publication . Preprint . 2015

Theoretical Investigation of Creeping Viscoelastic Flow Transition Around a Rotating Curved Pipe

Hamza, S. E. E.; El-Bakry, Mostafa Y.;
Open Access English
  • Published: 29 Apr 2015
The study of creeping motion of viscoelastic fluid around a rotating rigid torus is investigated. The analysis of the problem is performed using a second-order viscoelastic model. The study is carried out in terms of the bipolar toroidal system of coordinates where the toroid is rotating about its axis of symmetry (z-axis). The problem is solved within the frame of slow flow approximation. Therefore, all variables in the governing equations are expanded in a power series of angular velocity. A set of successive partial differential equations is obtained. The equations of motion governing the first and second-order are formulated and solved for the first-order on...
free text keywords: Physics - Fluid Dynamics
Download from
31 references, page 1 of 3

1. W.R. Dean, "Note on the motion of fluid in a curved pipe," Phil. Mag., vol. 4, pp. 208, 1927.

2. W.R. Dean, "The streamline motion of fluid in a curved pipe," Phil. Mag., vol. 5, pp. 673, 1928.

3. J. Zhang, and B. Zang, "Theoretical and numerical investigation of flow transition in rotating curved annular pipes," Theoret. Comput. Fluid Dynamics., vol. 16, pp. 99, 2002.

4. W.M. Collins and S.C.R. Dennis, "The steady motion of a viscous fluid in a curved tube," Q.J. Mech. Appl. Math., vol. 28, pp. 133, 1975.

5. S.C.R. Dennis, "Calculation of the steady flow through a curved tube using a new finitedifference method," J. Fluid Mech., vol. 99, pp. 449, 1980.

6. M.A. Petrakis, and G.T. Karahalios, "Fluid flow behavior in a curved annular conduit," Int. J. Non-Linear Mech., vol. 34, no. 1, pp. 13, 1999. [OpenAIRE]

7. G. Jayaraman, and K. Tewari, "Flow in catheterized curved artery," Med. Biol. Eng. Comput., vol. 34, no. 5, pp. 720, 1995.

8. R.K. Dash, G. Jayaraman, and K.N. Mehta, "Flow in a catheterized curved artery with stenosis," J. BioMech., vol 32, pp. 49, 1999.

9. S.N. Barua, "On secondary flow in stationary curved pipes," Q. J. Mech. appl. Math. vol. 16, pp. 61, 1963. [OpenAIRE]

10. H. Ito, "Laminar flow in curved pipes," Z. angew. Math. Mech. vol. 49, pp. 653, 1969.

11. S.C.R. Dennis, and N. Riley, "On the fully developed flow in a curved pipe at high Dean number," Proc. R. Soc. London, A 434, pp. 473, 1991.

12. S.A. Berger, L. Talbot, and L.S. Yao, "Flow in curved pipes," Annu. Rev. Fluid Mech. vol. 15, pp. 461, 1983. [OpenAIRE]

13. Z.H. Yang and H. Keller, "Multiple laminar flows through curved pipes," Appl. Numer. Maths. vol. 2, pp. 257, 1986.

14. J.H. Siggers, and S.L. Waters, "Steady flows in pipes with finite curvature," Phys. Fluids. vol. 17, pp. 077102, 2005. [OpenAIRE]

15. J.H. Siggers, and S.L. Waters, "Unsteady flows in pipes with finite curvature," J. Fluid Mech. vol. 600, pp. 133, 2008. [OpenAIRE]

31 references, page 1 of 3
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue