The effect of added pollutant along a river on the pollutant concentration described by one dimensional advection diffusion equation.

摘要

Analytical solutions are obtained, by using Laplace transformation method , for one dimensional advection diffusion equation with variable coefficients in a longitudinal finite initially pollutant concentration free domain . Two cases for the boundary conditions, are studied . The first is the case of uniform continuous input condition and the second is the case of input condition of increasing nature .By writing the equations in the dimensionless form , the five physical parameters controlling the pollutant concentration is reduced to only two dimensionless parameters the dimensionless added pollutant concentration and the dimensionless dispersion .It is found that some physical parameters in the dimensional form have the same effect on the concentration of the pollutant, while other physical parameters have opposite effect. It is shown that the dimensionless concentration pollutant increases, as the dimensionless added pollutant increases along the river. But the concentration decreases , as the dimensionless dispersion increases. The details are demonstrated in graphs.