Steady flow of thin film over porous moving and non-flat sheet with nonlinear kinematics of exponential type

A generalized model of flow of viscous thin film has been presented and the film is maintained over a porous, moving and non-flat sheet. We categorically emphasized on the nonuniform and nonlinear kinematics of the sheet and deformation of thin film and variation of all quantities specified at the boundaries are taken of exponential type. The combined effects of deformation of both thin film and sheet along with the nonlinear kinematics of sheet have been analyzed on the characteristics of flow. The governing partial differential equations are transformed into ordinary differential equations (ODEs) by using similarity transformations and the final problem of ODEs is solved with the help of bvp4c technique, whereas, the result for the velocity and skin friction are graphed for different values of the injection (suction), stretching (shrinking) and deformation (contraction/expansion) of both thin film and sheet parameters. Note that the increasing, decreasing, uniform, linear, nonlinear and boundary layer behaviors of the velocity profiles and skin friction are noted for multiple choices of the parameters. Moreover, flows in upstream and downstream directions have been observed for different values and diverse nature of the parameters.