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Flow of a Hydromagnetic Viscous Fluid between Parallel Disks with Slip

Published online by Cambridge University Press:  18 May 2015

N. Khan ,
M. Sajid  and
T. Mahmood
N. Khan*
Affiliation:
Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan
M. Sajid
Affiliation:
Theoretical Physics Division, The Pakistan Institute of Nuclear Science and Technology, Islamabad, Pakistan
T. Mahmood
Affiliation:
Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan
*
*Corresponding author ([email protected])
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Abstract

The present paper is devoted to the investigation of steady MHD axi-symmetric flow between two infinite stretching disks with slip effects. Our attention lies in obtaining the similarity solutions of the governing partial differential equations. The transformed boundary value problem is solved analytically for a series solution using homotopy analysis method. The convergence of the obtained solution is established and fluid velocity and pressure are analyzed for various set of parameter values. The obtained results are valid for both moderate and large values of Reynolds number.

Keywords

MagnetohydrodynamicsStretching disksSlip boundary conditionHomotopy analysis method
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 6 , December 2015 , pp. 713 - 726
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

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References

REFERENCES

1.Altan, T., Oh, S. and Gegel, H., Metal Forming Fundamentals and Applications, American Society of Metals, Metals Park, OH (1979).Google Scholar
2.Fisher, E. G., Extrusion of Plastics, Wiley, New York (1976).Google Scholar
3.Tadmor, Z. and Klein, I., Engineering Principles of Plasticating Extrusion, Polymer Science and Engineering Series, Van Norstrand Reinhold Co., New York (1970).Google Scholar
4.Sakiadis, B. C., “Boundary-Layer Behavior on Continuous Solid Surface: I. Boundary-Layer Equations for Two-Dimensional and Axi-Symmetric Flow,” AIChE Journal, pp. 26–28 (1961).Google Scholar
5.Sakiadis, B. C., “Boundary-Layer Behavior on Continuous Solid Surface: II. Boundary-Layer on Continuous Flat Surface,” AIChE Journal, pp. 221–225 (1961).Google Scholar
6.Crane, L. J., “Flow Past a Stretching Plate,” Zeitschrift für angewandte Mathematik Und Physik., (ZAMP), 21, pp. 645–647 (1970).Google Scholar
7.Gupta, P. S. and Gupta, A. S., “Heat and Mass Transfer on a Stretching Sheet with Suction and Blowing,” The Canadian Journal of Chemical Engineering, 58, pp. 744–746 (1977).CrossRefGoogle Scholar
8.Brady, J. F. and Acrivos, A., “Steady Flow in a Channel or Tube with Accelerating Surface Velocity. An Exact Solution to the Navier-Stokes Equations with Reverse Flow,” Journal of Fluid Mechanics, 112, pp. 127–150 (1981).CrossRefGoogle Scholar
9.McLeod, J. B. and Rajagopal, K. R., “On the Uniqueness of Flow of a Navier-Stokes Fluid Due to a Stretching Boundary,” Archive for Rational Mechanics and Analysis, 98, pp. 385–393 (1987).Google Scholar
10.Wang, C. Y., “The Three Dimensional Flow Due to a Stretching Flat Surface,” Physics of Fluids., 27, pp. 1915–1917 (1984).Google Scholar
11.Wang, C. Y., “Fluid Flow Due to a Stretching Cylinder,” Physics of Fluids, 31, pp. 466–468 (1988).Google Scholar
12.Mahapatra, T. R. and Gupta, A. S., “Heat Transfer in Stagnation-Point Flow Towards a Stretching Surface,” Heat and Mass Transfer, 38, pp. 517–521 (2002).Google Scholar
13.Fang, T., “Flow over a Stretchable Disk,” Physics of Fluids, 19, p. 128105 (2007).Google Scholar
14.Fang, T. and Zhang, J., “Flow Between Two Stretchable Disks-An Exact Solution of the Navier-Stokes Equations,” International Communication in Heat and Mass Transfer, 35, pp. 892–895 (2008).CrossRefGoogle Scholar
15.Gorder, R. A. V., Sweet, E. and Vajravelu, K., “Analytical Solutions of a Coupled Nonlinear System Arising in a Flow Between Stretching Disks,” Applied Mathematics and Computations, 216, pp. 1513–1523 (2010).Google Scholar
16.Wang, C. Y., “Flow Due to a Stretching Boundary with Partial Slip-An Exact Solution of the Navier-Stokes Equations,” Chemical Engineering Science, 57, pp. 3745–3747 (2002).Google Scholar
17.Anderson, H. I., “Slip Flow Past a Stretching Surface,” Acta Mechanica, 158, pp. 121–125 (2002).CrossRefGoogle Scholar
18.Ariel, P. D., “Axisymmetric Flow Due to a Stretching Sheet with Partial Slip,” Computers and Mathematics with Applications, 54, pp. 1169–1183 (2007).Google Scholar
19.Sajid, M., Ahmad, I. and Hayat, T., “Unsteady Boundary Layer Flow Due to a Stretching Sheet in Porous Medium with Partial Slip,” Journal of Porous Media, 12, pp. 911–917 (2009).CrossRefGoogle Scholar
20.Sajid, M., Ali, N., Abbas, Z. and Javed, T., “Stretching Flows with General Slip Boundary Condition,” International Journal of Modern Physics B, 30, pp. 5939–5947 (2010).Google Scholar
21.Davidson, P. A., An Introduction to Magnetohydrodynamics, Cambridge University Press, Cambridge (2001).Google Scholar
22.Hayat, T., Shafiq, A., Nawaz, M. and Alsaedi, A., “MHD Axisymmetric Flow of Third Grade Fluid Between Porous Disks with Heat Transfer,” Applied Mathematics and Mechanics (English Edition), 33, pp. 749–764 (2012).Google Scholar
23.Hayat, T., Naz, R. and Sajid, M., “On the Homotopy Solution for Poiseuille Flow of a Fourth Grade Fluid,” Communication in Nonlinear Science and Numerical Simulation, 15, pp. 581–589 (2010).CrossRefGoogle Scholar
24.Sajid, M., Awaisb, M., Nadeemb, S. and Hayat, T., “The Influence of Slip Condition on Thin Film Flow of a Fourth Grade Fluid by the Homotopy Analysis Method,” Computers Mathematics with Applications, 56, pp. 2019–2026 (2008).CrossRefGoogle Scholar
25.Sajid, M. and Hayat, T., “The Application of Homotopy Analysis Method to Thin Film Flows of a Third Order Fluid,” Chaos Solitons and Fractals, 38, pp. 506–515 (2008).Google Scholar
26.Sajid, M. and Hayat, T., “The Application of Homotopy Analysis Method for MHD Viscous Flow Due to a Shrinking Sheet,” Chaos Solitons and Fractals, 39, pp. 1317–1323 (2009).Google Scholar
27.Sajid, M., Abbas, Z. and Hayat, T., “Homotopy Analysis for Boundary Layer Flow of a Micropolar Fluid Through a Porous Channel,” Applied Mathematical Modelling, 33, pp. 4120–4125 (2009).Google Scholar
28.Sajid, M., Siddiqui, A. and Hayat, T., “Wire Coating Analysis Using MHD Oldroyd 8-Constant Fluid,” International Journal of Engineering Sciences, 45, pp. 381–392 (2007).CrossRefGoogle Scholar
29.Sajid, M., Hayat, T. and Asghar, S., “Non-Similar Analytic Solution for MHD Flow and Heat Transfer in a Third-Order Fluid over a Stretching Sheet,” International Journal of Heat and Mass Transfer, 50, pp. 1723–1736 (2007).Google Scholar
30.Sajid, M., Hayat, T. and Asghar, S., “Non-Similar Solution for the Axisymmetric Flow of a Third-Grade Fluid over Radially Stretching Sheet,” Acta Mechanica, 189, pp. 193–205 (2007).Google Scholar
31.Liao, S. J., Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman and Hall, Boca Raton (2003).Google Scholar
32.Liao, S. J., “On the Analytic Solution of Magneto-hydrodynamic Flow of Non-Newtonian Fluids over a Stretching Sheet,” Journal of Fluid Mechanics, 488, pp. 189–212 (2003).CrossRefGoogle Scholar
33.Liao, S. J., “Notes on Homotopy Analysis Method: Some Definitions and Theorems,” Communications in Nonlinear Science and Numerical Simulation, 14, pp. 983–997 (2009).Google Scholar
34.Liao, S. J., “An Optimal Homotopy Analysis Approach for Strongly Nonlinear Differential Equations,” Communications in Nonlinear Science and Numerical Simulation, 15, pp. 2003–2016 (2010).Google Scholar