Stokes Flow Before a Plane Boundary With Mixed Stick-Slip Boundary Conditions

N. Akhtar; G. A. H. Chowdhury; S. K. Sen

doi:10.3879/j.issn.1000-0887.2011.06.012

Volume 32 Issue 6

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N. Akhtar, G. A. H. Chowdhury, S. K. Sen. Stokes Flow Before a Plane Boundary With Mixed Stick-Slip Boundary Conditions[J]. Applied Mathematics and Mechanics, 2011, 32(6): 746-753. doi: 10.3879/j.issn.1000-0887.2011.06.012

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Stokes Flow Before a Plane Boundary With Mixed Stick-Slip Boundary Conditions

doi: 10.3879/j.issn.1000-0887.2011.06.012

1.
Department of Mathematics, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh;

Received Date: 2010-07-09
Rev Recd Date: 2011-04-11
Publish Date: 2011-06-15

Abstract

Abstract

A general theorem for Stokes flow about a plane boundary with mixed stick-slip boundary conditions was established.This was done by making use of a representation for the velocity and pressure fields in three-dimensional Stokes flow,in terms of a biharmonic function A and a harmonic function B. The earlier theorem on Stokes flow before a no-slip plane boundary was shown to be a special case of the present theorem.Furthermore,a corollary of the theorem was also derived which offers the solution to a problem of axisymmetric Stokes flow about a rigid plane with stick-slip boundary conditions,in terms of the Stokes stream function.The formulae for the drag and torque exerted by the fluid on the boundary were found.An illustrative example was given.
- Stokes flow,
- Stokes’s stream function,
- stick-slip boundary conditions,
- harmonic function,
- biharmonic function

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References(17)

References

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