Lie symmetry and exact homotopic solutions of a non-linear double-diffusion problem

The Lie symmetry method is applied, and exact homotopic solutions of a non-linear double-diffusion problem are obtained. Additionally, we derived Lie point symmetries and corresponding transformations for equations representing heat and mass transfer in a thin liquid film over an unsteady stretching surface, using MAPLE. We used these symmetries to construct new (Lie) similarity transformations that are different from those that are commonly used for flow and mass transfer problems. These new (Lie) similarity transformations map the partial differential equations of a mathematical model under consideration to ordinary differential equations along with boundary conditions. Lie similarity transformations are shown to lead to new solutions for the considered flow problem. These solutions are obtained using the homotopy analysis method to analytically solve the ordinary differential equations that resulted from the reduction of considered flow equations through Lie similarity transformations. With the aid of these solutions, effects of various parameters on the flow and heat transfer are discussed and presented graphically in this study.