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1

Upper Bounds for the Complex Growth Rate of a Disturbance in Ferrothermohaline Convection

Ram Kaka, Prakash Jyoti, Kumari Kultaran, Kumar Pankaj

Studia Geotechnica et Mechanica

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2022

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Vol. 44, nr 2

114--122

EN

It is proved analytically that the complex growth rate σ= σr+iσi (σr and σi are the real and imaginary parts of σ, respectively) of an arbitrary oscillatory motion of neutral or growing amplitude in ferrothermohaline convection in a ferrofluid layer for the case of free boundaries is located inside a semicircle in the right half of the σrσi-plane, whose center is at the origin and (formula) where Rs is the concentration Rayleigh number, Pr′ is the solutal Prandtl number, M1′ is the ratio of magnetic flux due to concentration fluctuation to the gravitational force, and M5 is the ratio of concentration effect on magnetic field to pyromagnetic coefficient. Further, bounds for the case of rigid boundaries are also derived separately.

2

A revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layer

Alharbi Ozwah S., Abdullah Abdullah A.

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

488--499

EN

A revised model of the nanoparticle mass flux is introduced and used to study the thermal instability of the Rayleigh-Benard problem for a horizontal layer of nanofluid heated from below. The motion of nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. The nanofluid layer is confined between two rigid boundaries. Both boundaries are assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition. The material properties of the nanofluid are allowed to depend on the local volume fraction of nanoparticles and are modelled by non-constant constitutive expressions developed by Kanafer and Vafai based on experimental data. The results show that the profile of the nanoparticle volume fraction is of exponential type in the steady-state solution. The resulting equations of the problem constitute an eigenvalue problem which is solved using the Chebyshev tau method. The critical values of the thermal Rayleigh number are calculated for several values of the parameters of the problem. Moreover, the critical eigenvalues obtained were real-valued, which indicates that the mode of instability is via a stationary mode.

3

Wybrane zagadnienia stateczności liniowej konstrukcji prętowych

Pałkowski Szymon

Inżynieria i Budownictwo

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2020

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R. 76, nr 1-2

56--60

PL

Przedstawiono wybrane zagadnienia dotyczące stateczności liniowej konstrukcji prętowych. Wykazano, że w niektórych konstrukcjach (np. w ramach stężonych) rozwiązanie oparte na stateczności liniowej może prowadzić do błędnych wyników. Omówiono sposoby korekty błędnego rozwiązania oraz przedstawiono kilka poglądowych przykładów liczbowych.

EN

The article presents selected issues coneerning the linear stability of bar structures. It has been shown that in some structures (e.g. braced frames) the solution based on linear stability can lead to erroneous results. The paper discusses this problem, shows how to correct an incorrect solution and presents some numerical examples.

4

Study of magnetic field dependent viscosity on a soret driven ferrothermohaline convection in a rotating porous medium

Hemalatha R.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 1

61--77

EN

The effect of a magnetic field dependent viscosity on a Soret driven ferro thermohaline convection in a rotating porous medium has been investigated using the linear stability analysis. The normal mode technique is applied. A wide range of values of the Soret parameter, magnetization parameter, the magnetic field dependent viscosity, Taylor number and the permeability of porous medium have been considered. A Brinkman model is used. Both stationary and oscillatory instabilities have been obtained. It is found that the system stabilizes only through oscillatory mode of instability. It is found that the magnetization parameter and the permeability of the porous medium destabilize the system and the Soret parameter, the magnetic field dependent viscosity and the Taylor number tend to stabilize the system. The results are presented numerically and graphically.

5

Marangoni convection in a relatively hotter or cooler liquid layer with free boundaries

Gupta A. K., Shandil R. G.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 2

581--588

EN

In this paper, we study the onset of cellular convection in a horizontal fluid layer heated from below, with a free-slip boundary condition at the bottom when the driving mechanism is surface tension at the upper free surface, in the light of the modified analysis of Banerjee et al. (Jour. Math. & Phys. Sci., 1983, 17, 603). This leads to a formulation of the problem which depends upon whether the liquid layer is relatively hotter or cooler. It is found that the phenomenon of surface tension driven instability problems should not only depend upon the Marangoni number which is proportional to the maintained temperature differences across the layer but also upon another parameter that arises due to variation in the specific heat at constant volume on account of the variations in temperature. Numerical results are obtained for the problem wherein the lower free boundary is perfectly thermally conducting.

6

Boundary conditions effect on linearized mud-flow shallow model

Di Cristo C., Iervolino M., Vacca A.

Acta Geophysica

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2013

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Vol. 61, no. 3

649--667

EN

The occurrence of roll-waves in mud-flows is investigated based on the formulation of the marginal stability threshold of a linearized onedimensional viscoplastic (shear-thinning) flow model. Since for this kind of non-Newtonian rheological models this threshold may occur in a hypocritical flow, the downstream boundary condition may have a nonnegligible effect on the spatial growth/decay of the perturbation. The paper presents the solution of the 1D linearized flow of a Herschel and Bulkley fluid in a channel of finite length, in the neighbourhood of a hypocritical base uniform flow. Both linearly stable and unstable conditions are considered. The analytical solution is found applying the Laplace transform method and obtaining the first-order analytical expressions of the upstream and downstream channel response functions in the time domain. The effects of both the yield stress and the rheological law exponent are discussed, recovering as particular cases both power-law and Bingham fluids. The theoretical achievements may be used to extend semi-empirical criteria commonly employed for predicting roll waves occurrence in clear water even to mud-flows.

7

Stability analyses and experimental investigation of doubly corrugated steel arch panels

Walentyński R., Cybulski R.

Architecture Civil Engineering Environment

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2012

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Vol. 5, no. 4

79--92

EN

This paper describes briefly the stability analyses of doubly corrugated thin-walled steel panels which are used as a solution for arch buildings and roofing structures. As an example of such system the ABM MIC 120 prefabrication technology is chosen where factory on wheels makes cold-formed arch steel buildings or roofs in a very short time period as self-supporting panels. The main problem of such structures lies in the lack of proper theoretical model of the element due to its complex geometry. In order to understand the panel behavior, linear and non-linear stability analyses have been carried out with the use of ABAQUS software. The achieved results are compared with preliminary compression tests performed on steel samples. The main aim of this paper is to show how the complex geometry of such panel influences the magnitude of axial compression critical force.

PL

Artykuł zwięźle przedstawia analizę stateczności podwójnie giętych elementów cienkościennych, które są używane jako rozwiązanie dla budynków i przekryć dachowych. Przykładem takiego rozwiązania jest technologia prefabrykacji elementów cienkościennych zwana ABM MIC 120, gdzie mobilna fabryka produkuje w bardzo krótkim czasie zimno gięte samonośne panele do konstrukcji budynków stalowych o kształcie łuku lub łukowych przekryć dachowych. Główny problem tej technologii leży w braku odpowiedniego modelu teoretycznego tych paneli ze względu na ich złożoną geometrię. Aby zrozumieć zachowanie się paneli pod działaniem obciążeniem, liniowe i nieliniowe analizy stateczności zostały przeprowadzone w programie ABAQUS. Uzyskane wyniki porównano z wynikami otrzymanymi ze wstępnych badań laboratoryjnych przeprowadzonych na ściskanych próbkach paneli. Głównym celem tego artykułu jest pokazanie w jakim stopniu złożona geometria panelu wpływa na wielkość siły krytycznej.

8

Instability of viscous incompressible flow in a channel with transversely corrugated walls

Szumbarski J.

Journal of Theoretical and Applied Mechanics

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2007

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Vol. 45 nr 3

659-683

EN

Destabilization of the laminar flow in a channel with transversly wavy walls is investigated. The basic flow is determined by a semi-analytical method based on the concept of immersed boundaries. The stability equations are discretized by the spectrally accurate Chebyshev-tau method. It is demonstrated that the transversal wall waviness can be used in order to achieve destabilization of the laminar flow at low Reynolds numbers. Possible applications include the improvement of mixing and heat/mass transfer in various devices used in heat technology, biotechnology and medicine.

PL

Praca poświęcona jest zjawisku destabilizacji przepływu laminarnego w kanale wywołanej poprzecznym pofalowaniem ścian. Przepływ niezaburzony wyznaczono przy pomocy semi-analitycznej metody zanurzonych granic. Wyprowadzono równania stateczności, które następnie poddano dyskretyzacji przy użyciu wielomianów Czebyszewa. Pokazano, że poprzeczne pofalowanie ścian o odpowiedniej geometrii prowadzi do destabilizacji przepływu przy niskich liczbach Reynoldsa i omówiono własności pola zaburzeń. Wydaje się, że opisany efekt może mieć znaczenie dla intensyfikacji mieszania i poprawy efektywności procesów transportu w technice cieplnej, biotechnologii i medycynie.

9

The effect of rotation on thermosolutal convection in a ferromagnetic fluid

Sunil, Bharti P. K., Sharma D., Sharma R. C.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no 4

713-730

EN

The effcct of rotation on the thermosolutal convection in a ferromagnetic fluid is analyzed for a fluid layer heated and soluted from below in the presence of a uniform magnetic field. Using the linearized stability theory and the normal mode analysis, an exact solution is obtained for the case of two free boundaries. For the case of stationary convection, non-buoyancy magnetization has a destabilizing effect on the system, whereas the stable solute gradient and rotation have a stabilizing effect on the system for lower vaIues of buoyancy magnetization M 1 . The critical magnetic thermal Rayleigh number for the onset of instabiIity is also determined numerically for large vaIues of buoyancy magnetization M 1 and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid heated from below in the absence of a stabIe solute gradient and rotation. The oscillatory modes are introduced due to the presence of the stabIe solute gradient and rotation, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

10

Stability of stratified Walters' (Model B') viscoelastic fluid in stratified porous medium

Sunil D., Sharma R., Sharma V.

Studia Geotechnica et Mechanica

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2004

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Vol. 26, nr 1-2

35-52

PL

Przedstawiono liniową stabilność uwarstwionej cieczy Waltersa (model B') w uwarstwionym ośrodku porowatym. Rozważono przypadki zmian wykładniczych gęstości, lepkości, lepkosprężystości, porowatości i przepuszczalności środowiska. Stwierdzono, że w przypadku potencjalnie stabilnego uwarstwienia układ jest stabilny lub niestabilny w zależności od kinematycznej lepkosprężystości, która może osiągać wartość mniejszą lub większą od wartości otrzymanej przez podzielenie przepuszczalności środowiska przez jego porowatość. Stanowi to przeciwieństwo stabilności uwarstwionej cieczy Newtona. Jednakże układ jest niestabilny w przypadku zakłóceń wszystkich liczb falowych dla potencjalnie niestabilnego uwarstwienia. Jeżeli wprowadzi się pewne ograniczenia, to szybkość wzrostu zwiększa się lub zmniejsza wraz ze zwiększającymi się wartościami parametrów uwarstwienia. Oddzielnie omówiono wpływ zmiennego poziomego pola magnetycznego i jednorodnej rotacji. Szybkość wzrostu stabilności w zależności od prędkości Alfvena (w przypadku pola magnetycznego) oraz w zależności od prędkości kątowej (w przypadku rotacji) zbadano analitycznie i stwierdzono, że w pewnych warunkach zarówno pole magnetyczne, jak i rotacja mają sprzężony wpływ na stabilność.

EN

The linear stability of stratified Walters' (model B') fluid in stratified porous medium is presented. The case of exponentially varying density, viscosity, viscoelasticity, medium porosity and medium permeability is considered. It is found that for the potentially stable stratifications the system is stable or unstable, depending on the kinematic viscoelasticity which can be smaller or greater than the medium permeability divided by medium porosity. This is in contrast to the stability of stratified Newtonian fluid. However, the system is found to be unstable for disturbances of all wave numbers for potentially unstable stratifications. If some restrictions are imposed, then the growth rates are found to increase or decrease with increasing values of stratification parameters. The effects of variable horizontal magnetic field and uniform vertical rotation have also been discussed separately. The behaviour of growth rate with respect to the Alfven velocity (in the case of magnetic field) and angular velocity (in the case of rotation) are examined analytically and it is found that under certain conditions both magnetic field and rotation have a dual effect on this stability problem.

11

On origin of unstable modes in viscous channel flow subject to periodically distributed surface suction

Szumbarski J.

Journal of Theoretical and Applied Mechanics

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2002

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Vol. 40 nr 4

847-871

EN

The linear stability of a flow in a channel subject to periodically distributed suction applied at the wallsis investigated. The focus is on the relation between unstable modes observed in such a flow and the stability properties of the flow without suction (the Poiseuille flow). It is demonstrated that linearly unstable modes appearing in the presence of suction can be interpreted as modified Orr-Sommerfeld's or Squire's eigenmodes of the Poiseuille flow. Originally, these modes have the streamwise wave number equal to zero, i.e. they are invariant in the streamwise direction. When the surface suction is applied, the modes are additionally modulated along the channel and they become dependent on the streamwise variable. In the range of the parameters studied, a pair of such modes, one Orr-Sommerfeld's and one Squire's, can be simultaneously unstable. Certain properties of these modes are discussed in some details. Specifically, the influence of non-symmetric suction on stability characteristics is analysed.

PL

W pracy rozważa się zagadnienie liniowej stateczności przepływu cieczy w płaskim kanale, w obecności periodycznie rozłożonego odsysania/wypływu przez ściany. Celem analizy jest identyfikacja zaburzeń krytycznych i objaśnienia ich związku z rozwiązaniami własnymi zagadnienia stateczności dla przepływu Poiseuille'a. Stosując metodę kontynuacji wartości i rozwiązań własnych po parametrze wykazano, że obserwowane formy niestabilności to zmodyfikowane okresowo w kierunku przepływu poprzeczne, symatryczne mody Squire'a i Orra-Sommerfelda, którym odpowiadają czysto urojone wartości własne. Zbadano numerycznie wpływ parametrów odsysania/wypływu na własności tych modów.

12

The effect of heating/cooling on the upper-branch stability of boundary layer flows over a compliant boundary

Motsa S. S., Gajjar J. S., Sibanda P.

Computer Assisted Mechanics and Engineering Sciences

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2002

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Vol. 9, No. 2

163-181

EN

We investigate the evolution of Tollmien-Schlichting waves in boundary layers in the presence of moderate buoyancy arising from the heating or cooling of a compliant wall. We exploit the multi-deck structure of the flow in the limit of large Reynolds numbers to make an asymptotic analysis of the pertubed flow, along the upper-branch of the neutral stability curve, to derive linear neutral results. These results are discussed and are compared to rigid wall results. Also, a brief parametric study, based on the linear neutral results, is presented and the results are discussed.

13

Linear stability of a 1D flow in porous media under transversal disturbance with adsorption

Albers B.

Archives of Mechanics

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2002

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Vol. 54, nr 5-6

361-375

EN

In this paper we investigate the linear stability behavior of a flow within an adsorption/diffusion model for porous materials summarized in Section 2. We consider a 1D stationary flow through a poroelastic medium which is perturbed by transversal (2D) disturbances with mass exchange. The eigenvalue problem for the first step field equations is solved using a finite-difference scheme. We present the instability regions in dependence on the three most important model parameters, namely the bulk and surface permeability coefficients, and the mass density of the adsorbate on the inner surface.