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1
Content available Triple diffusive convection of a non-Newtonian fluid under the combined effect of compressibility and variable gravity
Aggarwal A. K., Dixit D.
International Journal of Applied Mechanics and Engineering
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2019
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Vol. 24, no. 4
1--11
EN
In this paper, triple diffusive convection in a Rivlin-Ericksen fluid layer, which is permeated with suspended particles in the porous medium under the effect of compressibility and variable gravity, is investigated. Linear stability theory and normal mode analysis have been used to study the problem under consideration. It is observed that, for stationary convection, suspended particles, compressibility and medium permeability have destabilizing/stabilizing effects under certain conditions. The variable gravity parameter destabilizes the system whereas stable solute gradients have a stabilizing effect.
2
Content available Radiation absorption and chemical reaction effects on Rivlin-Ericksen flow past a vertical moving porous plate
Sravanthi C. S., Gorla R. S. R.
International Journal of Applied Mechanics and Engineering
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2019
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Vol. 24, no. 3
675--689
EN
An analysis has been carried out to study the combined effects of radiation absorption and chemical reaction on an incompressible, electrically conducting and radiating flow of a Rivlin-Ericksen fluid along a semi-infinite vertical permeable moving plate in the presence of a transverse applied magnetic field. It is assumed that the suction velocity, the temperature and the concentration at the wall are exponentially varying with time. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. A comparison is made with the available results in the literature for a special case and our results are in very good agreement with the known results. A parametric study of the physical parameters is made and results are presented through graphs and tables. The results indicate that the fluid velocity and temperature could be controlled by varying the radiation absorption.
3
Content available Effect of suspended particles on thermosolutal convection of Rivlin-Ericksen fluid in porous medium with variable gravity
Aggarwal A. K., Dixit D.
International Journal of Applied Mechanics and Engineering
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2018
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Vol. 23, no. 3
813--820
EN
The thermosolutal stability of a layer of the Rivlin-Ericksen fluid in a porous medium is considered under varying gravity conditions. It is found that for stationary convection, medium permeability and suspended particles have a destabilizing/stabilizing effect when gravity increases/decreases. The stable solute gradient has a stabilizing effect on the system.
4
Content available remote Thermal instability analysis of an elastico-viscous nanofluid layer
Chand R., Rana G. C., Puigjaner D.
Engineering Transactions
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2018
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Vol. 66, iss. 3
301--324
EN
The purpose of this paper is to study the thermal instability analysis of an elastico-viscous nanofluid layer heated from below. The Rivlin-Ericksen type fluid model is used to describe the rheological behavior of an elastico-viscous nanofluid. The linear stability criterion for the onset of both stationary and oscillatory convection is derived by applying the normal model analysis method. The presence of nanoparticles enhances the thermal conductivity of the fluid, and the model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The effect of the physical parameters of the system, namely the concentration Rayleigh number, Prandtl number, capacity ratio, Lewis number, and kinematic visco-elasticity coefficient, on the stability of the system is numerically investigated. In addition, sufficient conditions for the non-existence of oscillatory convection are reported.
5
Content available Stability of superposed fluids through magnetic field with suspended particles of different permeability saturated through porous layer
Singh M.
International Journal of Applied Mechanics and Engineering
|
2015
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Vol. 20, no. 4
889--898
EN
The instability of plane interface between two superposed Rivlin-Ericksen elastico-viscous fluids saturated through a porous medium has been studied to include the suspended (dust) particles effect. Following the linearized stability theory and normal mode analysis the dispersion relation is obtained. For stationary convection, the Rivlin-Ericksen elastico-viscous fluid behaves like Newtonian fluids. It found that for a potentially stable arrangement the Rivlin-Ericksen elastico-viscous fluid of different permeabilities in the presence of suspended particles in a porous medium is stable, whereas in a potentially unstable case instability of the system occurs. In the presence of a magnetic field for a potentially stable arrangement the system is always stable and for the potentially unstable arrangement, the magnetic field succeeds in stabilizing certain wave-number band which was unstable in the absence of the magnetic field.
6
Content available remote Thermosolutal convection in Rivlin-Ericksen fluid in the presence of Hall currents in a porous medium in hydromagnetics
Kango S. K., Singh V.
International Journal of Applied Mechanics and Engineering
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2012
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Vol. 17, no. 1
71-82
EN
The thermosolutal instability of a layer of a Rivlin-Ericksen elastico-viscous fluid is considered in the presence of a uniform horizontal magnetic field to include the Hall currents in a porous medium. For the case of stationary convection, the Hall currents hasten the onset of convection, the magnetic field postpones the onset of convection, medium permeability also postpones the onset of convection in the presence of the Hall currents, whereas the kinematic viscoelasticity has no effect on the onset of convection. The Hall currents, kinematic viscoelasticity, magnetic field, medium permeability and the solute parameter introduce oscillatory modes in the system, which were non-existent in their absence. The case of overstability is also considered wherein the sufficient conditions for the non-existence of overstability are obtained.
7
Content available remote A Characterization of the Rivlin-Ericksen Viscoelastic Fluid in the Presence of a Magnetic Field and Rotation
Banyal A. S.
Engineering Transactions
|
2012
|
Vol. 60, iss. 4
355-355
EN
A layer of Rivlin-Ericksen viscoelastic fluid heated from below is considered in the presence of an uniform vertical magnetic field and rotation. Following the linearized stability theory and normal mode analysis, this paper mathematically establishes the condition for characterizing oscillatory motion, which may be neutral or unstable, for rigid boundaries at the top and bottom of the fluid. It is established that all non-decaying slow motions starting from rest, in the configurations, are necessarily non-oscillatory in the regime TAF 2 + TA 4 + Qp2 2 1; where TA is the Taylor number, Q is the Chandrasekhar number, p2 is the magnetic Prandtl number, and F is the viscoelasticity parameter. This result is important, since it holds for all wave numbers for rigid boundaries of infinite horizontal extension at the top and bottom of the fluid, and the exact solutions of the problem investigated in closed form are not obtainable.
8
Content available remote 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.
9
Content available remote Stability of superposed viscous-viscoelastic (Rivlin-Ericksen) fluids through porous medium
Kumar P., Mohan H., Singh G.
Studia Geotechnica et Mechanica
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2004
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Vol. 26, nr 1-2
53-61
PL
Badano niestabilność typu Rayleigha-Taylora cieczy Newtona nakładającej się na lepkosprężystą ciecz Rivlina-Ericksena w ośrodku porowatym. Ponieważ zarówno w lepkiej cieczy Newtona, jak i w lepkiej cieczy układ jest stabilny w potencjalnie stabilnym przypadku, a niestabilny w potencjalnie niestabilnym przypadku, wniosek ten odnosi się też do badanego przez nas problemu. Rozważono oddzielnie wpływ jednorodnego poziomego pola magnetycznego i wpływ jednorodnej rotacji na niestabilność. Pole magnetyczne stabilizuje pewne pasmo liczby falowej, podczas gdy układ jest niestabilny dla wszystkich liczb falowych, gdy brak pola magnetycznego dla potencjalnie niestabilnej konfiguracji. Układ jest jednak stabilny w potencjalnie stabilnym przypadku, a niestabilny w potencjalnie niestabilnym przypadku dla bardzo lepkich cieczy poddanych jednostajnej rotacji.
EN
The Rayleigh-Taylor instability of a Newtonian viscous fluid overlying a Rivlin-Ericksen viscoelastic fluid through porous medium is considered. As in both Newtonian viscous-viscous fluids, the system is stable in the potentially stable case and unstable in the potentially unstable case, this holds for the present problem as well. The effects of a uniform horizontal magnetic field and a uniform rotation on the instability problem are also considered separately. The presence of magnetic field stabilizes a certain wave-number band, whereas the system is unstable for all wave-numbers in the absence of the magnetic field for the potentially unstable configuration. However, the system is stable in the potentially stable case and unstable in the potentially unstable case for highly viscous fluids in the presence of a uniform rotation.
10
Content available remote Linear and non-linear analyses of convection in a Rivlin-Ericksen fluid-saturated porous medium
Siddheshwar P. G., Sri Krishna C. V.
International Journal of Applied Mechanics and Engineering
|
2003
|
Vol. 8, no 4
677-692
EN
Linear and non-linear analyses of convection in a second-order Boussinesquian fluid-saturated porous medium are made. The Rivlin-Ericksen constitutive equation is considered to effect a viscoelastic correction to the Brinkman momentum equation together with a single-phase heat transport equation. The linear and non-linear analyses are respectively based on the normal mode technique and the truncated representation of Fourier series. The linear theory reveals that the critical eigenvalue is independent of viscoelastic effects and the principle of exchange of stabilities holds. The non-linear study of cellular convection leads to an autonomous system of differential equations which is solved numerically. The finite amplitude disturbances are found to be independent of transient conditions and viscoelasticity is shown to stabilize the system. The Nusselt number is calculated for different values of the parameters arising in the problem. The possibility of chaotic motion and its similarity to the problem of magnetoconvection are discussed.
11
Content available remote Flow of a viscoelastic fluid of Rivlin-Ericksen between rotating surfaces of revolution
Walicka A.
International Journal of Applied Mechanics and Engineering
|
2003
|
Vol. 8, no spec.
179-186
EN
A theoretical aspect of a flow of a viscoelastic fluid of Rivlin-Ericksen in a gap between two surfaces of revolution is considered. The effect of centrifugal (rotational) inertia forces on the flow field is examined. The examples of flows in the gap between two disks and two concentric spheres arediscussed. The obtained results show that the fluid inertia forces have significant effects on the velocities and pressure distributions.
12
Hall effect on thermal instability of Rivlin-Ericksen fluid in porous medium
Sharma R. C., Thakur K. D.
Applied Mechanics and Engineering
|
2000
|
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.
13
Pressure distribution in a curvilinear bearing lubricated by viscoelastic fluid of Rivlin-Ericksen
Walicka A., Walicki E.
Applied Mechanics and Engineering
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1999
|
Vol. 4, no spec.
73-80
EN
A flow of a viscoelastic fluid of Rivlin-Ericksen in a clearance of a thrust curvilinear bearing was considered. The equations of motion in thin layers presented in the orthogonal curvilinear coordinate system were solved by a method of averaged inertia. As a result the formula for pressure distribution was obtained. Examples of a flow between two disks and two concentric spherical surfaces were given.
14
Thermosolutal convection in Rivlin-Ericksen fluid in porous medium in hydromagnetics
Sharma R. C., Sunil, Chand S.
Applied Mechanics and Engineering
|
1998
|
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.
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