Multiple series solutions of viscous flows over a stretching/shrinking and porous sheet

Abstract

The viscous fluid-flow over a stretching (shrinking) and porous sheets of non-uniform thickness is investigated in this paper. The modeled problem is presented by utilizing the stretching/shrinking and porous velocities and variable thickness of the sheet. Consequently, the new problem reproduces the different available forms of flow motion maintained over a stretching/shrinking and porous sheet of variable thickness in one go. As a result, the governing equations are embedded in several parameters which can be transformed into classical cases of stretched/shrunk flows over porous sheets. A set of general, unusual and new variables is formed in order to simplify the governing PDE and boundary conditions. Three different series solutions of the final ODE are presented. A single analytical solution is not sufficient to predict the exact effects of all parameters on the flow field properties. The problem is solved by a power and two asymptotic series methods. The results are verified by providing a powerful numerical solution the problem. A complete set of solutions is provided and comparison of the solutions with classical models is established for appropriate values of the parameters which is shown in different graphs and tables.