Abstract
This paper deals with an Eulerian formulation of the theory of directed fluid sheets appropriate for incompressible, linear viscous fluid flow in channels with arbitrary shapes for their major boundaries which may be moving or fixed. Special cases of the theory are applied to a number of two-dimensional fluid flow problems and these solutions are in general discussed for unsteady flow. Specific applications include fluid flow in a channel whose boundaries are symmetric with respect to a middle plane in the channel, subjected to time-dependent pressure gradient at one end; and to lubrication problems in a general shaped channel when one of the channel walls is a fixed plane while the other is moving with a constant velocity. Flow of a viscous fluid with a free surface over a fixed boundary is also discussed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Duck, P. W. (1978) Oscillating flow through constricted or dilated channels and axisymmetric pipes. Proc. Roy. Soc. Lond. A 363, 335–353.
Green, A. E., N. Laws, & P. M. Naghdi (1974) On the theory of water waves. Proc. Roy. Soc. Lond. A 338, 43–55.
Green, A. E., & P. M. Naghdi (1976) Directed fluid sheets. Proc. Roy. Soc. Lond. A 347, 447–473.
Green, A. E., & P. M. Naghdi (1977) Water waves in a nonhomogeneous incompressible fluid. J. Appl. Mech. 44, 523–528.
Green, A. E., & P. M. Naghdi (1979) Directed fluid sheets and gravity waves in compressible and incompressible fluids. Int. J. Engng. Sci. 17, 1257–1272.
Naghdi, P. M. (1982) Finite deformation of elastic rods and shells. Proc. IUTAM Symp. on “Finite Elasticity” (Bethlehem, PA, 1980, edited by D. E. Carlson and R. T. Shield), Martinus Nijhoff Publishers, Hague, Netherlands, pp. 47–103.
Phan-Thien, N. (1981 a) On the effect of parallel and transverse stationary random surface roughness in hydrodynamic lubrication. Proc. Roy. Soc. Lond. A 374, 569–591.
Phan-Thien, N. (1981 b) On the effects of the Reynolds and Stokes surface roughnesses in a two-dimensional slider bearing. Proc. Roy. Soc. Lond. A 337, 349–362.
Phan-Thien, N. (1982) Hydrodynamic lubrication of rough surfaces. Proc. Roy. Soc. Lond. A 383, 439–446.
Sun, D.-C., & K.-K. Chen (1977) First effects of Stokes roughness on hydrodynamic lubrication. J. Lubrication Technology, Trans. Amer. Soc. Mech. Eng. F 99, 2–9.
Author information
Authors and Affiliations
Additional information
Dedicated to J. L. Ericksen on the occasion of his Sixtieth Birthday
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Green, A.E., Naghdi, P.M. (1986). A Direct Theory of Viscous Fluid Flow in Channels. In: The Breadth and Depth of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61634-1_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-61634-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16219-3
Online ISBN: 978-3-642-61634-1
eBook Packages: Springer Book Archive