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 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.

scholarly journals Effect of anisotropy on the onset of convection in rotating bi-disperse Brinkman porous media

2021 ◽  
Author(s):  
Florinda Capone ◽  
Roberta De Luca ◽  
Giuliana Massa
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Steady State ◽  
Nonlinear Stability ◽  
Linear Instability ◽  
Combined Effects ◽  
Nonlinear Stability Analysis ◽  
Onset Of Convection ◽  
Linear And Nonlinear ◽  
The Stability

AbstractThermal convection in a horizontally isotropic bi-disperse porous medium (BDPM) uniformly heated from below is analysed. The combined effects of uniform vertical rotation and Brinkman law on the stability of the steady state of the momentum equations in a BDPM are investigated. Linear and nonlinear stability analysis of the conduction solution is performed, and the coincidence between linear instability and nonlinear stability thresholds in the $$L^2$$ L 2 -norm is obtained.

A nonlinear stability analysis in a double-diffusive magnetized ferrofluid with magnetic-field-dependent viscosity saturating a porous medium

2009 ◽  
Vol 87 (6) ◽  
pp. 659-673 ◽  
Author(s):  
Sunil ◽  
Amit Mahajan
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Nonlinear Stability ◽  
Stability Result ◽  
Darcy Number ◽  
Linear Instability ◽  
Nonlinear Stability Analysis ◽  
Field Dependent ◽  
Magnetized Ferrofluid ◽  
Mfd Viscosity

A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional for a magnetized ferrofluid layer heated and soluted from below with magnetic-field-dependent (MFD) viscosity saturating a porous medium, in the stress-free boundary case. The mathematical emphasis is on how to control the nonlinear terms caused by the magnetic-body and inertia forces. For ferrofluids, we find that there is possibility of existence of subcritical instabilities, however, it is noted that, in case of a non-ferrofluid, the global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of the magnetic parameter, M3; solute gradient, Sf; Darcy number, Da; and MFD viscosity parameter, δ; on the subcritical instability region has also been analyzed.

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.

Global stability for thermal convection in a fluid overlying a highly porous material

2008 ◽  
Vol 465 (2101) ◽  
pp. 207-217 ◽  
Author(s):  
Antony A Hill ◽  
Brian Straughan
Keyword(s):  
Porous Medium ◽  
Porous Material ◽  
Nonlinear Stability ◽  
Thermal Convection ◽  
Linear Instability ◽  
Brinkman Equation ◽  
Onset Of Convection ◽  
Unconditional Nonlinear Stability ◽  
Highly Porous ◽  
Highly Porous Material

This paper investigates the instability thresholds and global nonlinear stability bounds for thermal convection in a fluid overlying a highly porous material. A two-layer approach is adopted, where the Darcy–Brinkman equation is employed to describe the fluid flow in the porous medium. An excellent agreement is found between the linear instability and unconditional nonlinear stability thresholds, demonstrating that the linear theory accurately emulates the physics of the onset of convection.

scholarly journals Nonlinear Stability Analysis of a Spinning Top with an Interior Liquid-Filled Cavity

2020 ◽  
Author(s):  
Giovanni Paolo Galdi ◽  
Giusy Mazzone
Keyword(s):  
Nonlinear Stability ◽  
Center Of Mass ◽  
Coupled System ◽  
Vertical Axis ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Nonlinear Stability Analysis ◽  
Spinning Top ◽  
Axis Passing

Consider the  motion of the the coupled system, $\mathscr S$, constituted by a (non-necessarily symmetric) top, $\mathscr B$, with an interior cavity, $\mathscr C$, completely filled up with a Navier-Stokes  liquid, $\mathscr L$. A particular steady-state motion $\bar{\sf s}$ (say) of $\mathscr S$, is when $\mathscr L$ is at rest with respect to $\mathscr B$, and $\mathscr S$, as a whole rigid body, spins with a constant angular velocity $\bar{\V\omega}$ around a vertical axis passing through its center of mass $G$ in its highest position ({\em upright spinning top}). We then provide a completely characterization of the nonlinear stability of $\bar{\sf s}$ by showing, roughly speaking, that $\bar{\sf s}$ is stable if and only if $|\bar{\V\omega}|$ is sufficiently large, all other physical parameters being fixed. Moreover we show that, unlike the case when $\mathscr C$ is empty, under the above stability conditions, the top will eventually return to the unperturbed upright configuration.

A nonlinear-stability analysis of second-order fluid in porous medium in presence of magnetic field

Analysis ◽  
2005 ◽  
Vol 25 (2) ◽  
Author(s):  
Lanxi Xu
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Nonlinear Stability ◽  
Stability Boundary ◽  
Second Order ◽  
Nonlinear Stability Analysis ◽  
Onset Of Convection ◽  
Medium Permeability ◽  
Lyapunov’S Second Method ◽  
Chandrasekhar Number

AbstractNonlinear stability of the motionless state of the second-order fluid in porous medium in presence of magnetic field is studied by the Lyapunov’s second method. Through defining a Lyapunov function we will prove the inhibiting effect of the magnetic field on the onset of convection. If the Chandrasekhar number is below a computable constant depending on system parameters, we even prove the coincidence of linear and nonlinear stability boundary. Moreover, the medium permeability has a destabilizing effect.

scholarly journals Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 75 ◽  
Author(s):  
Leiv Storesletten ◽  
D. Andrew S. Rees
Keyword(s):  
Porous Layer ◽  
Heat Generation ◽  
Internal Heat ◽  
Convective Motion ◽  
Linear Instability ◽  
Internal Heat Generation ◽  
Anisotropy Ratio ◽  
Heat Sources ◽  
Onset Of Convection ◽  
Set Up

The onset of convection in an inclined porous layer which is heated internally by a uniform distribution of heat sources is considered. We investigate the combined effects of inclination, anisotropy and internal heat generation on the linear instability of the basic parallel flow. When the Rayleigh number is sufficiently large, instability occurs and a convective motion is set up. It turns out that the preferred motion at convection onset depends quite strongly on the anisotropy ratio, ξ , and the inclination angle. When ξ < 1 the preferred motion is in the form of longitudinal rolls for all inclinations. When ξ > 1 transverse rolls are preferred for small inclinations but, at high inclinations, longitudinal rolls are preferred. At intermediate inclinations the preferred roll orientation varies smoothly between these two extremes.

scholarly journals Anisotropic bidispersive convection

2019 ◽  
Vol 475 (2227) ◽  
pp. 20190206 ◽  
Author(s):  
B. Straughan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Rayleigh Number ◽  
Nonlinear Stability ◽  
Thermal Convection ◽  
Linear Instability ◽  
Solid Skeleton ◽  
Nonlinear Stability Analysis ◽  
Cell Structures ◽  
Linear Instability Analysis

This paper investigates thermal convection in an anisotropic bidisperse porous medium. A bidisperse porous medium is one which possesses the usual pores, but in addition, there are cracks or fissures in the solid skeleton and these give rise to a second porosity known as micro porosity. The novelty of this paper is that the macro permeability and the micro permeability are each diagonal tensors but the three components in the vertical and in the horizontal directions may be distinct in both the macro and micro phases. Thus, there are six independent permeability coefficients. A linear instability analysis is presented and a fully nonlinear stability analysis is inferred. Several Rayleigh number and wavenumber calculations are presented and it is found that novel cell structures are predicted which are not present in the single porosity case.

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