Nonlinear Stability of Convection in a Porous Layer with Solid Partitions

2014 ◽  
Vol 16 (4) ◽  
pp. 727-736 ◽  
Author(s):  
B. Straughan
Keyword(s):  
Porous Layer ◽  
Nonlinear Stability

scholarly journals Optimal Stability Thresholds in Rotating Fully Anisotropic Porous Medium with LTNE

2021 ◽  
Author(s):  
Florinda Capone ◽  
Maurizio Gentile ◽  
Jacopo A. Gianfrani
Keyword(s):  
Porous Layer ◽  
Nonlinear Stability ◽  
Steady Motion ◽  
Vertical Axis ◽  
Linear Instability ◽  
List Type ◽  
Nonlinear Stability Analysis ◽  
Onset Of Convection ◽  
Anisotropic Porous Medium ◽  
Necessary And Sufficient

Abstract The onset of thermal convection in an anisotropic horizontal porous layer heated from below and rotating about vertical axis, under local thermal non-equilibrium hypothesis is studied. Linear and nonlinear stability analysis of the conduction solution is performed. Coincidence between the linear instability and the global nonlinear stability thresholds with respect to the L2—norm is proved. Article Highlights A necessary and sufficient condition for the onset of convection in a rotating anisotropic porous layer has been obtained. It has been proved that convection can occur only through a steady motion. A detailed proof is reported thoroughly. Numerical analysis shows that permeability promotes convection, while thermal conductivities and rotation stabilize conduction.

scholarly journals On the stability of carbon sequestration in an anisotropic horizontal porous layer with a first-order chemical reaction

2019 ◽  
Vol 475 (2226) ◽  
pp. 20180365 ◽  
Author(s):  
K. Gautam ◽  
P. A. L. Narayana
Keyword(s):  
Chemical Reaction ◽  
Porous Layer ◽  
Nonlinear Stability ◽  
Anisotropy Ratio ◽  
Neutral Stability ◽  
First Order ◽  
Order Chemical Reaction ◽  
Linear And Nonlinear ◽  
First Order Chemical Reaction ◽  
The Stability

Carbon dioxide (CO 2 ) sequestration in deep saline aquifers is considered to be one of the most promising solutions to reduce the amount of greenhouse gases in the atmosphere. As the concentration of dissolved CO 2 increases in unsaturated brine, the density increases and the system may ultimately become unstable, and it may initiate convection. In this article, we study the stability of convection in an anisotropic horizontal porous layer, where the solute is assumed to decay via a first-order chemical reaction. We perform linear and nonlinear stability analyses based on the steady-state concentration field to assess neutral stability curves as a function of the anisotropy ratio, Damköhler number and Rayleigh number. We show that anisotropy in permeability and solutal diffusivity play an important role in convective instability. It is shown that when solutal horizontal diffusivity is larger than the vertical diffusivity, varying the ratio of vertical to horizontal permeabilities does not significantly affect the behaviour of instability. It is also noted that, when horizontal permeability is higher than the vertical permeability, varying the ratio of vertical to horizontal solutal diffusivity does have a substantial effect on the instability of the system when the reaction rate is dominated by the diffusion rate. We used the Chebyshev-tau method coupled with the QZ algorithm to solve the eigenvalue problem obtained from both the linear and nonlinear stability theories.

scholarly journals Coriolis effect on thermal convection in a rotating bidispersive porous layer

2020 ◽  
Vol 476 (2235) ◽  
pp. 20190875 ◽  
Author(s):  
F. Capone ◽  
R. De Luca ◽  
M. Gentile
Keyword(s):  
Porous Medium ◽  
Linear Theory ◽  
Porous Layer ◽  
Nonlinear Stability ◽  
Thermal Convection ◽  
Linear Instability ◽  
Instability Threshold ◽  
Coriolis Effect ◽  
Single Temperature

We obtain the linear instability and nonlinear stability thresholds for a problem of thermal convection in a rotating bidispersive porous medium with a single temperature. We show that the linear instability threshold is the same as the nonlinear stability one. This means that the linear theory is capturing completely the physics of the onset of thermal convection.

scholarly journals Thermal convection for a Darcy-Brinkman rotating anisotropic porous layer in local thermal non-equilibrium

2021 ◽  
Author(s):  
Florinda Capone ◽  
Jacopo A. Gianfrani
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Nonlinear Stability ◽  
Critical Rayleigh Number ◽  
Vertical Axis ◽  
Linear Instability ◽  
Brinkman Model ◽  
Linear Instability Analysis ◽  
Non Equilibrium

AbstractThe onset of natural convection in a fluid-saturated anisotropic porous layer, which rotates about the vertical axis, under the hypothesis of local thermal non-equilibrium, is analysed. Since the porosity of the medium is assumed to be high, the more suitable Darcy-Brinkman model is adopted. Linear instability analysis of the conduction solution is carried out. Nonlinear stability with respect to $$L^2$$ L 2 -norm is performed in order to prove the coincidence between the linear instability and the global nonlinear stability thresholds. The effect of both rotation and thermal and mechanical anisotropies on the critical Rayleigh number for the onset of instability is discussed.

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