Hydromagnetic flow over a plane wall with uniform suction

Zusammenfassung Diese Abhandlung behandelt die Strömung einer inkompressiblen, zähen und elektrisch leitenden Flüssigkeit über eine ebene Wand mit homogener Absaugung und senkrechtem Magnetfeld. Eine exakte Lösung der hydromagnetischen Gleichungen kann erhalten werden, wenn die magnetische Druckzahl kleiner als eins ist.Aus den Rechnungen findet man, dass sowohl die Reibungsschubspannung als auch die Wärmeübertragung an der Wand unabhängig sind von der hydromagnetischen Wirkung, aber dass die Grenzschichtdicke zunimmt mit der Zunahme des hydromagnetischen Einflusses.Es sei bemerkt, dass keine stationäre Lösung erhalten wird für den Fall des Ausblasens.     

Spatial behaviour of solutions in the plane Stokes flow

Some new methods are described in the study of the spatial behaviour of solutions in the slow flow of an incompressible viscous fluid along a semi-infinite strip subject to zero velocity on the lateral sides, a prescribed time-dependent specified velocity on the end and zero initial conditions. These methods provide an improved estimated decay rate over those previously predicted on the subject.     

A note on plane Stokes flow past a shear free impermeable cylinder

Summary The slow steady two-dimensional motion of a viscous incompressible fluid in the unbounded region exterior to a shear free circular cylinder which is impermeable is examined. It is shown that the above problem requires a certain consistency condition for the existence of a solution. In addition, a circle theorem for the biharmonic equation is presented, for the above plane Stokes flow. Some examples are also given.     

Transient magneto-thermoviscoelastic plane waves in a non-homogeneous anisotropic thick strip subjected to a moving heat source

The aim of this paper is to study the transient wave propagations in a non-homogeneous anisotropic thermoviscoelastic thick strip placed in a constant primary magnetic field and subjected to a moving heat source. The governing equations for temperature and displacement fields are solved by means of a dual reciprocity boundary element method (DRBEM). In the case of plane deformation, a numerical scheme for the implementation of the method is presented and the numerical computations are carried out for the temperature, displacement components and thermal stress components. The validity of DRBEM is examined by considering a magneto-thermo-visco-elastic thick strip occupies a rectangular region and good agreement is obtained with existent results. The results obtained are presented graphically to show the effect of inhomogeneity on the displacement components and thermal stress components. Relevant results of previous investigations are deduced as special cases from this study.     

Stokes flow for the axisymmetric motion of several spherical particles perpendicular to a plane wall

The creeping flow around several spherical particles moving on a line perpendicular to a plane wall is calculated numerically using the boundary integral method. The locations of the point forces on the surfaces of the spheres are chosen so as to describe precisely the lubrication regions when the surfaces are close to one another. Earlier results are recovered for the cases of a single sphere and a wall and of two equal spheres far from a wall. New results are presented for two (equal or unequal) spheres close to a plane wall and several equal spheres far from a wall.     

Accurate solutions for steady plane flow in the driven cavity. I. Stokes flow

The problem considered here is the steady, incompressible plane Stokes flow in a rectangular cavity generated by uniform translation of the upper wall. An exact analytical solution of the governing biharmonic equation is derived which not only contains the leading term of the required singularities at the upper corners, but also approximately satisfies the boundary conditions at all four walls. A standard numerical algorithm is employed to correct the small deviations in the boundary conditions satisfied by the analytical solution. This technique enables accurate computation of the solution uniformly throughout the domain; in particular, near the singular corners and in those regions where the flow is extremely weak, for example, in the secondary vortex regions of the deep cavity. The method is illustrated for the square cavity and also for a deep cavity with a depth-to-width ratio of five, and the results are compared with previous analytical and numerical solutions.     

A benchmark solution for 2D Stokes flow over cavity

Two-dimensional Stokes flow in a half plane with coupled cavity having the form of semi-ellipse is considered. The exact solution for the boundary problem is obtained. The solution can be a benchmark for numerical approaches. An example of the benchmarking is given.     

On the thermal-creep flow of a binary gas mixture over a plane wall with imperfect accommodation

The thermal-creep flow of a binary gas mixture over a plane wall is investigated analytically on the basis of the linearized Boltzmann equation of BGK type under the boundary condition of Maxwell's type or diffuse-specular reflection type. By an accurate analysis of the Knudsen layer formed near the wall, the Knudsen-layer structure of the velocity field has been clarified and, hence, the velocity distribution over the whole flow region is given explicitly together with the macroscopic slip coefficient. For future comparison with experimental data which may become available, the values of the slip coefficient of thermal-creep flow for several pairs of gases, Ne-Ar, He-Ne, He-Ar, N₂-Ar and N₂-O₂ are also given and listed in Table together with the values calculated based on the result given by other authors.     

Stokes flow past a two-dimensional lens

Summary Two problems involving uniform Stokes flow past a two-dimensional lens are considered in an attempt to determine those geometric characteristics which cause separation and theresultant formation of large Stokes eddies. Criteria are derived which identify lenses having this property. It is found that a necessary condition for separation is that the lens be convex-concave.

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Zusammenfassung Zwei Probleme werden untersucht, die die gleichförmige Stokes-Strömung über eine zweidimensionale Linse betreffen, als ein Versuch, die geometrischen Eigenschaften fetzustellen, die die Ablösung und die resultierende Formation von grossen Stokes-Wirbeln verursachen. Kriterien werden abgeleitet, welche Linsen, die diese Chharakteristik haben, identifizieren. Es zeigte sich, dass die konvex-konkave Form der Linse eine notwendige Bedingung ist.

     

On nonlinear plane vibration of a moving threadline

We consider plane vibrations of a moving threadline described by the model equations obtained in [1]. We study the propagation of weak discontinuities and their interaction with shock waves. We show that the only possible shocks satisfying the Lax conditions [3] and the evolutionary condition of Brun [9] are the characteristic shocks.

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Riassunto Vengono considerate le vibrazioni piane di un filo flessibile descritte dalle equazioni ottenute in [1], Viene studiata la propagazione di onde di discontinuita' e la loro interazione con un'onda d'urto. Viene anche mostrato che gli unici urti possibili che soddisfano le condizioni di Lax [3] e la condizione di evoluzione di Brun [9] sono gli urti caratteristici.

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This work was supported by C.N.R. through G.N.F.M. and by M.P.I, through Fondi del 40% e 60% per la Ricerca Scientifica.     

Smooth interface in a two-component Stokes flow

The problem considered is that of evolution of the free boundary Γ(t) separating two immiscible viscous fluids with different constant densities and viscosities. The motion is described by the Stokes equations driven by the gravity force. We prove the existence of classical solutions for small timet and establish that the free boundary Γ(t)∈C ^l+2 (l>0 is an arbitrary non-integer number)     

Stagnation point flow and heat transfer over a non-linearly moving flat plate in a parallel free stream with slip

An analysis is presented for the steady boundary layer flow and heat transfer of a viscous and incompressible fluid in the stagnation point towards a non-linearly moving flat plate in a parallel free stream with a partial slip velocity. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation, which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. Dual (upper and lower branch) solutions are found to exist for certain parameters. Particular attention is given to deriving numerical results for the critical/turning points which determine the range of existence of the dual solutions. A stability analysis has been also performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically possible.     

Stokes flow past a slightly deformed fluid sphere

Summary The Stokes flow past a fluid spheroid whose shape deviates slightly from that of a sphere, is examined. To the first order in the small parameter characterizing the deformation, an exact solution is obtained. As an application, the case of a fluid oblate spheroid is considered and the drag experienced by it is evaluated. Special well-known cases are then deduced.

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Zusammenfassung Die Stokes-Strömung um einen Flüssigkeitstropfen, der nur leicht von einer perfekten Kugel abweicht, wird untersucht. Eine Lösung wird gefunden, die exakt ist bis zur ersten Ordnung im Deformations-Parameter. Als Beispiel wird der Strömungswiderstand eines abgeplatteten Flüssigkeits-Sphäroids berechnet. Die Methode liefert für bekannte Spezialfälle korrekte Lösungen.

     

Stokes flow with slip and Kuwabara boundary conditions

The forces experienced by randomly and homogeneously distributed parallel circular cylinder or spheres in uniform viscous flow are investigated with slip boundary condition under Stokes approximation using particle-in-cell model technique and the result compared with the no-slip case. The corresponding problem of streaming flow past spheroidal particles departing but little in shape from a sphere is also investigated. The explicit expression for the stream function is obtained to the first order in the small parameter characterizing the deformation. As a particular case of this we considered an oblate spheroid and evaluate the drag on it.     

Dual solutions of boundary layer flow over an upstream moving plate

The homotopy analysis method is applied to study the boundary layer flow over a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream. The dual solutions in series expressions are obtained with the proposed technique, which agree well with numerical results. Note that, by introducing a new auxiliary function β(z), the bifurcation of the solutions is obtained. This indicates that the homtopy analysis method is a open system, in the framework of this technique, we have great freedom to choose the auxiliary parameters or functions. As a result, complicated nonlinear problems may be resolved in a simple way. The present work shows that the homotopy analysis method is an effective tool for solving nonlinear problems with multiple solutions.