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Appl. Sci. 2017, 7(4), 404; doi:10.3390/app7040404

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

1
Department of Mathematics, Abdul Wali Khan University, Mardan 23200, KPK, Pakistan
2
Department of Electrical Engineering, CECOS University, Peshawer 25000, KPK, Pakistan
3
Department of Mathematics, College of Engineering, Majmaah University, Majmaah 31750, Saudi Arabia
4
Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Perak 32610, Malaysia
5
Department of Mathematics, Islamia College, Peshawer 25000, KPK, Pakistan
6
Department of Physics, Abdul Wali Khan University, Mardan 23200, KPK, Pakistan
*
Author to whom correspondence should be addressed.
Received: 19 February 2017 / Revised: 26 March 2017 / Accepted: 5 April 2017 / Published: 18 April 2017
(This article belongs to the Special Issue Recent Developments of Nanofluids)

Abstract

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 obtained View Full-Text
Keywords: Thermophoretic effect and Brownian motion, thin film, porous medium, Williamson fluid, unsteady stretching sheet, HAM, ND-solve methods Thermophoretic effect and Brownian motion, thin film, porous medium, Williamson fluid, unsteady stretching sheet, HAM, ND-solve methods
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Ali, L.; Islam, S.; Gul, T.; Khan, I.; Dennis, L.C.C.; Khan, W.; Khan, A. The Brownian and Thermophoretic Analysis of the Non-Newtonian Williamson Fluid Flow of Thin Film in a Porous Space over an Unstable Stretching Surface. Appl. Sci. 2017, 7, 404.

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