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1

Magneto convection in a layer of nanofluid with soret effect

Chand R., Rana G. C.

Acta Mechanica et Automatica

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2015

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Vol. 9, no. 2

63--69

EN

Double diffusive convection in a horizontal layer of nanofluid in the presence of uniform vertical magnetic field with Soret effect is investigated for more realistic boundary conditions. The flux of volume fraction of nanoparticles is taken to be zero on the isothermal boundaries. The normal mode method is used to find linear stability analysis for the fluid layer. Oscillatory convection is ruled out because of the absence of the two opposing buoyancy forces. Graphs have been plotted to find the effects of various parameters on the stationary convection and it is found that magnetic field, solutal Rayleigh number and nanofluid Lewis number stabilizes fluid layer, while Soret effect, Lewis number, modified diffusivity ratio and nanoparticle Rayleigh number destabilize the fluid layer.

2

Przybliżona metoda badania drgających układów mechanicznych i mechatronicznych jako wprowadzenie do ich syntezy w ujęciu grafów

Buchacz A.

Górnictwo Odkrywkowe

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2010

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R. 51, nr 3

110-113

PL

Celem pracy jest wyznaczenie podatności dynamicznej drgającej belki swobodnej metodą dokładną i przybliżoną Galerkina oraz odwzorowanie modelu belki w hipergraf w przypadku obu metod analizy. Takie ujęcie polega na wyznaczeniu różnic pomiędzy biegunami i przebiegami charakterystyk, otrzymanymi metodą dokładną i przybliżoną. Ponadto "redukcja" współrzędnych w przypadku wyznaczania ich charakterystyk metodą przybliżoną stała się asumptem do opisu jej za pomocą hipergrafu trójwierzchołkowego i tym samym może być wprowadzeniem do syntezy drgających układów belkowych o odcinkowo stałym przekroju.

EN

Purpose of this paper is determination of dynamicalflexibliity of vibrating beam by the exact and approximate methods attf creating the hypergraphs of the beam in case of two methods of analysis. Approach was to nominale the relevance or irrelevance between the characteristics obtained by considered methods - especially concerning the relevance of the natural frequencies-poles of characteristics of beam. Moreover the reduction of coordinates in case of determination their characterisv by means the approximate method stood occasion to description it for help three-vertex hypergraph and it can be an intrno tion to synthesis of vibrating beam-systems with constant cross sections and class ofj fexibly vibrating discrete-continuom mechatronic systems as well.

3

An analysis of the exterior Neumann problem for the Poisson equation in connection with a numerical procedure

Roliński Tomasz

Matematyka Stosowana : matematyka dla społeczeństwa

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1993

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Nr 36

3--17

EN

This paper is concerned with transforming the exterior problem Δu=f on Ωc, (∂u/∂n)|Γ=g, where ΩR2 is a bounded region and Ω^(c)=int(R2\Ω), into a problem represented by two equations. The first one is posed on a bounded domain and the second one is posed on the outer part of the boundary of the domain. This new problem is suitable for a numerical method based on coupling the finite and boundary element methods.

4

A method for solving the Neumann problem for the Poisson equation on the exterior of a poligon

Roliński Tomasz

Matematyka Stosowana : matematyka dla społeczeństwa

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1993

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Nr 36

19--40

EN

This paper is concerned with a numerical method for solving the problem Δu=f in Ωc (=intR2\Ω), (du/dn)|Γ=g, where ΩR2 is a polygon and Γ is the boundary of Ω. The method is based on coupling finite and boundary element techniques. To compensate for the loss of smoothness of the solution u near the corners of the polygon Ω we refine the triangulation without changing the number of triangles. We apply the affine triangular Lagrangean element of degree kN and the Lagrangean boundary element of degree k−1 to obtain the optimal order of convergence via the Galerkin projection.