Table of Contents Author Guidelines Submit a Manuscript
Table of Contents Alerts

To receive news and publication updates for Mathematical Problems in Engineering, enter your email address in the box below.

Mathematical Problems in Engineering
Volume 2007, Article ID 42651, 11 pages
http://dx.doi.org/10.1155/2007/42651
Research Article

On the Steady Flow of a Second-Grade Fluid between Two Coaxial Porous Cylinders

M. Emin Erdoğan and C. Erdem İmrak

Mechanical Engineering Department, Faculty of Mechanical Engineering, Istanbul Technical University, Gümüşsuyu, Istanbul 34437, Turkey

Received 8 February 2007; Accepted 3 June 2007

Academic Editor: Kumbakonam Rajagopal

Copyright © 2007 M. Emin Erdoğan and C. Erdem İmrak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Rosenhead, Ed., Laminar Boundary Layers, Clarendon Press, Oxford, UK, 1963. View at Zentralblatt MATH · View at MathSciNet
  2. M. E. Erdoğan, “The effects of side walls on axial flow in rectangular ducts with suction and injection,” Acta Mechanica, vol. 162, no. 1–4, pp. 157–166, 2003. View at Zentralblatt MATH
  3. K. N. Mehta and R. K. Jain, “Laminar hydromagnetic flow in a rectangular channel with porous walls,” Proceedings of the National Institute of Sciences of India, Part A, vol. 28, pp. 846–856, 1962. View at Zentralblatt MATH · View at MathSciNet
  4. K. S. Sai and B. N. Rao, “Magnetohydrodynamic flow in a rectangular duct with suction and injection,” Acta Mechanica, vol. 140, no. 1-2, pp. 57–64, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. R. M. Terrill and P. W. Thomas, “On laminar flow through a uniform porous pipe,” Applied Scientific Research, vol. 21, no. 1, pp. 37–67, 1969. View at Publisher · View at Google Scholar
  6. R. M. Terrill and P. W. Thomas, “Spiral flow in a porous pipe,” Physics of Fluids, vol. 16, no. 3, pp. 356–359, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. C. L. Taylor, W. H. H. Banks, M. B. Zaturska, and P. G. Drazin, “Three-dimensional flow in a porous channel,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 44, no. 1, pp. 105–133, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. E. Erdoğan and C. E. İmrak, “On the axial flow of an incompressible viscous fluid in a pipe with a porous boundary,” Acta Mechanica, vol. 178, no. 3-4, pp. 187–197, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. A. S. Berman, “Laminar flow in an annulus with porous walls,” Journal of Applied Physics, vol. 29, pp. 71–75, 1958. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. P. Mishra and J. S. Roy, “Laminar elasticoviscous flow in an annulus with porous walls,” Physics of Fluids, vol. 10, no. 11, pp. 2300–2304, 1967. View at Publisher · View at Google Scholar
  11. E. Rukmangadachari, “Unsteady flow of an elastico-viscous fluid between two coaxial cylinders,” Rheologica Acta, vol. 21, no. 3, pp. 223–227, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. R. Bandelli and K. R. Rajagopal, “Start-up flows of second grade fluids in domains with one finite dimension,” International Journal of Non-Linear Mechanics, vol. 30, no. 6, pp. 817–839, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. C. Fetecau, “Analytical solutions for non-Newtonian fluid flows in pipe-like domains,” International Journal of Non-Linear Mechanics, vol. 39, no. 2, pp. 225–231, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  14. M. R. Mohyuddin, T. Hayat, F. M. Mahomed, S. Asghar, and A. M. Siddiqui, “On solutions of some non-linear differential equations arising in Newtonian and non-Newtonian fluids,” Nonlinear Dynamics, vol. 35, no. 3, pp. 229–248, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. K. R. Rajagopal and P. N. Kaloni, “Some remarks on boundary conditions for flows of fluids of the differential type,” in Continuum Mechanics and Its Applications, G. A. C. Graham and S. K. Malik, Eds., pp. 935–942, Hemisphere, New York, NY, USA, 1989. View at Zentralblatt MATH · View at MathSciNet
  16. K. R. Rajagopal, “On boundary conditions for fluids of the differential type,” in Navier-Stokes Equations and Related Nonlinear Problems, pp. 273–278, Plenum Press, New York, NY, USA, 1995. View at Zentralblatt MATH · View at MathSciNet
  17. R. L. Fosdick and B. Bernstein, “Nonuniqueness of second-order fluids under steady radial flow in annuli,” International Journal of Engineering Science, vol. 7, no. 6, pp. 555–569, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. K. R. Frater, “On the solution of some boundary-value problems arising in elastico-viscous fluid mechanics,” Zeitschrift für Angewandte Mathematik und Physik, vol. 21, no. 1, pp. 134–137, 1970. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. K. R. Rajagopal, “A note on unsteady unidirectional flows of a non-Newtonian fluid,” International Journal of Non-Linear Mechanics, vol. 17, no. 5-6, pp. 369–373, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. J. E. Dunn and K. R. Rajagopal, “Fluids of differential type: critical review and thermodynamic analysis,” International Journal of Engineering Science, vol. 33, no. 5, pp. 689–729, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. R. L. Fosdick and K. R. Rajagopal, “Uniqueness and drag for fluids of second grade in steady motion,” International Journal of Non-Linear Mechanics, vol. 13, no. 3, pp. 131–137, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. L. J. Slater, “Confluent Hypergeometric Functions,” Cambridge University Press, New York, NY, USA, 1960. View at Zentralblatt MATH · View at MathSciNet
  23. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, USA, 1965.