Summary
The problem considered is the steady flow of an Oldroyd 8-constant fluid in a convergent channel. Using series expansions in terms of decreasing powers ofr given by Strauss [8] for the stream function and stress components, the governing equations of the problem are reduced to ordinary differential equations. The resulting differential equations have been solved by employing a numerical technique. It is shown that the streamline patterns are strongly dependent on the non-Newtonian parameters.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Jeffrey, G. B.: The two-dimensional steady motion of a viscous fluid. Phil. Mag.29, 455–465 (1915).
Hamel, G.: Spiralförmige Bewegungen zäher Flüssigkeiten. Jahr. Deutsch. Math. Ver.25, 34–60 (1917).
Rosenhead, L.: The steady two-dimensional radial flow of a viscous fluid between two inclined walls. Proc. Roy. Soc. Lond.A175, 436–467 (1940).
Millsaps, K., Pohlhausen, K.: Thermal distributions in Jeffrey-Hamel flows between non-parallel plane walls. J. Aero. Sci.20, 187–196 (1953).
Birkhoff, G. D., Zarantanello, E. H.: Jets, Wakes and Cavities, p. 272. New York: Academic Press1957.
Moffatt, H. K., Duffy, B. R.: Local similarity solution and their limitations. J. Fluid Mech.96, 299–313 (1980).
Langlois, W. E., Rivlin, R. S.: Steady flow of slightly viscoelastic fluids. Technical Report No. DA-4725/3, Divison of Applied Mathematics, Brown University, Providence (1959).
Strauss, K.: Die Strömung einer einfachen viscoelastischen Flüssigkeit in einem konvergenten Kanal. Teil I: Die stationare Strömung. Acta Mech.20, 233–246 (1974).
Strauss, K.: Die Strömung einer einfachen viscoelastischen Flüssigkeit in einem konvergenten Kanal. Teil II: Die Stabilität der Strömung. Acta Mech.21, 141–152 (1975).
Han, C. D., Drexler, L. H.: Studies of converging flows of viscoelastic polymeric melts. III. Stress and velocity distributions in the entrance region of a tapered slit die. J. Appl. Polym. Sci.17, 2369–2393 (1973).
Yoo, H. J., Han, C. D.: Stress distribution of polymers in extrusion through a converging die. J. Rheol.25, 115–137 (1981).
Kaloni, P. N., Kamel, M. T.: A note on the Hamel flow of Cosserat fluids. Zamp31, 293–296 (1980)
Hull, A. M.: An exact solution for the slow flow of a general linear viscoelastic fluid through a slit. J. Non-Newt. Fluid Mech.8, 327–336 (1981).
Mansutti, D., Rajagopal, K. R.: Flow of a shear thinning fluid between intersecting planes. Int. J. Non-Linear Mech.26, 769–775 (1991).
Bhatnagar, R. K., Rajagopal, K. R., Gupta, G.: Flow of an Oldroyd-B fluid between intersecting planes. J. Non-Newt. Fluid Mech.46, 49–67 (1993).
Bird, R. B., Armstrong, R. C., Hassager, O.: Dynamics of polymeric liquids, vol. 1. Fluid Mech., p. 352. New York: Wiley 1987.
Huilgol, R. R.: Continuum mechanics of viscoelastic liquids. New York: Wiley 1975, p. 191.
Giesekus, H.: Zur Formulierung der Randbedingungen in Strömungen viskoelastischer Flüssigkeiten mit Injektion und Absaugung an den Wänden. Rheol. Acta9, 474–487 (1970).
Strauss, K.: Stability and overstability of the plane flow of a simple viscoelastic fluid in a converging channel. In: Theoretical rheology (Hutton, J. F., Pearson, J. R. A., Walters, K. (eds.), p. 56. New York: Wiley 1985.
Hull, A. M.: Die-entry flow of polymers. Ph. D. Thesis, London University 1981.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bari§, S. Flow of an Oldroyd 8-constant fluid in a convergent channel. Acta Mechanica 148, 117–127 (2001). https://doi.org/10.1007/BF01183673
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01183673