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Triple-diffusive convection in Walters' (Model B') fluid with varying gravity field saturating a porous medium

Kango S. K., Rana G. C., Chand R.

Studia Geotechnica et Mechanica

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2013

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Vol. 35, nr 3

45--56

EN

The Triple-Diffusive convection in Walters’ (Model B') fluid with varying gravity field is considered in the presence of uniform vertical magnetic field in porous medium. For the case of stationary convection, the magnetic field, varying gravity field and the stable solute gradients have stabilizing effects whereas the medium permeability has destabilizing (or stabilizing) effect on the system under certain conditions. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset convection. The kinematic viscoelasticity has no effect on the stationary convection. The solute gradients, magnetic field, varying gravity field, porosity and kinematic viscoelasticity introduce oscillatory modes in the system, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained. The results are also shown graphically.

2

Thermal instability of Walters' (model B') elastico-viscous compressible fluid in the presence of Hall current

Kumar S., Gupta D., Jaswal R., Rana G. C.

Studia Geotechnica et Mechanica

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2011

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Vol. 33, nr 3

61-72

EN

The thermal instability of a compressible elastico-viscous fluid is examined for viscoelastic polymeric solutions in the presence of uniform vertical magnetic field to include the Hall-current. These solutions are known as Walters' (model B') fluids and their rheology is approximated by the Walters' (model B') constitutive relations, proposed by WALTERS [12]. It is found that the stability criterion is independent of the effects of viscosity and viscoelasticity and is dependent on the magnitude of the magnetic field and Hall current. The magnetic field is found to stabilize a certain wave number range of the unstable configuration. The Hall current has destabilizing and stabilizing effects on the system.

3

Effect of Hall currents on thermal instability of compressible dusty viscoelastic fluid in porous medium

Kumar P.

Studia Geotechnica et Mechanica

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2011

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Vol. 33, nr 4

25-38

EN

The thermal instability of compressible Walters B' viscoelastic fluid in porous medium is considered to include the effects of Hall currents and suspended particles. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For the case of stationary convection, Hall currents and suspended particles are found to have destabilizing effects whereas compressibility and magnetic field have stabilizing effects on the system. The medium permeability, however, has stabilizing and destabilizing effects on thermal instability in contrast to its destabilizing effect in the absence of magnetic field. The magnetic field, Hall currents and viscoelasticity parameter are found to introduce oscillatory modes in the system.

4

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.