Research Papers: Flows in Complex Systems

Unsteady Flow of Power Law Fluids With Wall Slip in Microducts

[+] Author and Article Information
F. Talay Akyildiz

Department of Mathematics and Statistics,
Faculty of Science,
Al-Imam University,
Othman Ibn Affan St.,
Riyadh 11432, Saudi Arabia
e-mail: ftakyildiz@hotmail.com

Dennis A. Siginer

Fellow ASME
Centro de Investigación en Creatividad y
Educación Superior,
Departamento de Ingeniería Mecánica,
Universidad de Santiago de Chile,
Santiago 8320000, Chile;
Department of Mathematics and
Statistical Sciences;
Department of Mechanical, Energy and
Industrial Engineering,
Botswana International University of Science and
Palapye, Botswana,
e-mails: dennis.siginer@usach.cl;

M'hamed Boutaous

Université de Lyon,
CNRS, INSA-Lyon, CETHIL, UMR5008, F-69621,
Villeurbanne 69621, France
e-mail: mhamed.boutaous@insa-lyon.fr

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 9, 2018; final manuscript received January 10, 2019; published online February 19, 2019. Assoc. Editor: Ning Zhang.

J. Fluids Eng 141(8), 081107 (Feb 19, 2019) (6 pages) Paper No: FE-18-1400; doi: 10.1115/1.4042558 History: Received June 09, 2018; Revised January 10, 2019

Unsteady laminar nonlinear slip flow of power law fluids in a microchannel is investigated. The nonlinear partial differential equation resulting from the momentum balance is solved with linear as well as nonlinear boundary conditions at the channel wall. We prove the existence of the weak solution, develop a semi-analytical solution based on the pseudo-spectral-Galerkin and Tau methods, and discuss the influence and effect of the slip coefficient and power law index on the time-dependent velocity profiles. Larger slip at the wall generates increased velocity profiles, and this effect is further enhanced by increasing the power law index. Comparatively, the velocity of the Newtonian fluid is larger and smaller than that of the power law fluid for the same value of the slippage coefficient if the power index is smaller and larger, respectively, than one.

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Grahic Jump Location
Fig. 1

The difference between the exact solution (Eq. (26)) and the approximate solution for N=30, y=0.

Grahic Jump Location
Fig. 2

The difference between two approximate solutions: N=30 and N=34 for n=(3/2),t=2, and δ=0.05

Grahic Jump Location
Fig. 3

(a)–(c) Effect of the slip coefficient on the velocity profile: solid line δ=0.5, dash dot δ=0.05 at t=2

Grahic Jump Location
Fig. 4

Time development of centerline velocity for δ=0.05 and constant pressure gradient

Grahic Jump Location
Fig. 5

Time development of the centerline velocity for δ=0.05  and oscillatory pressure gradient Ft=1+sinωt with ω=10 rad/sec

Grahic Jump Location
Fig. 6

Effect of the slip coefficient on velocity profiles for oscillatory pressure gradient and n=3/2: solid line δ=0.5 and dash dot δ=0.05. Time is fixed in the figure and spatial coordinate runs from −1 to 1.

Grahic Jump Location
Fig. 7

Velocity profiles for fixed t=3 and  δ=0.001, solid and dashed lines represent n = 3/2 and n = 1/2, respectively

Grahic Jump Location
Fig. 8

Velocity profiles for fixed t=3 and  δ=0.0005, solid and dashed lines represent n = 3/2 and n = 1/2, respectively

Grahic Jump Location
Fig. 9

Velocity profiles for fixed t=3 and  δ=0.0001; solid and dashed lines represent n = 3/2 and n = 1/2, respectively



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