Mathematical model for dispersion and diffusion of chemically reactive pollutants from various sources into a boundary layer with dry deposition
Purpose - The purpose of this paper is to propose a mathematical model for dispersion and diffusion of chemically reactive primary pollutants emitted from an elevated line sources into a stable atmospheric boundary layer with generalized wind velocity of quadratic function of vertical heights. Design/methodology/approach - The governing partial differential equations are converted into the two-dimensional time dependent partial differential equation by suitable choice of meteorological parameters and non-dimensional variables, which is solved by the multiple inverse Laplace transform through Green's Function technique. Findings - The three different types' sources, viz, continuous, an instantaneous and step-function type sources are studied. The pollutants considered are chemically reactive primary pollutants emitted from the above sources. In many previous works, solutions are obtained through numerical technique or numerical inversion of the Laplace transform; but here, an analytical method is carried out to find the exact solution through multiple inversion of Laplace transform, which yields an effective and accurate solution. Originality/value - The paper describes how the authors obtained exact solutions for the elevated line sources into a stable atmospheric boundary layer arising in the chemically reactive primary pollutants model by inverse Laplace transform through Green's Function technique. The graphical results show that this method is very accurate. The gaseous pollutants converted into particulate matter and settled on surface terrain are also considered in this theoretical model.
mathematical modelling chemically reactive pollutants pollutants atmosphere winds step-function type source settling velocity stable boundary layer instantaneous line source continuous line source quadratic diffusion coefficient generalized parabolic wind profile