Summary
In this study the velocity fields and the associated tangential stresses corresponding to some helical flows of Oldroyd-B fluids between two infinite coaxial circular cylinders and within an infinite circular cylinder are determined in forms of series in terms of Bessel functions. At time t = 0 the fluid is at rest and the motion is produced by the combined action of rotating and sliding cylinders. The solutions that have been obtained satisfy the governing differential equations and all imposed initial and boundary conditions. For λ r = 0, λ = 0 or λ r = λ = 0 they reduce to the similar solutions for a Maxwell, second grade or Newtonian fluid, respectively. Finally, for comparison, the velocity profiles corresponding to the four models are plotted for different values of t.
Similar content being viewed by others
References
G. I. Taylor (1923) ArticleTitleStability of a viscous liquid contained between two rotating cylinders Phil. Trans. A 223 289–298
G. K. Batchelor (1967) An introduction to fluid dynamics Cambridge University Press Cambridge Occurrence Handle0152.44402
C. S. Yih (1969) Fluid mechanics McGraw-Hill New York
N. D. Waters M. J. King (1971) ArticleTitleThe unsteady flow of an elasto-viscous liquid in a straight pipe of circular cross section J. Phys. D: Appl. Phys. 4 204–211 Occurrence Handle10.1088/0022-3727/4/2/304
K. D. Rahaman H. Ramkissoon (1995) ArticleTitleUnsteady axial viscoelastic pipe flows J. Non-Newtonian Fluid Mech. 57 27–38 Occurrence Handle10.1016/0377-0257(94)01293-Q
W. P. Wood (2001) ArticleTitleTransient viscoelastic helical flows in pipes of circular and annular cross-section J. Non-Newtonian Fluid Mech. 100 115–126 Occurrence Handle1014.76004 Occurrence Handle10.1016/S0377-0257(01)00130-6
T. Hayat A. M. Siddiqui S. Asghar (2001) ArticleTitleSome simple flows of an Oldroyd-B fluid Int. J. Engng. Sci. 39 135–147 Occurrence Handle10.1016/S0020-7225(00)00026-4
C. Fetecau (2004) ArticleTitleAnalytical solutions for non-Newtonian fluid flows in pipe-like domains Int. J. Non-Linear Mech. 39 225–231 Occurrence Handle10.1016/S0020-7462(02)00170-1 Occurrence Handle2009252
Rajagopal, K. R.: Mechanics of non-Newtonian fluids. In: Recent developments in theoretical fluid mechanics, Pitman Research Notes in Mathematics, vol. 291, pp. 129–162. New York: Longman 1993.
K. R. Rajagopal R. K. Bhatnagar (1995) ArticleTitleExact solutions for some simple flows of an Oldroyd-B fluid Acta Mech. 113 233–239 Occurrence Handle0858.76010 Occurrence Handle10.1007/BF01212645 Occurrence Handle1361701
R. Bandelli K. R. Rajagopal G. P. Galdi (1995) ArticleTitleOn some unsteady motions of fluids of second grade Arch. Mech. 47 661–676 Occurrence Handle0835.76002 Occurrence Handle1364699
R. Bandelli K. R. Rajagopal (1995) ArticleTitleStart-up flows of second grade fluids in domains with one finite dimension Int. J. Non-Linear Mech. 30 817–839 Occurrence Handle0866.76004 Occurrence Handle10.1016/0020-7462(95)00035-6 Occurrence Handle1365862
P. N. Srivastava (1966) ArticleTitleNon-steady helical flow of a visco-elastic liquid Arch. Mech. Stos. 18 145–150
W. Tan T. Masuoka (2005) ArticleTitleStokes' first problem for an Oldroyd-B fluid in a porous half space Physics of Fluids 17 023101–7 Occurrence Handle10.1063/1.1850409 Occurrence Handle2118221
C. Truesdell W. Noll (1965) The nonlinear field theories of mechanics. Encyclopedia of Physics, vol. III/3 Springer Berlin Heidelberg New York
Sneddon, I. N.: Functional analysis. In: Encyclopedia of Physics, vol. II. Berlin Göttingen Heidelberg: Springer 1955.
C. Fetecau Corina Fetecau (1985) ArticleTitleOn the uniqueness of some helical flows of a second grade fluid Acta Mech. 57 247–252 Occurrence Handle0589.76010 Occurrence Handle10.1007/BF01176922 Occurrence Handle830259
C. Fetecau Sharat C. Prasad (2005) ArticleTitleA note on the flow induced by a constantly accelerating edge in an Oldroyd-B fluid IJMMS 16 2677–2688 Occurrence Handle10.1155/IJMMS.2005.2677 Occurrence Handle2184841
Fetecau, C., Prasad, Sharat C., Rajagopal, K. R.: A note on the flow induced by a constantly accelerating plate in an Oldroyd-B fluid. To appear in AMM (Applied Mathematical Modelling).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fetecau, C., Fetecau, C. & Vieru, D. On some helical flows of Oldroyd-B fluids. Acta Mechanica 189, 53–63 (2007). https://doi.org/10.1007/s00707-006-0407-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-006-0407-7