Analytical water quality model for a sinusoidally varying BOD discharge concentration

Biochemical oxygen demand modeling in a river involves derivation and solution of the governing partial differential equation which describes concentration change with time and space brought on by convective, dispersive, and decay processes and the loading function. The boundary condition applied in this study describes a sinusoidal variation in waste discharge concentration. The governing partial differential equation is solved analytically by introducing complex variables, using a transform method and by applying the Laplace transform. The resulting exact analytical solution is compared with three other solutions. The analytical solution produces results that are exact for any location at any time. The analytical solution extends the number of boundary conditions which a modeler can apply to describe real engineering problems.