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.
