## 1 Introduction  
Thin-film flows have various applications in the fields of engineering and industry. In chemical engineering, thin film layers have an effective role in the developments of thin-film reactors, distillation columns, condensers and evaporators. The huge advantages of a thin layer depends on its minute thickness, which provides its flow through micro channels. Thin film layers have vital roles in physical engineering and have broad applications in providing cooling methods for nanotechnology through heat sinks. In geophysical engineering, a lot of problems emerge related to thin film flows such as mudslides, debris flows and lava [1; 2]. In the available literature, studies of thin film flows are mostly related to Newtonian fluids and very little work has been done related to non-Newtonian fluids. These too are of great importance, as shear-thickening and pseudoplastic or shear-thinning fluids are considered to be in the class of non-Newtonian fluids. The studies of thin film flow of shear-thinning fluids have vast importance in the industries involving photographic films and the extrusion of polymer sheets, etc. The behavior of pseudoplastic fluids has been explained comprehensively in the Ostwald de Waele power law, [PERSON], Carreaus and Ellis models, but little attention has been given to the Williamson fluid model. The flow of pseudoplastic fluids has been experimentally described by [PERSON] [3], with verified results. [PERSON] and [PERSON] [4] have discussed the analytical solution of Williamson fluid by using the perturbation technique. Most of the problems related to Williamson fluid have been modeled in steady state. Very little work has been done on unsteady non-Newtonian fluids. [PERSON] and [PERSON] [5] have discussed the unsteady magnetohydrodynamic flow of non-Newtonian fluids obeying the power law model. [PERSON] [6] has discussed [PERSON] fluid flow using scaling transformation. [PERSON] et al. [7] have studied the [PERSON] fluid flow on a stretching cylinder with thermal radiations and Ohmic dissipation. [PERSON] et al. [8] have discussed the [PERSON] fluid flow on a stretching surface. They studied the effect of physical parameters involved in the problem. [PERSON] et al. [9] have investigated the nanofluid study of the thin film Williamson fluid flow on a stretching surface. [PERSON] et al. [10] have examined the numerical simulation of Williamson fluid flow amongst binary parallel vertical Walls with slip effects. Thin film nanofluid spray on the stretching cylinder surface has been examined by [PERSON] et al. [11]. The spray rate under the applied pressure force has been scrutinized in their study. [PERSON] et al. [12] have discussed the variable properties of thin layer third order differential type fluid. [PERSON] et al. [13] and [PERSON] et al. [14] have studied the thin film flow of non-Newtonian fluids using different geometries. The unsteady fluid problems have been evaluated in the study of Fetecau [15]. The similar study of fluid flows in its unsteady state can also be seen in [16; 17; 18; 19]. The fluid flow with oscillatory physical conditions has important applications, such as those that [PERSON] and [PERSON] [20] have examined in their experimental analysis of the friction factor correlation for a regenerator using oscillatory phenomena in a thermo acoustic system. [PERSON] et al. [21] have experimentally studied the empirical correlation for finned heat exchangers using oscillating analysis. The thin film flow on an oscillatory belt in the field of mechanical engineering has been studied by [PERSON] et al. [22]. Heat transmission in fluid flows has much importance in basic engineering. Still, a lot of work remains to be done regarding oscillatory flow problems. Various applications related to Stirling machines, heat exchangers, pulsed-tube coolers in cryogenics and wire coating have been explored by [PERSON] et al. [23].