Effect of inclined temperature gradient on thermal instability in an anisotropic porous medium

The convective instability of a horizontal fluid-saturated anisotropic porous layer, with internal heat source and inclined temperature gradient, subject to a gravity field varying with distance in the layer, is investigated. A linear stability analysis is performed and the resulting eigenvalue problem solved using a Galerkin technique. In the absence of an inclined temperature gradient, an increase in the variable gravity parameter above −1 destabilizes the system. In its presence interesting developments occur. An increase in the heat generation destabilizes the system when the variable gravity parameter is nonnegative. When it is negative the opposite effect is seen.

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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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Three-Dimensional instability analysis in a porous medium with inclined temperature gradient and horizontal and vertical throughflow

10.26678/abcm.encit2018.cit18-0386 ◽

2018 ◽

Author(s):

Mateus Schuabb ◽

Leonardo Santos de Brito Alves

Keyword(s):

Porous Medium ◽

Temperature Gradient ◽

Three Dimensional ◽

Instability Analysis ◽

Vertical Throughflow ◽

Dimensional Instability ◽

Inclined Temperature Gradient

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Three-dimensional absolute and convective instabilities at the onset of convection in a porous medium with inclined temperature gradient and vertical throughflow

Journal of Fluid Mechanics ◽

10.1017/s0022112009992163 ◽

2009 ◽

Vol 641 ◽

pp. 475-487 ◽

Cited By ~ 26

Author(s):

LEONID BREVDO

Keyword(s):

Porous Medium ◽

Rayleigh Number ◽

Temperature Gradient ◽

Three Dimensional ◽

Onset Of Convection ◽

Convective Instabilities ◽

Homogeneous Porous Medium ◽

Vertical Throughflow ◽

Speed Of Propagation ◽

Inclined Temperature Gradient

By using the mathematical formalism of absolute and convective instabilities, we study in this work the nature of unstable three-dimensional localized disturbances at the onset of convection in a flow in a saturated homogeneous porous medium with inclined temperature gradient and vertical throughflow. It is shown that for marginally supercritical values of the vertical Rayleigh numberRvthe destabilization has the character of absolute instability in all the cases in which the horizontal Rayleigh numberRhis zero or the Péclet numberQvis zero. In all the cases in whichRhandQvare both different from zero, at the onset of convection the instability is convective. In the latter cases, the growing emerging disturbance has locally the structure of a non-oscillatory longitudinal roll, and its group velocity points in the direction opposite the direction of the applied horizontal temperature gradient, i.e. parallel to the axis of the roll. The speed of propagation of the unstable wavepacket increases withQvand generally increases withRh.

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