cosine variation of waste discharge concentration at upstream boundary and nonzero initial condition throughout the river. The solutions give correct results along the whole length of the river for all times in contrast to those available in the literature which yield sensible results under quasisteady-state assumption and for large times only. Appropriate expressions for memory length and memory time have been derived so as to include the effect of decay rate of the pollutant in terms of the Thomann number.