Full Text:   <3103>

CLC number: O35

On-line Access: 2008-03-27

Received: 2007-08-10

Revision Accepted: 2007-12-06

Crosschecked: 0000-00-00

Cited: 2

Clicked: 5282

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.5 P.672-680


Exact solutions for different vorticity functions of couple stress fluids

Author(s):  Saeed ISLAM, Chao-ying ZHOU, Xiao-juan RAN

Affiliation(s):  Department of Mechanical Engineering and Automation Harbin Institute of Technology, Shenzhen Graduate School, Shenzhen 518055, China; more

Corresponding email(s):   saeed@hitsz.edu.cn, saeed_nihar@yahoo.com.au

Key Words:  Exact solutions, Vorticity functions, Beltrami flow, Couple stress fluid

Saeed ISLAM, Chao-ying ZHOU, Xiao-juan RAN. Exact solutions for different vorticity functions of couple stress fluids[J]. Journal of Zhejiang University Science A, 2008, 9(5): 672-680.

@article{title="Exact solutions for different vorticity functions of couple stress fluids",
author="Saeed ISLAM, Chao-ying ZHOU, Xiao-juan RAN",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Exact solutions for different vorticity functions of couple stress fluids
%A Saeed ISLAM
%A Chao-ying ZHOU
%A Xiao-juan RAN
%J Journal of Zhejiang University SCIENCE A
%V 9
%N 5
%P 672-680
%@ 1673-565X
%D 2008
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A071433

T1 - Exact solutions for different vorticity functions of couple stress fluids
A1 - Saeed ISLAM
A1 - Chao-ying ZHOU
A1 - Xiao-juan RAN
J0 - Journal of Zhejiang University Science A
VL - 9
IS - 5
SP - 672
EP - 680
%@ 1673-565X
Y1 - 2008
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A071433

In this paper, inverse solutions are obtained for the class of 2D steady incompressible couple stress fluid flows. This class consists of flows for which the vorticity distribution is given by ▽2ψ=ψ+f(x,y). The solutions are obtained by applying the inverse method, which makes certain hypotheses regarding the form of the velocity field and pressure but without making any regarding the boundaries of the domain occupied by the fluid. Inverse solutions are derived for three different forms of f(x,y).

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Bogoyavlenskij, O.I., 2003. Exact unsteady solutions to the Navier-Stokes and viscous MHD equations. Phy. Lett. A, 307(5-6):281-286.

[2] Chandna, O.P., Oku-Ukpong, E.O., 1994. Flows for chosen vorticity functions—Exact solutions of the Navier Stokes equations. Int. J. Math. & Math. Sci., 17(1):155-164.

[3] El-Dabe, N.T.M., El-Mohandis, S.M.G., 1995. Effect of couple stresses on pulsatile hydromagnetic poiseuille flow. Fluid Dyn. Res., 15(5):313-324.

[4] Gupta, R.S., Sharma, L.G., 1988. Analysis of couple stresses lubricant in hydrostatic thrust bearings. Wear, 125(3):257-269.

[5] Hui, W.H., 1987. Exact solutions of the 2-dim Navier-Stokes equations. J. Appl. Math. Phys. ZAMP, 38(5):689-702.

[6] Islam, S., Zhou, C.Y., 2007a. Certain Inverse Solutions of a Second-Grade Magnetohydrodynamic Aligned Fluid Flow in a Porous Medium. Journal of Porous Media, 10(4):401-408.

[7] Islam, S., Zhou, C.Y., 2007b. Exact solutions for two dimensional flows of couple stress fluids. ZAMP, 58(6):1035-1048.

[8] Kaloni, P.N., Huschilt, K., 1984. Semi-inverse solutions of non-Newtonian fluid. Int. J. Non-Linear Mech., 19(4):373-381.

[9] Kovaznay, L.I.G., 1948. Laminar flow behind a two dimensional grid. Proc. Cambridge, Phil. Soc., 44:58-62.

[10] Labrapulu, F., 2000. A few more exact solutions of a second grade fluid via inverse method. Mechanics Research Communications, 27(6):713-720.

[11] Lin, S.P., Tobak, M., 1986. Reversed flow above a plate with suction. AIAAJ, 24:334-335.

[12] Mindlin, R.D., Tierstea, H.F., 1962. Effect of couple stresses in linear elasticity. Arch. Rat. Mech. Anal., 11(1):415-448.

[13] Rajagopal, K.R., 1980. On the decay of vortices of a second grade fluid. Mechanics, 9:185-188.

[14] Rajagopal, K.R., 1982. A note on unsteady unidirectional flows of a non-Newtonian fluid. Int. J. Non-Linear Mech., 17(5-6):369-373.

[15] Ramanaiah, G., 1979. Squeeze films between finite plates lubricated by fluids with couple stress. Wear, 54:315-320.

[16] Siddiqui, A.M., 1986. Some inverse solutions of a non-Newtonian fluid. Mech. Res. Comm., 17(3):157-163.

[17] Siddiqui, A.M., Hayat, T., Asghar, S., 2001. Some exact solutions of an elastico-viscous fluid. Appl. Math. Lett., 14(5):571-579.

[18] Siddiqui, A.M., Islam, S., Ghori, Q.K., 2006. Two dimensional viscous incompressible flows in a porous medium. Journal of Porous Media, 9(6):591-596.

[19] Sinha, P., Singh, C., 1981. Couple stress in the lubrication of rolling contact bearings considering cavitations. Wear, 67(1):85-98.

[20] Stokes, V.K., 1966. Couple stresses in fluid. Physics of Fluids, 9(9):1709-1715.

[21] Taylor, G.I., 1923. On the decay of vortices in a viscous fluid. Phil. Mag., 46:671-674.

[22] Wang, C.Y., 1991. Exact solutions of the steady state Navier Stokes equations. Ann. Rev. Fluid Mech., 23(1):159-177.

[23] Wang, L., Zhu, Q., Zhu, W., 2002. On the performance of dynamically loaded journal bearings with couple stress fluids. Tribology Int., 35(3):185-191.

[24] Wu, C.P., Ji, Z.Z., Zhang, Y.X., Hao, J.Z., Jin, X., 2007. Some new exact solutions for the two-dimensional Navier-Stokes equations. Phy. Lett. A, 371(5-6):438-452

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE