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Analytic Approximate Solutions and Numerical Results for Stagnation Point Flow of Jeffrey Fluid Towards an Off-Centered Rotating Disk

Published online by Cambridge University Press:  23 October 2014

N. A. Khan ,
S. Khan  and
F. Riaz
N. A. Khan*
Affiliation:
Department of Mathematical Sciences, University of Karachi Karachi, Pakistan
S. Khan
Affiliation:
Department of Mathematical Sciences, University of Karachi Karachi, Pakistan
F. Riaz
Affiliation:
Department of Mathematical Sciences, University of Karachi Karachi, Pakistan
*
* Corresponding author (njbalam@yahoo.com
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Abstract

The present paper studies the three-dimensional, off centered stagnation flow of a Jeffrey fluid over a rotating disk. The governing non-linear equations and their associated boundary conditions are transformed into coupled ordinary differential equations by utilizing an appropriate similarity transformation. Homotopy analysis method is utilized to evaluate the analytical solution in the form of infinite series. Also, the convergence region of the obtained solution is determined and plotted. The effects of pertaining parameters on radial, azimuthal and induced velocities of the fluid flow are presented graphically and discussed. Moreover comparisons have also been made with the previous results as a special case.

Keywords

Jeffrey fluidOff centered flowRotating diskHomotopy analysis method
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 2 , April 2015 , pp. 201 - 215
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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References

1.Williamson, R. V. “The Flow of Pseudo Plastic Materials,” Industrial & Engineering Chemistry Research, 21, pp. 1108–1111 (1929).CrossRefGoogle Scholar
2.Powell, R. E. and Eyring, H., “Mechanisms for the Relaxation Theory of Viscosity,” Nature, 154, pp. 427–428 (1944).CrossRefGoogle Scholar
3.Stokes, V. K., “Couple Stresses in Fluid,” Physics Fluids, 9, pp. 1709–1715 (1966).CrossRefGoogle Scholar
4.Bingham, E. C., “An Investigation of the Laws of Plastic Flow,” U.S. Bureau of Standards Bulletin, 13, pp. 309–353 (1916).CrossRefGoogle Scholar
5.Casson, N., Rheology of Disperse Systems, in Flow Equation for Pigment Oil Suspensions of the Printing Ink Type, Rheology of Disperse Systems, Mill, C. C., Ed., Pergamon Press, London, UK, pp. 84–102 (1959).Google Scholar
6.Qasim, M., Hayat, T., Asad, S. and Hendi, A. A., “Boundary Layer Flow of a Jeffrey Fluid with Convective Boundary Conditions,” International Journal for Numerical Methods in Fluids, 69, pp. 1350–1362 (2012).Google Scholar
7.Malik, M. Y., Zehra, I. and Nadeem, S., “Numerical Treatment of Jeffrey Fluid Withpressure-Dependent Viscosity,” International Journal for Numerical Methods in Fluids, 68, pp. 196–209 (2012).CrossRefGoogle Scholar
8.Hayat, T., Awais, M., Alsaedi, A. and Alhothuali, M. S., “3-D Flow of Jeffery Fluid in a Channel with Stretched Wall,” European Physics Journal Plus, 127, p. 128 (2012).CrossRefGoogle Scholar
9.Turkyilmazoglu, M., “I. Pop, Exact Analytical Solutions for the Flow and Heat Transfer Near the Stagnation Point on a Stretching/Shrinking Sheet in a Jeffrey Fluid,” International Journal of Heat and Mass Transfer, 57, pp. 82–88 (2013).CrossRefGoogle Scholar
10.Qasim, M., “Heat and Mass Transfer in a Jeffrey Fluid Over a Stretching Sheet with Heat Source/Sink,” Alexandria Engineering Journal, 52, pp. 571–575 (2013).CrossRefGoogle Scholar
11.Hayat, T., Shehzad, S. A. and Alsaedi, A., “Three-Dimensional Stretched Flow of Jeffrey Fluid with Variable Thermal Conductivity and Thermal Radiation,” Applied Mathematics and Mechanics, 34, pp. 823–832 (2013).CrossRefGoogle Scholar
12.Von, T., “Kármán, Uber Laminare Und Turbulente Reibung,” Zeitschrift Für Angewandte Mathematik Und Mechanik, 1, pp. 233–252 (1921).Google Scholar
13.Hashmi, M. M., Hayat, T. and Alsaedi, A., “On the Analytic Solutions for Squeezing Flow of Nanofluid Between Parallel Disks,” Nonlinear Analysis: Modelling and Control, 17, pp. 418–430 (2012).CrossRefGoogle Scholar
14.Hayat, T., Nawaz, M., Awais, M. and Obaidat, S., “Axisymmetric Magnetohydrodynamic Flow of Jeffrey Fluid Over a Rotating Disk,” International Journal for Numerical Methods in Fluids, 70, pp. 764–774 (2012).CrossRefGoogle Scholar
15.Ahmadpour, A. and Sadeghy, K., “Swirling Flow of Bingham Fluids Above a Rotating Disk: An Exact Solution,” Journal of Non-Newtonian Fluid Mechanics, 197, pp. 41–47 (2013).CrossRefGoogle Scholar
16.Ram, P. and Bhandari, A., “Effect of Phase Difference Between Highly Oscillating Magnetic Field and Magnetization on the Unsteady Ferro Fluid Flow Due to a Rotating Disk,” Results in Physics, 3, pp. 55–60 (2013).CrossRefGoogle Scholar
17.Rashidi, M. M., Kavyani, N. and Abelman, S., “Investigation of Entropy Generation in MHD and Slip Flow Over a Rotating Porous Disk with Variable Properties,” International Journal of Heat and Mass Transfer, 70, pp. 892–917 (2014).CrossRefGoogle Scholar
18.Turkyilmazoglu, M., “MHD Fluid Flow and Heat Transfer Due to a Shrinking Rotating Disk,” Computers & Fluids, 90, pp. 51–56 (2014).CrossRefGoogle Scholar
19.Wang, C. Y., “Off-Centered Stagnation Flow Towards a Rotating Disk,” International Journal of Engineering Science, 46, pp. 391–396 (2008).CrossRefGoogle Scholar
20.Dinarvand, S., “On Explicit, Purely Analytic Solutions of Off-Centered Stagnation Flow Towards a Rotating Disk by Means of HAM,” Nonlinear Analysis: Real World Applications, 11, pp. 3389–3398 (2010).Google Scholar
21.Erfani, E., Rashidi, M. M. and Parsa, A. B., “The Modified Differential Transform Method for Solving Off-Centered Stagnation Flow Toward a Rotating Disk,” International Journal of Computational Methods, 7, pp. 655–670 (2010).CrossRefGoogle Scholar
22.Nourbakhsh, S. H., Pasha Zanoosi, A. A. and Shateri, A. R., “Analytical Solution for Off-Centered Stagnation Flow Towards a Rotating Disc Problem by Ho-motopy Analysis Method with Two Auxiliary Parameters,” Communications in Nonlinear Science and Numerical Simulation, 16, pp. 2772–2787 (2011).CrossRefGoogle Scholar
23.Khan, N. A. and Riaz, F., “Off-Centered Stagnation Point Flow of a Couple Stress Fluid Towards a Rotating Disk,” The Scientific World Journal, 2014, Article ID 163586 (2014).CrossRefGoogle ScholarPubMed
24.Liao, S. J., “The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems,” Ph.D. Dissertation, Shanghai Jiao Tong University, Shanghai, China (1992).Google Scholar
25.Khan, N. A., Mahmood, A. and Ara, A., “Approximate Solution of Couple Stress Fluid with Expanding or Contracting Porous Channel,” Engineering Computations, 30, pp. 399–408 (2013).CrossRefGoogle Scholar
26.Fardi, M., Kazemi, E., Ezzati, R. and Ghasemi, M., “Periodic Solution for Strongly Nonlinear Vibration Systems by Using the Homotopy Analysis Method,” Mathematical Sciences, 6, p. 65 (2012).CrossRefGoogle Scholar
27.Sakar, M. G. and Erdogan, F., “The Homotopy Analysis Method for Solving the Time-Fractional Fornberg-Whitham Equation and Comparison with Adomian's Decomposition Method,” Applied Mathematical Modelling, 37, pp. 8876–8885 (2013).CrossRefGoogle Scholar
28.Khan, N. A. and Riaz, F., “Effects of Slip Factors and Couple Stresses for Stagnation Point Flow Over a Moving Plate,” Chinese Journal of Engineering, Article ID 727826 (2013).CrossRefGoogle Scholar
29. Ali-Asgari, M., Mirdamadi, H. R. and Ghayour, M., “Coupled Effects of Nano-Size, Stretching, and Slip Boundary Conditions on Nonlinear Vibrations of Nano-Tube Conveying Fluid by the Homotopy Analysis Method,” Physica E: Low-Dimensional Systems and Nanostructures, 52, pp. 77–85 (2013).Google Scholar
30.Rashidi, M. M., Mohimanian Pour, S. A., Hayat, T. and Obaidat, S., “Analytic Approximate Solutions for Steady Flow Over a Rotating Disk in Porous Medium with Heat Transfer by Homotopy Analysis Method,” Computers and Fluids, 54, pp. 1–9 (2012).CrossRefGoogle Scholar
31.Turkyilmazoglu, M., “Numerical and Analytical Solutions for the Flow and Heat Transfer Near the Equator of an MHD Boundary Layer Over a Porous Rotating Sphere,” International Journal of Thermal Sciences, 50, pp. 831–842 (2011).CrossRefGoogle Scholar
32.Turkyilmazoglu, M., “Purely Analytic Solutions of Magneto Hydrodynamic Swirling Boundary Layer Flow Over a Porous Rotating Disk,” Computers and Fluids, 39, pp. 793–799 (2010).CrossRefGoogle Scholar