Application of similarity solution on gaseous pollutant problems

Abstract

This study concentrates on dispersion of the gaseous pollutants. The diffusion equation is used to model the concentration from a various distance by the temperature invariants. This study features the group-theoretical method form the similarity techniques. This method is applicable and appropriate to nonlinear partial differential equations. From the similarity solutions, a one-parameter group of transformation provides the equation to be conformally invariance. By introducing of similarity variables, the nonlinear partial differential equation can be reduced to a second order differential equation. Applying boundary conditions and assuming the arbitrary constant for some unknowns, a particular solution of the diffusion equation is obtained. The result is shown for two cases where no pollutant is absorbed by the ground and where all pollutants are absorbed by the ground.