Radiative MHD thin film flow of Williamson fluid over an unsteady permeable stretching sheet

In this research work we have examined the flow of Williamson liquid film fluid with heat transmission and having the impact of thermal radiation embedded in a permeable medium over a time dependent stretching surface. The fluid flow of liquid films is assumed in two dimensions. By using suitable similarity transformation the governing non-linear partial differential equations have been transformed into non-linear differential equations. An optimal approach has been used to acquire the solution of the modelled problem. The convergence of the technique has been shown numerically. The impact of the Skin friction and Nusslet number and their influence on thin film flow are shown numerically. Thermal radiation, unsteadiness effect and porosity have mainly focused in this paper. Furthermore, for conception and physical demonstration the entrenched parameters, like porosity parameter $k$ , Prandtl number $\mathrm{Pr}$ , unsteadiness parameter $S$ , Radiation parameter $Rd$ , Magnetic parameter $M$ , and Williamson fluid parameter have been discussed graphically in detail with their effect on liquid film flow.