Summary
The role that the normal stresses play in the generation of non-Newtonian secondary flows in straight tubes of non-circular cross-section, is examined from a theoretical standpoint. It is proven independent of any constitutive assumptions that in order for these secondary flows to occur in the absence of body forces, the axial velocity must give rise to some non-zero difference in the transverse normal stresses. This necessary condition is utilized to demonstrate that the development of secondary flows in certain non-Newtonian fluids can be influenced by the precise structure of the time derivatives in the constitutive equations. In particular, it is shown that certain frame-indifferent convected time rates give rise to secondary flows whereas others do not.
Similar content being viewed by others
References
Ericksen, J. L.: Overdetermination of the speed in rectilinear motion of non-Newtonian fluids. Quart. Appl. Math.14, 318 (1956).
Green, A. E., Rivlin, R. S.: Steady flow of non-Newtonian fluids through tubes. Quart. Appl. Math.14, 299 (1956).
Langlois, W. E., Rivlin, R. S.: Slow steady-state flow of viscoelastic fluids through non-circular tubes. Rend. Mat.22, 169 (1963).
Stone, D. E.: On the non-existence of rectilinear motion in plastic solids and non-Newtonian fluids. Quart. Appl. Math.15, 257 (1957).
Truesdell, C., Noll, W.: The non-linear field theories of mechanics. Handbuch der Physik III/3. Berlin-Heidelberg-New York: Springer 1965.
Fosdick, R. L., Serrin, J.: Rectilinear steady flow of simple fluids. Proc. Royal Soc. Lond.A 332, 311 (1973).
Speziale, C. G.: On turbulent secondary flows in pipes of non-circular cross-section. Int. J. Engng. Sci.20, 863 (1982).
Pipkin, A. C., Rivlin, R. S.: Normal stresses in flow through tubes of non-circular cross-section. ZAMP14, 738 (1963).
Townsend, P., Walters, K., Waterhouse, W. M.: Secondary flows in pipes of square cross-section and the measurement of the second normal stress difference. J. Non-Newtonian Fluid Mech.1, 107 (1976).
Speziale, C. G.: Closure models for rotating two-dimensional turbulence. Geophys. Astrophys. Fluid Dynamics23, 69 (1983).
Author information
Authors and Affiliations
Additional information
With 2 Figures
Rights and permissions
About this article
Cite this article
Speziale, C.G. On the development of non-Newtonian secondary flows in tubes of non-circular cross-section. Acta Mechanica 51, 85–95 (1984). https://doi.org/10.1007/BF01176390
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01176390