Nonlinear convection of a viscoelastic fluid with inclined temperature gradient

2005 ◽  
Vol 17 (1) ◽  
pp. 17-27 ◽  
Author(s):  
P. N. Kaloni ◽  
J. X. Lou
Keyword(s):  
Temperature Gradient ◽  
Viscoelastic Fluid ◽  
Nonlinear Convection ◽  
Inclined Temperature Gradient

Effect of a Variable Gravity Field on Convection in an Anisotropic Porous Medium With Internal Heat Source and Inclined Temperature Gradient

2001 ◽  
Vol 124 (1) ◽  
pp. 144-150 ◽  
Author(s):  
Sherin M. Alex ◽  
Prabhamani R. Patil
Keyword(s):  
Temperature Gradient ◽  
Heat Source ◽  
Gravity Field ◽  
Convective Instability ◽  
Opposite Effect ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Anisotropic Porous Medium ◽  
Variable Gravity ◽  
Inclined Temperature Gradient

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.

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

2009 ◽  
Vol 641 ◽  
pp. 475-487 ◽  
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.

Stability of thermocapillary flows with inclined temperature gradient

2001 ◽  
Vol 442 ◽  
pp. 141-155 ◽  
Author(s):  
ALEXANDER A. NEPOMNYASHCHY ◽  
ILYA B. SIMANOVSKII ◽  
LEONID M. BRAVERMAN
Keyword(s):  
Temperature Gradient ◽  
Water System ◽  
Vertical Direction ◽  
Instability Mechanism ◽  
Mean Flow ◽  
Thermocapillary Flows ◽  
The Mean ◽  
The Stability ◽  
Inclined Temperature Gradient ◽  
Convective Rolls

The stability of a two-layer return thermocapillary flow in the presence of an inclined temperature gradient is investigated. Both a linear stability analysis and nonlinear simulations have been performed for an air–water system. It is found that a rather weak deviation of the mean temperature gradient from the vertical direction suppresses Pearson's instability mechanism and leads to the appearance of oblique hydrothermal waves. In a certain region of parameters, transverse convective rolls drifting with the mean flow appear.

scholarly journals Rayleigh-Benard convection in a viscoelastic fluid-filled high-porosity medium with nonuniform basic temperature gradient

2001 ◽  
Vol 25 (9) ◽  
pp. 609-619 ◽  
Author(s):  
Pradeep G. Siddheshwar ◽  
C. V. Sri Krishna
Keyword(s):  
Stability Analysis ◽  
Temperature Gradient ◽  
Viscoelastic Fluid ◽  
High Porosity ◽  
Rigid Boundary ◽  
Viscoelastic Problem ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The qualitative effect of nonuniform temperature gradient on the linear stability analysis of the Rayleigh-Benard convection problem in a Boussinesquian, viscoelastic fluid-filled, high-porosity medium is studied numerically using the single-term Galerkin technique. The eigenvalue is obtained for free-free, free-rigid, and rigid-rigid boundary combinations with isothermal temperature conditions. Thermodynamics and also the present stability analysis dictates the strain retardation time to be less than the stress relaxation time for convection to set in as oscillatory motions in a high-porosity medium. Furthermore, the analysis predicts the critical eigenvalue for the viscoelastic problem to be less than that of the corresponding Newtonian fluid problem.

Slippage effect on the flow stability induced by an inclined temperature gradient

2021 ◽  
Vol 159 ◽  
pp. 106549
Author(s):  
D. Barrera-Román ◽  
A.S. Ortiz-Pérez ◽  
E.S. Durazo-Romero ◽  
J.B. Sosa-Coeto ◽  
A. Acuña-Ramírez ◽  
...  
Keyword(s):  
Temperature Gradient ◽  
Flow Stability ◽  
Slippage Effect ◽  
Inclined Temperature Gradient
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