Symmetry analysis for the nonlinear model of diffusion and reaction in porous catalysts

In this paper the nonlinear problem arising due to diffusion and reaction in catalyst is investigated. This problem was studied before using the Adomian decomposition, finite differences and homotopy analysis methods. Mathematical analysis for the case of the nnth order reactions is performed and exact analytical solutions are investigated by the Lie symmetry method. Moreover, we look for exact solutions for negative reaction constants and show that the solutions exist for various values of nn and the Thiele modulus ϕϕ. Graphs are plotted for these parameters and discussed.