Symmetry reductions and solutions for pollutant diffusion in a cylindrical system

This study is devoted to investigating transient coupled fluid flow and mass transfer partial differential equations (PDEs) describing pollutant transport in cylindrical coordinates. Symmetry analysis of the system of coupled PDEs is performed and some large Lie algebras are obtained for some special cases of the arbitrary and special choices of constants, and the source term. Optimal systems are constructed for all the admitted symmetries. We perform reductions for different choices of the source term. In some cases invariant solution is sought, however some cases resulted in coupled systems of highly nonlinear ordinary differential equations (ODEs). Imposing realistic boundary conditions and considering a constant source term, we then use the Adomain decomposition techniques to solve the boundary value problem.