Stokes flow due to fundamental singularities before a plane boundary

Aktar, Nazira; Rahman, Faiz; Sen, S. K.

doi:10.1007/bf02437572

Cited by 4 publications

(5 citation statements)

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“…The last two results are in agreement with the general formulae given by Akhtar et al [1] for the viscous flow bounded by a no-slip plane boundary. …”

Section: Corollary 31 For the Axisymmetric Stokes Flow About The Z-asupporting

confidence: 81%

“…A general solution to the Stokes equation (1) suggested by Akhtar et al [1] in terms of the cylindrical coordinates (ρ, φ, z) admits the representation aŝ…”

Section: Basic Theorymentioning

confidence: 99%

“…Then, following the method of Akhtar et al [1] , the corresponding expressions for the biharmonic function A 0 and the harmonic function B 0 are found to be…”

Section: Example Of Rotlet Along Plane Boundarymentioning

confidence: 99%

“…[1], a representation for the velocity and pressure fields in the Stokes flow was given and shown to be more general than that in Ref. [2].…”

Section: Introductionmentioning

confidence: 98%

“…Here, we use the representation in Ref. [1] to derive a general theorem that may solve the problem of three-dimensional slow viscous fluid motion before a plane boundary with the mixed stick-slip boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Stokes flow before plane boundary with mixed stick-slip boundary conditions

Akhtar

Chowdhury

Sen

2011

Appl. Math. Mech.-Engl. Ed.

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A general theorem for the Stokes flow over a plane boundary with mixed stick-slip boundary conditions is established. This is done by using a representation for the velocity and pressure fields in the three-dimensional Stokes flow in terms of a biharmonic function and a harmonic function. The earlier theorem for the Stokes flow due to fundamental singularities before a no-slip plane boundary is shown to be a special case of the present theorem. Furthermore, in terms of the Stokes stream function, a corollary of the theorem is also derived, providing a solution to the problem of the axisymmetric Stokes flow along a rigid plane with stick-slip boundary conditions. The formulae for the drag and torque exerted by the fluid on the boundary are established. An illustrative example is given.

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“…The last two results are in agreement with the general formulae given by Akhtar et al [1] for the viscous flow bounded by a no-slip plane boundary. …”

Section: Corollary 31 For the Axisymmetric Stokes Flow About The Z-asupporting

confidence: 81%

“…A general solution to the Stokes equation (1) suggested by Akhtar et al [1] in terms of the cylindrical coordinates (ρ, φ, z) admits the representation aŝ…”

Section: Basic Theorymentioning

confidence: 99%

“…Then, following the method of Akhtar et al [1] , the corresponding expressions for the biharmonic function A 0 and the harmonic function B 0 are found to be…”

Section: Example Of Rotlet Along Plane Boundarymentioning

confidence: 99%

“…[1], a representation for the velocity and pressure fields in the Stokes flow was given and shown to be more general than that in Ref. [2].…”

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations