Flow generated due to longitudinal and torsional oscillations of a circular cylinder with suction/injection in a micropolar fluid

Main Article Content

Ramana Murthy Venkata Josyula
Nagaraju Gajjela
Muthu Poosnar

Abstract

The flow generated by performing longitudinal and torsional oscillations of a porous circular cylinder which is subjected to constant suction/injection at the surface of the porous cylinder is studied. A finite difference method is proposed to analyse the velocity components and micro-rotation components, in an infinite expanse of an incompressible micropolar fluid. The effects of cross viscosity parameter, couple stress parameter, Reynolds number and Gyration parameter on the axial and torsional velocity components and on the micro-rotation components are shown graphically. Drag force acting on the wall of the cylinder is derived and the effects of micropolar parameters and suction parameter on the drag are shown graphically.

Article Details

How to Cite
Josyula, R. M. V., Gajjela, N., & Poosnar, M. (2012). Flow generated due to longitudinal and torsional oscillations of a circular cylinder with suction/injection in a micropolar fluid. Tamkang Journal of Mathematics, 43(3), 339–356. https://doi.org/10.5556/j.tkjm.43.2012.614
Section
Papers
Author Biographies

Ramana Murthy Venkata Josyula, National Institute of Technology, Warangal

Associate Professor,

Department of Mathematics

Nagaraju Gajjela, National Institute of Technology, Warangal

Research Scholar, Dept. of Mathematics

Muthu Poosnar, National Institute of Technology, warangal

Assistant Professor, Dept. of Mthematics

References

A. C. Eringen, Simple microfluids, Int. J. Engng. Sci.,2(1964), 205--217.

A. C. Eringen, Proceedings of XI'th International Congress of Applied Mechanics, Springer-Verlag, Berlin (1965), 131.

A. C. Eringen, Theory of micropolar fluids, J. Math. Mech,16(1966), 1--18.

T. Ariman, M. A. Turk and N. D. Sylvester, Microcontinuum fluid mechanics-a review, Int. J. Engng. Sci., 11(1973),905--930.

T. Ariman, M. A. Turk and N. D. Sylvester, Applications of microcontinuum fluid mechanics, Int. J. Engng. Sci, 12(1974),273--293.

C. Calmelet-Eluhu and D. R. Mazumdar, Flow of Micropolar fluid through a circular cylinder subject to longitudinal and torsinal oscillations, Mathl. Comput. Modelling, 27(1998),69--78.

G. G. Stokes, On the effect of rotation of cylinders and spheres about their own axes in increasing the logarithmic decrement of the arc of vibration, Mathematical and Philosophical Papers 5 Cambridge: Cambridge University Press, England(1886), 207--214.

M. J. Casarella and P. A. Laura, Drag on oscillating rod with longitudinal and torsional Motion, J. Hydronaut,3(1969), 180--183.

K. R. Rajagopal, Longitudinal and Torsional oscillation of a rod in a non-Newtonian fluid, Acta. Mech., 49(1983),281--285.

H. Ramkissoon and S. R. Majumdar, Flow due to the longitudinal and torsinal oscillations of a cylinder, ZAMP, 41(1990), 598--603.

H. Ramkissoon, C. V. Easwaran and S. R. Majumdar, Longitudinal and Torsional oscillation of a rod in a polar fluid, Int. J. Engng. Sci., 29(1991), 215--221.

D. Owen and K. Rahaman, On the flow of an Oldroyd-B liquid through a straight circular tube performing longitudinal and torsional oscillations of different frequencies, Mathematica, 14(2006), 1--9.

A. S. Berman, Laminar flow in channels with porous walls, J. Appl. Phys., 24(1953), 1232--1235.

J. N. Kapur, Flow of a non-Newtonian fluid between rotating cylinders with suction and injection, Phys. Fluids,6(1963), 626--631.

Jangi Lal, Unsteady flow and Heat Transfer in a viscous incompressible fluid due to the oscillations of a porous cylinder with suction, Def. Sci. J., 20(1970), 45--52.

G. Pontrelli, The axisymmetric flow of a homogeneous Oldroyd-B fluid due to the longitudinal and torsional oscillations of an infinite rod, Acta. Mech., 123(1997), 57--68.

M. Emin Erdogan and C. Erdem Imrak, Steady Flow of a Second-Grade Fluid in an annulus with Porous Walls, Mathematical Problems in Engineering, 2008(2008), 1--11.

P. M. Rao, K. Kuwahara and K. Tsuboi, Study of unsteady viscous flow around a transversely and longitudinally oscillating circular cylinder in a uniform flow at high Reynolds number, Comput. Mech., 10(1992), 414--428.

G. Pontrelli and R. K. Bhatnagar, Flow of a viscoelastic fluid between two rotating circular cylinders subject to suction or injection, Int. J. for Numer. Methods in Fluids, 24(1997),337--349.

Lokendra Kumar, Rama Bhargava and H. S. Takhar, Finite element solution of mixed convection on a moving vertical cylinder with suction in a moving micropolar fluid medium, Meccanica,41(2006), 63--78.

Mehrdad Massoudi and Tran X. Phouc, On the motion of a second grade fluid due to longitudinal and torsional oscillations of a cylinder-A numerical study, Appl. Math. Comput, 203(2008), 471--481.

P. Muthu, B. V. Rathish Kumar and Peeyush Chandra, Peristaltic motion of micropolar fluid in cylindrical tubes: effect of wall properties, Appl. Math. Modelling,

(2008), 2019--2033.