Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-14T03:30:05.942Z Has data issue: false hasContentIssue false
  • English
  • Français

Swirling Flow Over an Oscillatory Stretchable Disk

Published online by Cambridge University Press:  17 June 2014

S. Munawar ,
A. Ali ,
N. Saleem  and
A. Naqeeb
S. Munawar*
Affiliation:
Department of Informatics and Systems, School of Science & Technology, University of Management & Technology, Lahore 54000, Pakistan
A. Ali
Affiliation:
Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
N. Saleem
Affiliation:
Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia
A. Naqeeb
Affiliation:
Department of Mathematics, Karakoram International Univeristy, Gilgit-Baltistan, Pakistan
*
*[email protected]
Get access

Abstract

In this work a numerical investigation has been conducted to study the unsteady oscillatory flow of a viscous fluid induced by a swirling disk. The disk stretches radially with the time-based sinusoidal oscillations. The governing equations for the three-dimensional boundary layer-flow are normalized using a suitable set of similarity transformations. The normalized partial differential equations are then solved numerically using a finite difference scheme by altering the semi-infinite domain to a finite domain. The effects of various imperative parameters on the oscillatory flow are discussed with graphs and tables.

Keywords

Oscillatory flowViscous fluidRotating diskNumerical solution
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 4 , August 2014 , pp. 339 - 347
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Sakiadis, B. C., “Boundary-Layer Behavior on Continuous Solid Surfaces: I. Boundary-Layer Equations for Two-Dimensional and Axisymmetric Flow,” AIChE Journal, 7, pp. 26–28 (1961).Google Scholar
2.Crane, L. J., “Flow Past a Stretching Plate,” Zeitschrift Fur Angewandte Mathematik Und Physik, 21, pp. 645–647 (1970).Google Scholar
3.Wang, C. Y., “The Three-Dimensional Flow due to a Stretching Flat Surface,” Physics of Fluids, 27, pp. 1915–1916 (1984).Google Scholar
4.Banks, W. H. H., “Similarity Solutions of the Boundary-layer Equations for a Stretching,” Journal De Mecanique Theorique Et Appliquee, 2, pp. 375–392 (1983).Google Scholar
5.Kumari, M., Takhar, H. S. and Nath, G., “MHD Flow and Heat Transfer over a Stretching Surface with Prescribed Wall Temperature or Heat Flux,” Wärme - und Stoffübertragung, 25, pp. 331–336 (1990).Google Scholar
6.Grubka, L. J. and Bobba, K. M., “Heat Transfer Characteristics of a Continuous Stretching Surface with Variable Temperature,” Journal of Heat Transfer, 107, pp. 248–250 (1985).Google Scholar
7.Tamayol, A., Hooman, K. and Bahrami, M., “Thermal Analysis of Flow in a Porous Medium over a Permeable Stretching Wall,” Transport in Porous Media, 85, pp. 661–676 (2010).Google Scholar
8.Mehmood, A. and Ali, A., “Analytic Solution of Three-Dimensional Viscous Flow and Heat Transfer over a Stretching Flat Surface by Homotopy Analysis Method,” Journal of Heat Transfer, 130, 121701 (7 pages) (2008).Google Scholar
9.Munawar, S., Mehmood, A. and Ali, A., “Time-Dependent Flow and Heat Transfer over a Stretching Cylinder,” Chinese Journal of Physics, 50, pp. 828–848 (2012).Google Scholar
10.Mehmood, A., Munawar, S. and Ali, A., Comments to: “Homotopy Analysis Method for Solving the MHD Flow over a Nonlinear Stretching Sheet, Commun. Nonlinear Sci. Numer. Simul.,” Communications in Nonlinear Science and Numerical Simulation, 15, pp. 4233–4240 (2010).Google Scholar
11.Wang, C. Y., “Nonlinear Streaming due to the Oscillatory Stretching of a Sheet in a Viscous Fluid,” Acta Mechanica, 72, pp. 261–268 (1988).Google Scholar
12.Rajagopal, K., Veena, P. H. and Pravin, V. K., “Oscillatory Motion of an Electrically Conducting Viscoelastic Fluid over a Stretching Sheet in a Saturated Porous Medium With Suction/Blowing,” Mathematical Problems in Engineering, Article ID 60560, pp. 1–14 (2006).Google Scholar
13.Abbas, Z., Wang, Y., Hayat, T. and Oberlack, M., “Slip Effects and Heat Transfer Analysis in a Viscous Fluid over an Oscillatory Stretching Surface,” International Journal for Numerical Methods in Fluids, 59, pp. 443–458 (2009).Google Scholar
14.Munawar, S., Mehmood, A. and Ali, A., “Unsteady Flow of Viscous Fluid over the Vacillate Stretching Cylinder,” International Journal for Numerical Methods in Fluids, 70, pp. 671–681 (2012).Google Scholar
15.Kármán, T. V., “Über Laminare und Turbulente Reibung,” ZAMM-Zeitschrift Fur Angewandte Mathematik Und Mechanik, 1, pp. 233–252 (1921).Google Scholar
16.Cochran, W. G., “The Flow due to a Rotating Disc,” Mathematical Proceedings of the Cambridge Philosophical Society, 30, pp. 365–375 (1934).Google Scholar
17.Stuart, J. T., “On the Effects of Uniform Suction on the Steady Flow Due to a Rotating Disk,” Quarterly Journal of Mechanics and Applied Mathematics, 7, pp. 446–457 (1954).Google Scholar
18.Sparrow, E. M. and Gregg, J. L., “Mass Transfer, Flow, and Heat Transfer about a Rotating Disk,” Journal of Heat Transfer, 82, pp. 294–302 (1960).Google Scholar
19.Kuiken, H. K., “The Effect of Normal Blowing on the Flow Near a Rotating Disk of Infinite Extent,” Journal of Fluid Mechanics, 47, pp. 789–798 (1971).Google Scholar
20.Ackroyd, J. A. D., “On the Steady Flow Produced by a Rotating Disc with Either Surface Suction or Injection,” Journal of Engineering Mathematics, 12, pp. 207–220 (1978).Google Scholar
21.Kakutani, T., “Hydromagnetic Flow Due to a Rotating Disk,” Journal of the Physical Society of Japan, 17, pp. 1496–1506 (1962).Google Scholar
22.Sparrow, E. M. and Chess, R. D., “Magnetohydrodynamic Flow and Heat Transfer about a Rotating Disk,” Journal of Applied Mechanics, ASME, 29, pp. 181–187 (1962).Google Scholar
23.Thacker, W. I., Kumar, S. K. and Watson, L. T., “Magnetohydrodynamic Flow and Heat Transfer about a Rotating Disk with Suction and Injection at the Disk Surface,” Computers and Fluids, 16, pp. 183–193 (1988).Google Scholar
24.Frusteri, F. and Osalusi, E., “On MHD and Slip Flow over a Rotating Porous Disk with Variable Properties,” International Communications in Heat and Mass Transfer, 34, pp. 492–501 (2007).Google Scholar
25.Ariel, P. D., “Axisymmetric Flow of a Second Grade Fluid Past a Stretching Sheet,” International Journal of Engineering Science, 39, pp. 529–553 (2001).Google Scholar
26.Sajid, M., Ahmed, I., Hayat, T. and Ayub, M., “Series Solution for Unsteady Axisymmetric Flow and Heat Transfer over a Radially Stretching Sheet,” Communications in Nonlinear Science and Numerical Simulation, 13, pp. 2193–2202 (2008).Google Scholar
27.Fang, T. and Zhang, J., “Flow Between two Stretchable Disks - An Exact Solution of the Navier-Stokes Equations,” International Communications in Heat and Mass Transfer, 35, pp. 892–895 (2008).Google Scholar
28.Munawar, S., Mehmood, A. and Ali, A., “Effects of Slip on Flow between Two Stretchable Disks using Optimal Homotopy Analysis Method,” Canadian Journal of Applied Sciences, 1, pp. 50–68 (2011).Google Scholar
29.Fang, T., “Flow over a Stretchable Disk,” Physics of Fluids, 19, 128105 (2007).Google Scholar
30.Munawar, S., Mehmood, A. and Ali, A., “Time-Dependent Stagnation-Point Flow over Rotating Disk Impinging Oncoming Flow,” Applied Mathematics and Mechnics, English Edition, 34, pp. 85–96 (2013).Google Scholar