A direct theory of viscous fluid flow in channels
type: Item
instance of: scholarly article
title: A direct theory of viscous fluid flow in channels
zbMATH Open document ID: 0588.76050
DOI: 10.1007/BF00280647
author: A. E. Green
author: P. M. Naghdi
published in: Archive for Rational Mechanics and Analysis
publication date: 1984-01-01T00:00:00Z
review text: In this paper the authors continue their studies of fluid flow in channels using their theory of directed fluid sheets. To do this it is necessary to develop a procedure for expressing the conservation laws arising in the theory in an Eulerian form. This done they obtain local equations in Eulerian form by postulating two-dimensional conservation laws for a Cosserat surface of order K, that is one comprising a material surface with K directors. The theory is worked out for application to incompressible, linear viscous fluid flow in a channel whose principal boundaries have given velocities. Examples considered include effects of a time-dependent pressure gradient on flow in a channel with fixed boundaries symmetric about a middle plane, aspects of lubrication theory of flow in a general channel when one channel boundary is a fixed plane and the other moves with constant velocity and flow of a layer of viscous fluid over a fixed boundary.
Mathematics Subject Classification ID: 76D10
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76M99
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 3945655
zbMATH Keywords: moving boundaries
zbMATH Keywords: directed sheets
zbMATH Keywords: two-dimensional conservation laws
zbMATH Keywords: Cosserat surface
zbMATH Keywords: flow in a channel
zbMATH Keywords: time-dependent pressure gradient
zbMATH Keywords: lubrication theory of flow
MaRDI profile type: Publication
cites work: Oscillatory flow through constricted or dilated channels and axisymmetric pipes
cites work: On the theory of water waves
cites work: Directed fluid sheets
cites work: Water Waves in a Nonhomogeneous Incompressible Fluid
cites work: Directed fluid sheets and gravity waves in compressible and incompressible fluids
cites work: On the effect of parallel and transverse stationary random surface roughness in hydrodynamics lubrication
cites work: On the effects of the Reynolds and Stokes surface roughnesses in a two-dimensional slider bearing
cites work: Hydrodynamic lubrication of rough surfaces
description: scientific article; zbMATH DE number 3945655