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Appl. Sci. 2017, 7(4), 369; doi:10.3390/app7040369

Heat Transfer Investigation of the Unsteady Thin Film Flow of Williamson Fluid Past an Inclined and Oscillating Moving Plate

1
Department of Mathematics, Abdul Wali Khan University, Mardan 32300, KP, Pakistan
2
Department of Mathematics, Bacha Khan University, Charsadda 244420, KP, Pakistan
3
Department of Mathematics, Princess Nourah bint Abdulrahman University, Riyadh 11564, Saudi Arabia
4
Basic Engineering Department, College of Engineering, Majmaah University, Majmaah 11952, Saudi Arabia
5
Department of Mathematics, King Abdul Aziz University, Jeddah 21577, Saudi Arabia
6
Department of Mathematics, Islamia College, Peshawar 25000, Pakistan
*
Author to whom correspondence should be addressed.
Received: 30 January 2017 / Revised: 4 April 2017 / Accepted: 4 April 2017 / Published: 7 April 2017
(This article belongs to the Special Issue Heat Transfer Processes in Oscillatory Flow Conditions)
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Abstract

This investigation aims at analyzing the thin film flow passed over an inclined moving plate. The differential type non-Newtonian fluid of Williamson has been used as a base fluid in its unsteady state. The physical configuration of the oscillatory flow pattern has been demonstrated and especial attention has been paid to the oscillatory phenomena. The shear stresses have been combined with the energy equation. The uniform magnetic field has been applied perpendicularly to the flow field. The principal equations for fluid motion and temperature profiles have been modeled and simplified in the form of non-linear partial differential equations. The non-linear differential equations have been solved with the help of a powerful analytical technique known as Optimal Homotopy Asymptotic Method (OHAM). This method contains unknown convergence controlling parameters C 1 , C 2 , C 3 , ... which results in more efficient and fast convergence as compared to other analytical techniques. The OHAM results have been verified by using a second method known as Adomian Decomposition Method (ADM). The closed agreement of these two methods and the fast convergence of OHAM has been shown graphically and numerically. The comparison of the present work and published work has also been equated graphically and tabulated with absolute error. Moreover, the effect of important physical parameters like magnetic parameter M , gravitational parameter m , Oscillating parameter ω , Eckert number E c and Williamson number W e have also been derived and discussed in this article. View Full-Text
Keywords: time dependent thin film fluid flow; Williamson fluid; oscillating inclined plane; heat transfer and magnetic field; Optimal Homotopy Asymptotic Method (OHAM) time dependent thin film fluid flow; Williamson fluid; oscillating inclined plane; heat transfer and magnetic field; Optimal Homotopy Asymptotic Method (OHAM)
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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

Gul, T.; Khan, A.S.; Islam, S.; Alqahtani, A.M.; Khan, I.; Alshomrani, A.S.; Alzahrani, A.K.; Muradullah. Heat Transfer Investigation of the Unsteady Thin Film Flow of Williamson Fluid Past an Inclined and Oscillating Moving Plate. Appl. Sci. 2017, 7, 369.

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