International Journal of Science, Engineering and TechnologyAuthors: Ashutosh Kumar Upadhyay, Meenakshi Vashisth, Amanpreet Kaur, Sapna Ratan Shah
Abstract: This study presents a mathematical model for the dispersion of atmospheric pollutants subjected to periodic emission sources and removal dynamics. Using an advection-diffusion-reaction framework, we derive and analyze the governing partial differential equation incorporating a sinusoidal source term and a constant atmospheric removal rate. The model captures real-world conditions such as diurnal emission cycles and steady pollutant decay. Analytical and numerical solutions are explored to understand the spatiotemporal behavior of pollutant concentrations. Numerical results highlight that pollutant concentration profiles evolve with time, showing spatial spreading, downstream advection, and amplitude attenuation due to decay. Furthermore, increasing the emission oscillation amplitude (α) leads to more pronounced temporal fluctuations in concentration at fixed locations. Importantly, given that the World Health Organization reports that air pollution contributes to nearly 7 million premature deaths annually, primarily due to respiratory and cardiovascular diseases, this work underscores the critical need for accurate pollution modeling to inform effective monitoring and mitigation strategies under oscillatory emission conditions.
DOI: https://doi.org/10.5281/zenodo.17276408
