Mathematical Modelling of Atmospheric Pollutant Dispersion under Steady State Conditions with Constant Eddy Diffusivity
DOI:
https://doi.org/10.31305/rrijm.2025.v10.n5.024Keywords:
Pollutant Dispersion, Air Quality, Mathematical Modeling, Public Health, Environmental Justice, PDEs, Urban PollutionAbstract
Air pollution remains a critical environmental challenge, posing significant risks to both ecological systems and human health. Accurate modeling of pollutant dispersion is essential for understanding transport mechanisms and informing regulatory strategies. This study presents a theoretical and analytical investigation of the dispersion of air pollutants emitted from a point source under steady-state conditions. The model incorporates variable wind velocity and a constant pollutant removal rate, assuming constant eddy diffusivity coefficients. Using separation of variables and Fourier transform techniques, explicit analytical solutions are derived to describe the spatial distribution of pollutant concentration. The results demonstrate that pollutant concentration decreases monotonically with increasing downwind distance and vertical height. The rate of vertical decline in concentration is more significant near the source and diminishes with distance. Additional analysis reveals that higher stack heights substantially reduce ground-level concentrations by enhancing vertical dispersion, while increased pollutant removal rates accelerate the decay of concentration along the wind direction. These findings provide important insights into atmospheric pollutant behavior and support the application of the model in environmental risk assessment, air quality management, and the design of effective pollution control strategies.
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