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1

Effect of compressibility and suspended particles on thermal convection in a Walters' B' elastico-viscous fluid in hydromagnetics

Sharma R. C., Aggarwal A. K.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 2

391-399

EN

A layer of a compressible, electrically conducting Walters' B' elastico-viscous fluid permeated with suspended particles heated from below in the presence of a magnetic field is considered. For the case of stationary convection, the Walters'(model B') elastico-viscous fluid behaves like a Newtonian fluid and the compressibility, magnetic field are found to have stabilizing effects, whereas the suspended particles have a destabilizing effect on the thermal convection. The presence of each - viscoelasticity, magnetic field and suspended particles introduces oscillatory modes in the system which were non-existent in their absence.

2

Thermosolutal instability of compressible Rivlin-Ericksen fluid with Hall currents

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

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no 2

329-343

EN

The thermosolutal instability of a compressible Rivlin-Ericksen viscoelastic fluid is predicted for a layer heated and soluted from below in the presence of the vertical magnetic field to include the effect of Hall currents. For the case of stationary convection, the Rivlin-Ericksen elastico-viscous fluid behaves like a Newtonian viscous fluid. The Hall currents found to hasten the onset of thermosolutal instability whereas the compressibility, stable solute gradient and magnetic field postpone the onset of thermosolutal instability. Also, the dispersion relation is analyzed numerically and results are depicted graphically. The stable solute gradient and magnetic field (and corresponding Hall currents) introduce oscillatory modes in the system, which were nonexistent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

3

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.

4

Thermosolutal convection in ferromagnetic fluid

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

Archives of Mechanics

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2004

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Vol. 56, nr 2

117-135

EN

The thermosolutal convection in ferromagnetic fluid is considered for a fluid layer heated and soluted from below in the presence of uniform vertical magnetic field. For the case of two free boundaries, an exact solution is obtained using a linear stability analysis. For the case of stationary convection, magnetization has a destabilizing effect, whereas stable solute gradient has a stabilizing effect on the onset of instability. Graphs have been plotted by giving numerical values to various parameters, to depict the stability characteristics. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid heated from below in porous medium in the absence of stable solute gradient. The oscillatory modes are introduced due to the presence of the stable solute gradient, which were non-existent in its absence. A sufficient condition for non-existence of the overstability is also obtained.

5

Kelvin-Helmholtz instability of Walters' (model B') viscoelastic fluid in porous medium in hydromagnetics

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

Studia Geotechnica et Mechanica

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2003

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Vol. 25, nr 3-4

53--63

EN

The instability of streaming Walters' B' viscoelastic fluid in porous medium in the presence of magnetic field in the direction of streaming and also transverse with respect to the direction of streaming is considered. The case of two uniform streaming fluids separated by a horizontal boundary is studied. It is observed that for the special case where perturbations in the direction of streaming are ignored, the system is unstable for unstable configuration, i.e. heavier fluid overlying lighter fluid. However for potentially stable configuration, the system can be stable or unstable, depending on kinematic viscoelasticity which is smaller or greater than the medium permeability divided by medium porosity. In every other direction, a minimum value of wave number has been found and the system is unstable for all wave numbers greater than this minimum wave number. It is also found that the development of the Kelvin-Helmholtz instability in the direction of streaming remains uninfluenced by the presence of magnetic field in the transverse direction.

PL

W polu magnetycznym badano niestateczność przepływu lepkosprężystej cieczy B' Waltersa w ośrodku porowatym w kierunku przepływu, a także w kierunku do niego poprzecznym. Rozważano przypadek dwóch jednorodnych cieczy, które oddziela pozioma granica. Zaobserwowano, że w szczególnym przypadku, gdy zakłócenia w kierunku przepływu zostaną pominięte, układ jest niestateczny w niestatecznej konfiguracji, co oznacza, że cięższa ciecz nakłada się na lżejszą. Jednakże dla potencjalnie statecznej konfiguracji układ może być stateczny lub niestateczny w zależności od tego, czy kinematyczna lepkosprężystość jest większa, czy mniejsza niż przepuszczalność ośrodka podzielona przez jego porowatość. Dla każdego innego kierunku określa się minimalną liczbę falową i układ jest niestateczny, jeśli wszystkie liczby falowe są od niej większe. Ustalono też, że rozwijanie się niestateczności Kelvina-Helmholtza w poprzecznym kierunku nie podlega wpływowi pola magnetycznego.

6

Stability of superposed couple-stress fluids in the presence of suspended particles in porous medium

Sunil, Sharma R. C., Chandel Rajender Singh

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 4

693-704

EN

The stability of two superposed couple-stress fluids of uniform densities, permeated with suspended particles, in a porous medium is considered. A stability analysis is carried out and for mathematical simplicity we consider two highly viscous fluids of equal kinematic viscosities and equal couple-stress kinematic viscosities. The system is found to be stable for a potentially stable configuration under certain condition whereas a potentially unstable configuration remains unstable for the couple-stress fluid permeated with suspended particles in a porous medium. The growth rates of perturbation are found to be both increasing (for some wave numbers) and decreasing (for other wave numbers) with the increase in medium permeability.

7

On Bénard convection in a porous medium in the presence of throughflow and rotation in hydromagnetics

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

Archives of Mechanics

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2003

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Vol. 55, nr 3

257-274

EN

The effect of throughflow on a layer of a rotating fluid heated from below in porous medium in the presence of vertical magnetic field is considered. For the case of stationary convection, the rotation has always a stabilizing effect. The medium permeability has always a destabilizing effect whereas the magnetic field and the throughflow have always a stabilizing effects in the absence of rotation. But in the presence of rotation, the medium permeability is found to have a destabilizing effect whereas the magnetic field and the throughflow have a stabilizing effects under certain conditions. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. The magnetic field and rotation introduce oscillatory modes in the system, which were nonexistent in their absence. The sufficient conditions for non-existence of the overstability are also obtained.

8

Rayleigh-Taylor instability of Walters' B' elastico-viscous fluid trough porous medium

Sharma R. C., Kumar P., Sharma S.

International Journal of Applied Mechanics and Engineering

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2002

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Vol. 7, no 2

433-444

EN

Rayleigh-Taylor instability of Walters' B' elastico-viscous fluid through a porous medium is considered. For the stable configuration, the system is found to be stable or unstable if the kinematic viscoelasticity (assumed equal for both fluids) is less than or greater than the medium permeability divided by the medium porosity. However, the system is found to be unstable for the potentially unstable configuration. The effects of a uniform horizontal magnetic field and a uniform rotation on the problem are considered separately.

9

On couple-stress fluid permeated with suspended particles heated from below

Sharma R. C., Sunil, Sharma Y. D., Chandel R. S.

Archives of Mechanics

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2002

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Vol. 54, nr 4

287-298

EN

A layer of a couple-stress fluid heated from below and permeated with suspended particles is considered. For the case of stationary convection, the couple-stress has a stabilizing effect whereas suspended particles have a destabilizing effect on the couple-stress fluid permeated with suspended particles, heated from below. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. The principle of exchange of stabilities is found to hold true for the couple-stress fluid in the presence of suspended particles, heated from below.

10

On superposed couple-stress fluids in a porous medium

Sharma R. C., Sunil, Pal M.

Studia Geotechnica et Mechanica

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2001

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Vol. 23, nr 3-4

55--66

EN

The Rayleigh-Taylor instability of two superposed couple-stress fluids of uniform densities through porous medium is studied. The stability analysis is carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities and couple-stress kinematic viscosities. The system is found to be stable for stable configuration and unstable for unstable configuration. The growth rates are found to be both increasing and decreasing with the increase in medium permeability.

PL

W porowatym środowisku badano niestateczność Rayleigha-Taylora dwóch nakładających się, sprężonych naprężeniem płynów o jednorodnych gęstościach. Ze względu na prostotę matematyczną, analizę stateczności przeprowadzono dla dwóch mocno lepkich płynów o jednakowych lepkościach kinematycznych i o sprzężonych naprężeniem lepkościach kinematycznych. Okazało się, że układ jest stabilny dla statecznej konfiguracji, a niestabilny dla niestatecznej konfiguracji. Szybkości wzrostu zarówno rosną, jak i maleją ze zwiększeniem przepuszczalności środowiska.

11

On electrically conducting couple-stress fluid heated from below in porous medium in presence of uniform horizontal magnetic field

Sharma R. C., Sharma S.

International Journal of Applied Mechanics and Engineering

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2001

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Vol. 6, no 2

251-263

EN

A layer of electrically conducting couple-stress fluid heated from below in porous medium is considered in the presence of uniform horizontal magnetic field. The medium permeability hastens the onset of convection whereas the magnetic field and couple-stress postpone the onset of convection, for the case of stationary convection. The oscillatory modes are introduced by the magnetic field which were not present in the absence of the magnetic field. The overstable case has been considered and a sufficient condition for the non-existence of overstability is obtained.

12

Hall effect on thermosolutal instability of Walters' (model B') fluid in porous medium

Sunil, Sharma R. C., Pal M.

Archives of Mechanics

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2001

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Vol. 53, nr 6

677-690

EN

The thermosolutal instability of Walters' (model B') fluid in porous medium is considered in the presence of uniform vertical magnetic field to include the effect of Hall currents. For the case of stationary convection, the stable solute gradient and magnetic field have stabilizing effects on the system, whereas the Hall currents have destabilizing effect on the system. The medium permeability has both stabilizing and destabilizing effects on the system depending on the Hall parameter M. The kinematic viscoelasticity has no effect for stationary convection. The kinematic viscoelasticity, stable solute gradient and magnetic field (and the corresponding Hall currents) 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.

13

Thermosolutal convection in Walter's (model B') fluid in porous medium in hydromagnetics.

Sunil D., Sharma R.C., Chand S.

Studia Geotechnica et Mechanica

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2000

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Vol. 22, nr 3-4

3-14

EN

The thermosolutal convection in Walters" (Model B') fluid in porous medium is considered in the presence of uniform vertical magnetic field. For the case of stationary convection, that solute gradient and magnetic field have stabilizing effects on the system, whereas the medium permeability has destabilizing effect on the systems. The kinematic viscoelasticity has no effect on stationary convection. The kinematic viscoelasticity, stable solute gradient and magnetic field introduce oscillatory modes into the system, which are non-existent in their absence. The sufficient conditions for the avoidance of over stability are also obtained.

PL

Opisano konwekcję substancji rozpuszczonych termicznie w płynie Waltera (model B') w ośrodku porowatym w obecności jednorodnego, pionowego pola magnetycznego. W przypadku ustalonej konwekcji stały gradient substancji rozpuszczonej i pole magnetyczne stabilizują układ, podczas gdy przepuszczalność ośrodka go destabilizuje. Lepkosprężystość kinematyczna nie ma wpływu na ustaloną konwekcję. Kinematyczna lepkosprężystość, ustalony gradient substancji rozpuszczonej i pole magnetyczne wprowadzają do układu oscylacyjne fale elektromagnetyczne, których w przeciwnym razie brak. Otrzymano także warunki, które wystarczają, aby uniknąć nadmiernej stabilności.

14

On couple-stress fluid heated from below in porous medium in the presence of rotation

Sharma R. C., Sunil, Pal M.

Applied Mechanics and Engineering

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2000

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Vol. 5, no 4

883-896

EN

A layer of a couple-stress fluid heated from below in a porous medium is considered to include the effect of uniform rotation. For the case of stationary convection, the couple stress may hasten the onset of convection in the presence of rotation while in the absence of rotation, it always postpones the onset of convection. For the case of stationary convection, rotation postpones the onset of convection. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. Rotation is found to introduce oscillatory modes in the system, which were non-existent in its absence. A sufficient condition for the non-existence of overstability is obtained.

15

Hall effect on thermal instability of Rivlin-Ericksen fluid in porous medium

Sharma R. C., Thakur K. D.

Applied Mechanics and Engineering

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2000

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Vol. 5, no 2

355-366

EN

The thermal instability of electrically conducting Rivlin-Ericksen elastico-viscous fluid in porous medium is considered to include the Hall current in the presence of a vertical magnetic field. For the stationary convection, the Rivlin-Ericksen elastico-viscous fluid behaves like a viscous (Newtonian) fluid. The Hall current and medium permeability are found to have destabilizing effect, whereas the magnetic field has a stabilizing effect on the thermal instability problem for stationary convection. A sufficient condition for the non-existence of overstability is obtained.

16

Thermal convection in Walters' viscoelastic fluid B' permeated with suspensed particles through porous medium

Sharma R.C.

Studia Geotechnica et Mechanica

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1999

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Vol. 21, nr 1-2

3--14

EN

The thermal convection in Walters' (model B') fluid permeated with suspended particles through porous medium is considered. For the case of stationary convection, the medium permeability and suspended particles have destabilizing effects on the system. The kinematic viscoelasticity has no effect on stationary convection. Also, the dispersion relation is analyzed numerically. The kinematic viscoelasticity is found to introduce oscillatory modes in the system which were non-existent in its absence. The sufficient conditions for the non-existence of overstability are also obtained.

PL

Przedstawiono konwekcję cieplną w płynie Waltersa (model B') przenikającym razem z zawiesiną przez ośrodek porowaty. W przypadku konwekcji ustalonej przepuszczalność ośrodka i zawiesina destabilizują układ. Lepkosprężystość kinematyczna nie wpływa na ustaloną konwekcję. Zanalizowano też numerycznie dyspersję. Stwierdzono, że kinematyczna lepko sprężystość powoduje oscylacyjne zachowania układu, których brak, gdy jej nie ma. Podano warunki wystarczające, aby nie istniała nadmierna stateczność.

17

Stability of two superposed Walters? B'viscoelastic fluids in the presence of suspended particles and variable magnetic field in porous medium

Sharma R. C., Kango S. K.

Applied Mechanics and Engineering

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1999

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Vol. 4, no 2

255-269

EN

The instability of plane interface between two superposed Walters' B' elastico-viscous fluids in porous medium has been studied to include the effects of suspended (dust) particles. It is found that the system is stable or unstable if the kinematic viscoelasticity (assumed equal for both fluids) is less than or greater than the medium permeability divided by medium porosity, for the potentially stable arrangement whereas the system is unstable for the potentially unstable arrangement. This problem has also been studied for electrically conducting Walters' fluid in the presence of a variable horizontal magnetic field. For a potentially stable case, the results are the same as in a hydrodynamic case. However, for a potentially unstable case, the magnetic field has got stabilizing effect and completely stabilizes certain wave-number band if kinematic viscoelasticity is less than the medium permeability divided by medium porosity.

18

Thermosolutal convection in Rivlin-Ericksen fluid in porous medium in hydromagnetics

Sharma R. C., Sunil, Chand S.

Applied Mechanics and Engineering

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1998

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Vol. 3, no 1

171-180

EN

The thermosolutal convection in Rivlin-Ericksen fluid in porous medium is considered in the presence of uniform vertical magnetic field. For the case of stationary convection, the stable solute gradient and magnetic field have stabilizing effects on the system, whereas, the medium permeability has destabilizing effect on the system. The kinematic viscoelasticity has no effect on stationary convection. The stable solute gradient and magnetic field 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.