Analysis of unsteady thin film flows over the porous and moving surfaces of variable thickness: Unsteady and non-linear kinematics of sheet

Abstract

Thin film flows over porous and moving sheets of variable thickness have been reconsidered here. New and multiple dimensions of classical problems of such type flow are analyzed. Here, we categorically emphasized on the nature and kinds of injection (suction) and moving velocities of the sheet, whereas, variable size of the sheet is also taken into account. We formed and investigated different cases and checked different options for kinematics of sheet, variable sizes of thin film and that of sheet. All possible cases of exact similarities are noticed by which the system of partial differential equations and boundary conditions are exactly transformed into ordinary differential equations. The final systems of exact equations are solved by bvp4c technique. The present simulations are exactly matched with the previously published analyses for special choices of functions and parameters. Strict behavioral changes have been observed in the velocity profiles by changing the nature of sheet’s kinematics.