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ARTICLE
Fractional Analysis of Thin Film Flow of Non-Newtonian Fluid
Farnaz Ismail1, Mubashir Qayyum2, *, Syed Inayat Ali Shah1
1 Department of Mathematics, Islamia College University, Peshawar, Pakistan
2 Department of Sciences and Humanities, National University of Computer & Emerging Sciences FAST, Lahore, Pakistan
* Corresponding Author: Mubashir Qayyum. Email:
Computer Modeling in Engineering & Sciences 2020, 124(3), 825-845. https://doi.org/10.32604/cmes.2020.011073
Received 17 April 2020; Accepted 16 June 2020; Issue published 21 August 2020
Abstract
Modeling and analysis of thin film flow with respect to magneto hydro
dynamical effect has been an important theme in the field of fluid dynamics, due
to its vast industrial applications. The analysis involves studying the behavior and
response of governing equations on the basis of various parameters such as thickness of the film, film surface profile, shear stress, liquid velocity, volumetric flux,
vorticity, gravity, viscosity among others, along with different boundary conditions. In this article, we extend this analysis in fractional space using a homotopy
based scheme, considering the case of a Non-Newtonian Pseudo-Plastic fluid for
lifting and drainage on a vertical wall. After applying similarity transformations,
the given problems are reduced to highly non-linear and inhomogeneous ordinary
differential equations. Moreover, fractional differential equations are obtained
using basic definitions of fractional calculus. The Homotopy Perturbation Method
(HPM), along with fractional calculus is used for obtaining approximate solutions.
Physical quantities such as the velocity profile, volume flux and average velocity
respectively for lift and drainage cases have been calculated. To the best of our
knowledge, the given problems have not been attempted before in fractional
space. Validity and convergence of the obtained solutions are confirmed by finding residual errors. From a physical perspective, a comprehensive study of the
effects of various parameters on the velocity profile is also performed. Study
reveals that Stokes number S
t, non-Newtonian parameter β and magnetic parameter
M have inverse relationship with fluid velocity in lifting case. In the drainage case, Stokes number S
t and non-Newtonian parameter β have direct
relationship with fluid velocity, but magnetic parameter
M shows inverse relationship with velocity. The investigation also shows that the fractional parameter α
has direct relationship with the fluid velocity in lifting case, while it has inverse
relationship with velocity in the drainage case.
Keywords
Cite This Article
Ismail, F., Qayyum, M., Inayat, S. (2020). Fractional Analysis of Thin Film Flow of Non-Newtonian Fluid.
CMES-Computer Modeling in Engineering & Sciences, 124(3), 825–845.