Modeling of Water Pollutant Concentration Using Laplace Transformation

Abstract

In this work, we introduce a mathematical framework to model water pollution in river channels. The level of pollutants is measured over time using a one dimensional, unsteady, nonlinear second-order advection-dispersion equation. This model assumes that the additional pollution rate along the river and the pollutants' dispersion coefficient are both constant. Additionally, K, the half-saturation oxygen demand concentration, should be zero. The Laplace transform method is applied to obtain the analytical solution for the concentration of water pollution the variation of pollution concentration is observed for different parametric values, i.e., with the variation of the rate of added pollutants, time, the rate of pollution concentration at the origin, and position. The work is analyzed geometrically. This work will be helpful for those researchers who are involved or want to be involved in the field of water pollution or the motion of contaminants in any medium where the concept of the advection-dispersion equation is used.