AN ANALYTIC STUDY OF DISSOLVED OXYGEN DEPENDENCY ON TEMPERATURE AND POLLUTANT CONCENTRATION IN A RIVER

Abstract

In this study, we develop a mathematical model of describing how the concentration of oxygen is affected by temperature variations and the pollutant concentration in a river. This is achieved by formulating a set of advection-diffusion reaction partial differential equations governing concentration of pollutant and the concentration of dissolved oxygen. We derive a pair of coupled advection diffusion equations that describe the dynamics of river pollution using conservation of mass laws. Analytical solutions are obtained using an asymptotic method. From the model, both concentration of dissolved oxygen and pollutant are obtained without and with the dispersion coefficient. Since temperature plays a crucial role in determining the amount of oxygen which enters in the water, its effects on the dissolved oxygen is studied. Simulation of the model is performed using Matlab. From the analysis of the model, it is observed that, when a river is highly polluted, a slight change in temperature leads to catastrophe and there is a temperature beyond which a river becomes ecologically dead. From the numerical simulations, we observe that, when there is high temperature, oxygen levels depletes rendering the river incapable of supporting aquatic life. From the analysis, setting up adaptive strategies to address extreme temperature fluctuations, their effects and reducing river pollution will help in protecting aquatic life and improving water quality.