On some helical flows of Oldroyd-B fluids
First Online: 06 November 2006 Received: 20 January 2006 Revised: 29 June 2006 DOI:
Cite this article as: Fetecau, C., Fetecau, C. & Vieru, D. Acta Mechanica (2007) 189: 53. doi:10.1007/s00707-006-0407-7 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 = 0, r 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. References Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders Phil. Trans. A 223 289 298 Batchelor, G. K. 1967An introduction to fluid dynamics Cambridge University Press Cambridge MATH Yih, C. S. 1969Fluid mechanics McGraw-Hill New York Waters, N. D., King, M. J. 1971 The unsteady flow of an elasto-viscous liquid in a straight pipe of circular cross section J. Phys. D: Appl. Phys. 4 204 211 CrossRef Rahaman, K. D., Ramkissoon, H. 1995 Unsteady axial viscoelastic pipe flows J. Non-Newtonian Fluid Mech. 57 27 38 CrossRef Wood, W. P. 2001 Transient viscoelastic helical flows in pipes of circular and annular cross-section J. Non-Newtonian Fluid Mech. 100 115 126 MATH CrossRef Hayat, T., Siddiqui, A. M., Asghar, S. 2001 Some simple flows of an Oldroyd-B fluid Int. J. Engng. Sci. 39 135 147 CrossRef Fetecau, C. 2004 Analytical solutions for non-Newtonian fluid flows in pipe-like domains Int. J. Non-Linear Mech. 39 225 231 CrossRef MathSciNet
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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).
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