Lie symmetry and exact homotopic solutions of a non-linear double-diffusion problem - Khan, R. A.; Taj, S.; Ahmed, S.; Khan, Ilyas; Eldin, Sayed M. (Frontiers in Physics, 2023)
Lie symmetry method is applied and exact homotopic solutions of nonlinear double diffusion problem are obtained. More exactly, 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 mathematical model under consideration to ordinary differential equations along with the boundary conditions. Lie similarity transformations are shown to lead to new solutions for the considered flow problem. These solutions are obtained using Homotopy analysis method to analytically solve the ordinary differential equations resulting from reduction of the 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 here.