Construction of similarity transformations and analytic solutions for a liquid film on an unsteady stretching sheet using lie point symmetries

Abstract

• Lie point symmetries concept is used to discuss the flow and heat transfer rate. • Similarity transformations are utilized to convert the governing system through invariants. • Series solutions are obtained via Homotopy Analysis Method. We obtain Lie point symmetries for the system of partial differential equations describing flow and heat transfer in a thin liquid film on an unsteady stretching sheet and use them to construct invariants. We derive similarity transformations using deduced invariants that reduce the independent variables of the considered flow model. Such reductions lead to systems of ordinary differential equations. We solve these systems of ordinary differential equations analytically by applying the Homotopy analysis method.