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This paper explores Liquid Film Flow of Williamson Fluid over an Unstable Stretching Surface in a Porous Space . The Brownian motion and Thermophoresis effect of the liquid film flow on a stretching sheet have been observed. This research include, to focus on the variation in the thickness of the liquid film in a porous space. The self-similarity variables have been applied to convert the modelled equations into a set of non-linear coupled differential equations. These non-linear differential equations have been treated through an analytical technique known as Homotopy Analysis Method (HAM). The effect of physical non-dimensional parameters like, Eckert Number, Prandtl Number, Porosity Parameter, Brownian Motion Parameter, Unsteadiness Parameter, Schmidt Number, Thermophoresis Parameter, Dimensionless Film Thickness, and Williamson Fluid Constant on the liquid film size are investigated and conferred in this endeavor. The obtained results through HAM are authenticated, from its comparison with numerical (ND-Solve Method). The graphical comparison of these two methods is elaborated. The numerical comparison with absolute errors are also been shown in the tables. The physical and numerical results using h curves for the residuals of the velocity, temperature and concentration profiles are obtaine

The Brownian and Thermophoretic Analysis of the Non-Newtonian Williamson Fluid Flow of Thin Film in a Porous Space over an Unstable Stretching Surface