Time dependent mathematical model for settling of primary air-pollutant and its secondary product

Abstract

A comprehensive three-dimensional unsteady mathematical model of primary as well as secondary pollutants is presented. This model deals with the various types of time dependent sources, like, (i) instantaneous (ii) continuous (constant flux) (iii) step function type to investigate mainly the effect of settling of larger particles due to gravitational acceleration. This intricate problem is solved analytically and explicit expressions for primary and secondary pollutants concentration are obtained for all the cases. It is found that when the source is of constant flux type (continuous) there will be an increase of ground level concentration near the source for small values of settling velocity compared to the no settling situation for all time. This increment will be maximum for large values of time. When settling is enhanced beyond that due to total deposition, the enhancement of concentration will prevail for all time at any location. However, when the source is of step function type, the enhancement of concentration for small values of settling velocity near the source is significantly only for a limited interval of time starting from the time of emission.