Abstract
This article aims to analyze the unsteady motion of Nano-fluid film on a stretching sheet. In this study, the nonNewtonian behaviour of Williamson fluid is used as a base fluid for Nano-liquid. This is the first attempt regarding the 2-dimensional liquid film flow of any non-Newtonian Nano-fluid caused by time dependent extending surface with a combination of shear-stress and temperature. The effective thermal conductivity on temperature has been adopted as a function of time for micro-mixing of the Nano-fluid particle motion. The main focus is to discuss the impacts of the Williamson and radiation parameters in the film thickness in the presence of constant reference temperature which completely affect the flow pattern and bring changes in the cooling/heating. The governing equations are exhibited under the Dufour and Soret approximations. The transformation of similarity has been applied to the modelled equations. The obtained nonlinear equations have been solved by using Homotopy Analysis Method (HAM) and Numerical Method. The HAM predictions of the structures formed are in close agreement with the obtained results from the Numerical Method. In order to comprehend the physical presentation of the embedded parameters such as Dofour number Du, Schmidt number Sc, Soret number Sr, the Brinkman Number Br, Williamson number and Radiation parameter R based on the characteristic length of the fluid film are plotted graphically and discussed.