Wyniki wyszukiwania - BazTech

1

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

|

2021

|

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.

2

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

|

2014

|

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.

3

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

|

2013

|

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.

4

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

Sunil D., Sharma R., Sharma V.

Studia Geotechnica et Mechanica

|

2004

|

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.

5

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

|

2002

|

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.