On the stability of the flow of a viscoelastic fluid down an inclined plane

AbstractConsideration is given to the flow of a micropolar liquid down an inclined plane. The steady state is analysed and Yih's technique is employed in an investigation of the stability of this flow with respect to long waves. Detailed calculations are given for thin films and it is shown that the micropolar properties of the liquid play an important role in the stability criterion.

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Thermosolutal Instability in Compressible Viscoelastic Dusty Fluid through Porous Medium

International Journal of Applied Mechanics and Engineering ◽

10.2478/ijame-2013-0007 ◽

2013 ◽

Vol 18 (1) ◽

pp. 99-112 ◽

Cited By ~ 1

Author(s):

P. Kumar ◽

H. Mohan

Keyword(s):

Porous Medium ◽

Viscoelastic Fluid ◽

Normal Mode Analysis ◽

Suspended Particles ◽

Mode Analysis ◽

Stationary Convection ◽

Linearized Stability ◽

Medium Permeability ◽

The Stability ◽

Solute Gradient

Thermosolutal instability in a compressible Walters B’ viscoelastic fluid with suspended particles through a porous medium is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the Walters B’ viscoelastic fluid behaves like a Newtonian fluid and it is found that suspended particles and medium permeability have a destabilizing effect whereas the stable solute gradient and compressibility have a stabilizing effect on the system. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient and viscoelasticity are found to introduce oscillatory modes in the system which are non-existent in their absence.

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Effect of Rotational Speed Modulation on the Weakly Nonlinear Heat Transfer in Walter-B Viscoelastic Fluid in the Highly Permeable Porous Medium

Mathematics ◽

10.3390/math8091448 ◽

2020 ◽

Vol 8 (9) ◽

pp. 1448

Author(s):

Anand Kumar ◽

Vinod K. Gupta ◽

Neetu Meena ◽

Ishak Hashim

Keyword(s):

Heat Transfer ◽

Porous Medium ◽

Prandtl Number ◽

Heat Transport ◽

Viscoelastic Fluid ◽

Rotational Speed ◽

Weakly Nonlinear ◽

Speed Modulation ◽

The Stability ◽

The Impact

In this article, a study on the stability of Walter-B viscoelastic fluid in the highly permeable porous medium under the rotational speed modulation is presented. The impact of rotational modulation on heat transport is performed through a weakly nonlinear analysis. A perturbation procedure based on the small amplitude of the perturbing parameter is used to study the combined effect of rotation and permeability on the stability through a porous medium. Rayleigh–Bénard convection with the Coriolis expression has been examined to explain the impact of rotation on the convective flow. The graphical result of different parameters like modified Prandtl number, Darcy number, Rayleigh number, and Taylor number on heat transfer have discussed. Furthermore, it is found that the modified Prandtl number decelerates the heat transport which may be due to the combined effect of elastic parameter and Taylor number.

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Overstability of a Viscoelastic Fluid Layer Oscillating in a Vertical Periodic Motion and Heated From Below

Journal of Applied Mechanics ◽

10.1115/1.3424570 ◽

1979 ◽

Vol 46 (2) ◽

pp. 454-456

Author(s):

S. O. Onyegegbu

Keyword(s):

Natural Frequency ◽

Viscoelastic Fluid ◽

Periodic Motion ◽

Oscillation Frequency ◽

Numerical Solutions ◽

Fluid Layer ◽

The Stability ◽

Oscillation Frequencies

This Note examines the effect of vertical periodic motion on the stability characteristics of a viscoelastic fluid layer in a classical Benard geometry. Numerical solutions show that a resonant type behavior which enhances stability occurs at oscillation frequencies near the convective natural frequency of the viscoelastic fluid, while the effect of the periodic motion vanishes as the oscillation frequency gets very large.

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Gravity Modulation of Thermal Instability in a Viscoelastic Fluid Saturated Anisotropic Porous Medium

Zeitschrift für Naturforschung A ◽

10.5560/zna.2011-0045 ◽

2012 ◽

Vol 67 (1-2) ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

Beer S. Bhadauria ◽

Atul K. Srivastava ◽

Nirmal C. Sacheti ◽

Pallath Chandran

Keyword(s):

Porous Medium ◽

Gravity Field ◽

Viscoelastic Fluid ◽

Thermal Instability ◽

Time Dependent ◽

Periodic Part ◽

Gravity Modulation ◽

Dependent Part ◽

Anisotropic Porous Medium ◽

The Stability

The present paper deals with a thermal instability problem in a viscoelastic fluid saturating an anisotropic porous medium under gravity modulation. To find the gravity modulation effect, the gravity field is considered in two parts: a constant part and an externally imposed time-dependent periodic part. The time-dependent part of the gravity field, which can be realized by shaking the fluid, has been represented by a sinusoidal function. Using Hill’s equation and the Floquet theory, the convective threshold has been obtained. It is found that gravity modulation can significantly affect the stability limits of the system. Further, we find that there is a competition between the synchronous and subharmonic modes of convection at the onset of instability. Effects of various parameters on the onset of instability have also been discussed.

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On the Stability of Two Superposed Viscous-Viscoelastic (Walters B′) Fluids

Journal of Fluids Engineering ◽

10.1115/1.2375135 ◽

2006 ◽

Vol 129 (1) ◽

pp. 116-119 ◽

Cited By ~ 1

Author(s):

Pardeep Kumar ◽

Roshan Lal

Keyword(s):

Viscous Fluid ◽

Viscoelastic Fluid ◽

Kinematic Viscosity ◽

Taylor Instability ◽

Stable Configuration ◽

Stabilizing Effect ◽

Unstable Configuration ◽

Rayleigh Taylor Instability ◽

Newtonian Viscous Fluid ◽

The Stability

The Rayleigh-Taylor instability of a Newtonian viscous fluid overlying Walters B′ viscoelastic fluid is considered. For the stable configuration, the system is found to be stable or unstable under certain conditions. However, the system is found to be unstable for the potentially unstable configuration. Further it is found numerically that kinematic viscosity has a destabilizing effect, whereas kinematic viscoelasticity has a stabilizing effect on the system.

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SUPG Approximation for the Oseen Viscoelastic Fluid Flow with Stabilized Lowest-Equal Order Mixed Finite Element Method

Mathematics ◽

10.3390/math7020128 ◽

2019 ◽

Vol 7 (2) ◽

pp. 128

Author(s):

Shahid Hussain ◽

Afshan Batool ◽

Md. Al Mahbub ◽

Nasrin Nasu ◽

Jiaping Yu

Keyword(s):

Finite Element ◽

Fluid Flow ◽

Viscoelastic Fluid ◽

Mixed Finite Element ◽

Mixed Finite Element Method ◽

Constitutive Law ◽

Optimal Error Estimates ◽

Fe Method ◽

The Stability ◽

Stability And Accuracy

In this article, a stabilized mixed finite element (FE) method for the Oseen viscoelastic fluid flow (OVFF) obeying an Oldroyd-B type constitutive law is proposed and investigated by using the Streamline Upwind Petrov–Galerkin (SUPG) method. To find the approximate solution of velocity, pressure and stress tensor, we choose lowest-equal order FE triples P 1 - P 1 - P 1 , respectively. However, it is well known that these elements do not fulfill the i n f - s u p condition. Due to the violation of the main stability condition for mixed FE method, the system becomes unstable. To overcome this difficulty, a standard stabilization term is added in finite element variational formulation. The technique is applied herein possesses attractive features, such as parameter-free, flexible in computation and does not require any higher-order derivatives. The stability analysis and optimal error estimates are obtained. Three benchmark numerical tests are carried out to assess the stability and accuracy of the stabilized lowest-equal order feature of the OVFF.

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