Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-19T14:11:47.489Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow of Second Grade Fluid between two Walls Induced by Rectified Sine Pulses Shear Stress

Published online by Cambridge University Press:  16 July 2015

Q. Sultan ,
M. Nazar ,
I. Ahmad  and
U. Ali
Q. Sultan
Affiliation:
Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University Multan, Pakistan
M. Nazar*
Affiliation:
Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University Multan, Pakistan Wenzhou Kean University Wenzhou, China
I. Ahmad
Affiliation:
Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University Multan, Pakistan
U. Ali
Affiliation:
Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University Multan, Pakistan
*
* Corresponding author (mudassar_666@yahoo.com)
Get access

Abstract

This paper concerns with the unsteady MHD flow of a second grade fluid between two parallel walls through porous media induced by rectified sine pulses shear stress. The analytical expressions for the velocity field and the adequate shear stress are determined by means of the Laplace transform technique and Fourier cosine and sine transforms and are written as a sum of steady state and transient solutions. The influence of side walls on the fluid motion, the distance between walls for which the velocity of the fluid in the middle of the channel is negligible, and the required time to reach the steady state are presented by graphical illustrations. As the second grade fluid parameter → 0 the problem reduces to the Newtonian fluids performing the same motion.

Keywords

Second grade fluidRectified sine pulsesMHD flowPorous medium
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 5 , October 2015 , pp. 573 - 582
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

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.Fetecau, C. and Fetecau, Corina, “Starting Solutions for Some Unsteady Unidirectional Flows of a Second Grade Fluid,” International Journal of Engineering Science, 43, pp. 781–789 (2005).CrossRefGoogle Scholar
2.Nazar, M., Corina Fetecau, Vieru, D. and Fetecau, C., “New Exact Solutions Corresponding to the Second Problem of Stokes for Second Grade Fluids,” Nonlinear Analysis: Real World Applications, 11, pp. 584–591 (2010).Google Scholar
3.Hayat, T., Wang, Y. and Hutter, K., “Hall Effects on the Unsteady Hydromagnetic Oscillatory Flow of a Second-Grade Fluid,” International Journal of Non-Linear Mechanics, 39, pp. 1027–1037 (2004).Google Scholar
4.Fetecau, Corina, Akhtar, W., Imran, M. A. and Vieru, D., “On the Oscillating Motion of an Oldroyd-B Fluid Between Two Infinite Circular Cylinders,” Computers and Mathematics with Applications, 59, pp. 2836–2845 (2010).Google Scholar
5.Liu, Y. and Zheng, L., “Axial Oscillation of a Generalized Oldroyd-B Fluid between Two Cylinders,” Scientific Journal of Mathematics Research, 2, pp. 90–95 (2012).Google Scholar
6.Nazar, M., Shahid, F., Akram, M. S. and Sultan, Q., “Flow on Oscillating Rectangular Duct for Maxwell Fluid,” Applied Mathematics and Mechanics-English Edition, 33, pp. 717–730 (2012).CrossRefGoogle Scholar
7.Sultan, Q., Nazar, M., Ali, U. and Imran, M., “Unsteady Flow of Oldroyd-B Fluid Through Porous Rectangular Duct,” International Journal of Nonlinear Science, 5, pp, 195–211 (2013).Google Scholar
8.Khan, M. and Anjum, A., “Some Oscillating Motions of a Burgers’ Fluid,” International Journal of Physical Sciences, 7, pp. 5834–5851 (2012).Google Scholar
9.Ghosh, A. K. and Pintu, S., “On Hydromagnetic Channel Flow of an Oldroyd-B Fluid Induced by Rectified Sine Pulses,” Computational and Applied Mathematics, 28, pp. 365–395, (2009).Google Scholar
10.Nazar, M., Sultan, Q., Athar, M. and Kamran, M., “Unsteady Longitudinal Flow of a Generalized Ol-droyd- B Fluid in Cylindrical Domains,” Communications in Nonlinear Science and Numerical Simulation, 16, pp. 2737–2744 (2011).Google Scholar
11.Fetecau, C., Vieru, D. and Fetecau, Corina, “Effect of the Side Walls on the Motion of a Viscous Fluid Induced by an Infinite Plate That Applies an Oscillating Shear Stress to the Fluid,” Central European Journal of Physics, 9, pp. 816–824 (2011).Google Scholar
12.Fetecau, C., Mahmood, A. and Jamil, M., “Exact Solutions for the Flow of a Viscoelastic Fluid Induced by a Circular Cylinder Subject to a Time Dependent Shear Stress,” Communications in Nonlinear Science and Numerical Simulation, 15, pp. 3931–3938 (2010).Google Scholar
13.Jamil, M. and Fetecau, C., “Helical Flows of Maxwell Fluid Between Coaxial Cylinders with Given Shear Stresses on the Boundary,” Nonlinear Analysis: Real World Applications, 11, pp. 4302–4311 (2010).Google Scholar
14.Vieru, D., Fetecau, Corina, and Rana, M., “Starting Solutions for the Flow of Second Grade Fluids in a Rectangular Channel Due to an Oscillating Shear Stress,” AIP Conference Proceedings 1450, 45, pp. 45–54, doi: 10.1063/1.4724116 (2012).CrossRefGoogle Scholar
15.Vieru, D., Corina Fetecau, and Sohail, A., “Flow Due to a Plate That Applies an Accelerated Shear to a Second Grade Fluid Between Two Parallel Walls Perpendicular to the Plate,” Zeitschrift Für An-gewandte Mathematik Und Physik, 62, pp. 161–172 (2011).Google Scholar
16.Khan, M. Hashim, and Fetecau, C., “On the Exact Solutions for Oscillating Flow of a MHD Second-Grade Fluid Through Porous Media,” Special Topics and Reviews in Porous Media — An International Journal, 3, pp. 13–22 (2012).Google Scholar
17.Khan, M., Iqbal, K. and Azram, M., “Closed-Form Solutions for MHD Flow of a Second-Grade Fluid Through Porous Space,” Special Topics and Reviews in Porous Media — An International Journal, 2, pp. 125–132 (2011).Google Scholar
18.Li, C., Zheng, L., Zhang, Y., Ma, L. and Zhang, X., “Helical Flows of a Heated Generalized Oldroyd-B Fluid Subject to a Time-Dependent Shear Stress in Porous Medium,” Communications in Nonlinear Science and Numerical Simulation, 17, pp. 5026–5041 (2012).CrossRefGoogle Scholar