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1

Asymptotic solution for laminar isothermic flow of compressible fluid between rotating surfaces of revolution

Walicka A.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 4

1101-1118

EN

A steady laminar flow of a compressible newtonian fluid is considered, in a narrow space between two surfaces of revolution, rotating with generally different angular velocities about a common axis of symmetry. The problem statement for two classes of throughflow, with full and rotational inertia, is formulated. A procedure for perturbing a creeping flow solution and an iteration scheme are developed to produce a solution for higher approximations. The solution depends on seven parameters and is asymptotic in the sense of its good convergence in the second approximation for both classes of throughflow. Results for the second class of throughflow are presented for the velocity components, the pressure and temperature distributions for typical shapes of surfaces such as disks and spherical surfaces.

2

Asymptotic solution for laminar flow of an incompressible fluid with variable viscosity and thermal conductivity between rotating surfaces of revolution

Walicka A.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 3

831-848

EN

A steady laminar flow of an incompressible Newtonian fluid with variable viscosity and thermal conductivity is considered, in a narrow space between two surfaces of revolution, rotating with generally different angular velocities about a common axis of symmetry. The problem statement for two classes of throughflow, with full and rotational inertia, is fonnulated. A procedure for perturbing a creeping flow solution and an iteration scheme are developed to produce a solution for higher approximations. The solution depends on eight or seven parameters and is asymptotic in the sense of its good convergence in the second approximation for both classes of throughflow. Results for second class of throughflow are presented for the velocity components, the pressure and the temperature distributions for typical shapes of surfaces as disks and spherical surfaces.

3

Flow of a viscoelastic fluid of Rivlin-Ericksen between rotating surfaces of revolution

Walicka A.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no spec.

179-186

EN

A theoretical aspect of a flow of a viscoelastic fluid of Rivlin-Ericksen in a gap between two surfaces of revolution is considered. The effect of centrifugal (rotational) inertia forces on the flow field is examined. The examples of flows in the gap between two disks and two concentric spheres arediscussed. The obtained results show that the fluid inertia forces have significant effects on the velocities and pressure distributions.

4

Inertia effects in the flow of a micropolar fluid in a slot between rotating surfaces of revolution

Walicka A.

International Journal of Applied Mechanics and Engineering

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2001

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Vol. 6, no 3

731-790

EN

At present there exist several approaches to the formulation of fluids that contain structures. These fluids have various names such as simple microfluids, micropolar fluids, deformable directed fluids, polar fluids, anisotropic fluids, etc. In this paper the steady laminar flow of micropolar fluid in a slot between rotating surfaces of revolution, having a common axis of symmetry, is considered. To solve this problem the boundary layer equations for micropolar fluid are used and expressed for the axially symmetric case in the intrinsic curvilinear orthogonal coordinate system _ . The method of small parameter is used to solve the boundary layer equations. As a result one obtains the formulae for the velocity field and pressure. The solution to the equations of motion have been illustrated by plots of velocity components _ microrotation _ and pressure p.

5

Surface patches modelling and computation of geometric properties

Velichova D.

Zeszyty Naukowe. Geometria i Grafika Inżynierska / Politechnika Śląska

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2000

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z. 3

23-31

EN

Some of the problems in the classical geometric theories can be successfully solved using Computer Graphics procedures and representations of geometric figures. Geometry of the Creative space offers a new approach to several problems (in [3], [5], [6]), based on the creative representations of geometric figures. Classical way of a geometric figure definition as a subset of the three dimensional extended Euclidean space [infinity]E[3] determined by the equation can be substituted by a creative law of the figure represented in the form of a creative representation, from which the point function determining the figure analytically can be expressed. The intrinsic geometric properties of the created figure can be calculated with respect to the Differential Geometry on the base of the partial derivatives of its related point function.

PL

Autorka przedstawia jeden z możliwych sposobów tworzenia płatów różnego rodzaju powierzchni za pomocą metod grafiki komputerowej. Na podstawie znajomości zasad tworzenia płatów w przestrzeni wirtualnej można określić ich formę analityczną w postaci funkcji opisanej za pomocą współrzędnych jednorodnych punktu, który leżąc na powierzchni jest zdefiniowany przez parę współrzędnych krzywoliniowych. Pochodne funkcji określającej płat względem obydwu zmiennych definiują wektory stycznych jedno-parametrowych łuków krzywych powierzchni, płaszczyznę styczności i wektor normalny. W pracy szczegółowo omówiono niektóre rodzaje powierzchni powstałych z translacji, obrotu, ruchu śrubowego i homotetii krzywych. Rozważania zilustrowano przykładami powierzchni utworzonych z prostoliniowego przesunięcia hipocykloidy Steinera i sinusoidalnej translacji lemniskaty Bernoulliego, obrotu spirali Archimedesa i asteroidy oraz ruchu śrubowego walcowego cissoidy, a także ruchu śrubowego stożkowego elipsy. Przedstawiono również przykład powierzchni generowanej przez związek homotetii krzywych podstawowych.

6

Flow of a Shvedov-Bingham fluid between surfaces of revolution with one porous wall

Walicki E., Walicka A., Makhaniok A.

Applied Mechanics and Engineering

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1999

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Vol. 4, no spec.

127-134

EN

The influence of the wall porosity on the pressure distribution of a Shvedov-Bingham fluid flowing in the clearance between two surfaces of revolution is considered. As a result one obtains the formulae expressing the pressure distribution. An example of a squeeze flow between parallel disks is discussed in detail.

7

Flow of a Vočadlo fluid in a slot between rotating surfaces of revolution

Walicki E., Walicka A.

Applied Mechanics and Engineering

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1998

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Vol. 3, no 2

339-358

EN

This paper contains formulae which define such parameters of the steady laminar flow of a Vočadlo fluid between rotating surfaces of revolution as the velocity components 'TETA'x, 'TETA'teta, 'TETA'y and pressure p. The quasi-linearized equations of motion of the Vočadlo fluid flow for axial symmetry in the intrinsic curvilinear coordinate system x, 'teta', y are used. The obtained solutions to the equations of motion have been illustrated by an example of flow through the slot of constant thickness between rotating disks and between rotating spherical surfaces.