Three-Dimensional Flow of a Second Grade Fluid along an Infinite Horizontal Plane Wall with Periodic Suction

Authors

  • M. Shoaib Department of Mathematics & Statistics, Riphah International University, Sector I-14, Islamabad, Pakistan, Barani Institute of Management Sciences, Rehman Abad, Rawalpindi, Pakistan
  • A. M. Siddiqui Department of Mathematics, York Campus, Pennsylvania State University, York, PA 17403, USA
  • M. A. Rana Department of Mathematics & Statistics, Riphah International University, Sector I-14, Islamabad, Pakistan, Barani Institute of Management Sciences, Rehman Abad, Rawalpindi, Pakistan
  • A. Imran COMSATS Institute of Information Technology, Kamra Road, Post code 43600, Attock Pakistan.

Keywords:

Differential type fluids, Three-dimensional flows, Periodic suction, Regular perturbation method, Series solutions.

Abstract

In this paper, three-dimensional flow of a second grade fluid along a horizontal infinite plate which is subjected to a transverse sinusoidal suction velocity distribution is studied. Due to variable suction velocity distribution the flow becomes three-dimensional and for constant suction the problem becomes two-dimensional. The free stream velocity is uniform and for small perturbation approximation, analytic technique is applied to obtain the expressions for velocity field and components of skin friction. The effect of second-grade parameter, Reynolds number and suction parameter on the velocity in the direction of main flow and on the stress components is investigated with the help of graphs. The existence of backflow is observed and it is noted that the Reynolds number and suction parameter are controlling parameters for the backflow.

References

[1]. G. V. Lachmann, Boundary layer and flow control. Its principles and application, Vol. I and II, Pergamon Press 1961.
[2]. K. Gersten and J. F. Gross, Flow and heat transfer along a plane wall with periodic suction, ZAMP 25 (1974), 399-408.
[3]. P. Singh, V. P. Sharma and U. N. Misra, Three dimensional fluctuating flow and heat transfer along a plate with suction, Int. J. Heat Mass Transfer. 21 (1978), 1117-1123.
[4]. P. Singh, V. P. Sharma and U. N. Misra, Three dimensional free convection flow and heat transfer along a porous vertical plate, Appl. Sci. Res. 34 (1978), no. 1, 105-115.
[5]. K. D. Singh, Three dimensional viscous flow and heat transfer along a porous plate, Z. Angew. Math. Mech. 73 (1993), no. 1, 58-61.
[6]. K. D. Singh, Hydromagnetic effects on the three-dimensional flow past a porous plate, Z. Angew. Math. Phys. 41 (1990), no. 13, 441-446.
[7]. P. Singh, V. P. Sharma and U. N. Misra, Transient three-dimensional flow along a porous plate, Acta Mechanica. 38,183-190 (1981).
[8]. M. Guria and R. N. Jana, Hydrodynamic effect on the three-dimensional flow past a vertical porous plate, Int. J of Mathematical Sciences. 2005:20 (2005) 3359-3372.
[9]. G. D. Gupta and Rajesh Johari, MHD three-dimensional flow past a porous plate, Indian J. pure appl. 32(3):377-386, March 2001.
[10]. H. Schlichting, Boundary layer theory, McGraw-Hill 1968.
[11]. R. S. Rivlin, J. L. Ericksen, Stress deformation Relations for isotropic material, J. Rat. Mech. Anal. 4:323-425, 1955.

Downloads

Additional Files

Published

2016-04-09

How to Cite

Shoaib, M., Siddiqui, A. M., Rana, M. A., & Imran, A. (2016). Three-Dimensional Flow of a Second Grade Fluid along an Infinite Horizontal Plane Wall with Periodic Suction. American Scientific Research Journal for Engineering, Technology, and Sciences, 18(1), 153–170. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/1000

Issue

Section

Articles