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Variational Method of Finding Streamlines in Ring Cascades for Creeping Flows

100%

Tesch K. , Banaszek M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2011

tom Vol. 15, No 1

71-84

This paper presents a new analytical method of finding streamlines for creeping flows in a ring cascade composed of an infinite number of infinitely thin blades. An analytical solution was obtained by minimizing the dissipation functional by means of the variational calculus. The necessary condition for the optimum of the functional yields the Stokes equation after certain additional assumptions are introduced. We considered different variants of fixing of the inlet and outlet of the cascade.

Slow motion of a rotating circular cylinder through a micropolar fluid

100%

Moosaie A. , Atefi G.

Archives of Mechanics

2008

tom Vol. 60, nr 3

199-220

Presented is an analytical solution to creeping flow of a micropolar fluid past a rotating circular cylinder of infinite length in spanwise direction. The solution is decomposed into two parts; first, the flow past a stationary circular cylinder is solved by the use of matched asymptotic expansions method. Afterwards, the rotation of a circular cylinder in a stationary ocean of a micropolar fluid is investigated. Due to linearity of the governing equations, the principle of superposition is then recalled to construct the desired flow field. Ultimately, several kinematic and kinetic quantities of the flow are studied by the use of the obtained closed-form analytical solution.

On Plane, Steady, Creeping Flow, Generated Around an Arbitrary Cylinder by a Translating Flat Plate

75%

Klonowska-Prosnak M. E. , Prosnak W. J. , Cześnik P.

2003

tom Vol. 51, nr 2

113-144

Plane, steady, creeping flow around an arbitrary cylinder situated in vicinity of a flat plate is considered, the flow being generated by translation of this plate along itself with constant speed, perpendicular to generatrices. The stream function of the flow satisfies the biharmonic equation, so that all properties of the flow - such as velocity and pressure fields as well as fields of other stress tensor components - are expressed in terms of the Goursat functions. Hence, the problem of determination of the flow reduces to determination of these functions. The two-step approach is applied to the solution of this problem. The first step consists in conformal mapping of the original domain of solution onto an annulus - by means of a suitable set of mapping functions. The second step consists in development of the two Goursat functions in Laurent series extended by two logarithmic terms each. Unknown coefficients of the series have to satisfy a system of linear algebraic equations, following from boundary conditions. The system is arrived at by means of the pseudospectral method. The so obtained velocity field is applied to generation of streamline patterns. Such a pattern is presented in the paper, and compared with an analogous one, corresponding to potential flow.

Remarks on Plane, Steady, Creeping Flows Generated by Singularities

75%

Klonowska-Prosnak M. E. , Cześnik P.

2002

tom Vol. 50, Nr 1

45--69

Two properties of plane, steady, creeping flow generated in the infinite domain around a given contour by a single singularity are investigated in the paper. The first property concerns velocity field. It is shown, that stream uniform at infinity must occur automatically in this case, and formulae for velocity of the stream are derived. The second property concerns similarity of streamline pattern of such flow, and the potential one, generated around the same contour by the same singularity. Investigation of the both properties concerns - in particular: a disc, an ellipse and the airfoil sections NACA 0012, RAE 2822.

An analytical study of couple stress fluid through a sphere with an influence of the magnetic field

63%

Krishna Prasad M. , Sarkar P.

Journal of Applied Mathematics and Computational Mechanics

2022

tom Vol. 21, nr 3

99--110

The present work concerns to study of the steady, axisymmetric slow flow of couple stress fluid through a rigid sphere in the transverse magnetic field. Boundary conditions on the sphere surface are the zero couple stress condition and tangential slip condition. The stream function, vorticity vector, and pressure term are obtained. The drag acting on the sphere in the presence of MHD is calculated. Here, we graphically represented the Hartmann number, couple stress, and slip parameters effect on the drag coefficient. Some well-known results of the drag are deduced.