Global nonlinear stability in porous convection with a thermal non-equilibrium model

2005 ◽  
Vol 462 (2066) ◽  
pp. 409-418 ◽  
Author(s):  
B Straughan
Keyword(s):  
Nonlinear Stability ◽  
Equilibrium Model ◽  
Linear Instability ◽  
Darcy Law ◽  
Optimal Result ◽  
Onset Of Convection ◽  
Stability Threshold ◽  
Instability Theory ◽  
Porous Medium Equations ◽  
Non Equilibrium

We show that the global nonlinear stability threshold for convection with a thermal non-equilibrium model is exactly the same as the linear instability boundary. This result is shown to hold for the porous medium equations of Darcy, Forchheimer or Brinkman. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. The equivalence of the linear instability and nonlinear stability boundaries is also demonstrated for thermal convection in a non-equilibrium model with the Darcy law, when the layer rotates with a constant angular velocity about an axis in the same direction as gravity.

scholarly journals GLOBAL STABILITY FOR THERMAL CONVECTION IN A COUPLE-STRESS FLUID WITH TEMPERATURE AND PRESSURE DEPENDENT VISCOSITY

2013 ◽  
Vol 35 (3) ◽  
pp. 85-102 ◽  
Author(s):  
◽  
Shalu Choudhary ◽  
P. K. Bharti
Keyword(s):  
Couple Stress ◽  
Linear Instability ◽  
Optimal Result ◽  
Onset Of Convection ◽  
Stability Threshold ◽  
Instability Theory ◽  
Pressure Dependent Viscosity ◽  
Temperature And Pressure ◽  
Dependent Viscosity ◽  
Instability Boundary

Abstract We show that the global nonlinear stability threshold for convection in a couple-stress fluid with temperature and pressure dependent viscosity is exactly the same as the linear instability boundary. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It has also been found that the couplestress fluid is more stable than the ordinary viscous fluid and then the effect of couple-stress parameter (F) and variable dependent viscosity (Γ) on the onset of convection is also analyzed.

Conditional stability for thermal convection in a rotating couple-stress fluid saturating a porous media with temperature- and pressure-dependent viscosity using a thermal non-equilibrium model

2014 ◽  
Vol 39 (2) ◽  
Author(s):  
Sunil ◽  
Shalu Choudhary ◽  
Amit Mahajan
Keyword(s):  
Equilibrium Model ◽  
Couple Stress ◽  
Linear Instability ◽  
Couple Stress Fluid ◽  
Conditional Stability ◽  
Onset Of Convection ◽  
Pressure Dependent Viscosity ◽  
Temperature And Pressure ◽  
Dependent Viscosity ◽  
Non Equilibrium

Abstract.A nonlinear stability threshold for convection in a rotating couple-stress fluid saturating a porous medium with temperature- and pressure-dependent viscosity using a thermal non-equilibrium model is found to be exactly the same as the linear instability boundary. This optimal result is important because it shows that linear theory has completely captured the physics of the onset of convection. The effects of couple-stress fluid parameter

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 Global Stability For Double-Diffusive Convection In A Couple-Stress Fluid Saturating A Porous Medium

2019 ◽  
Vol 41 (1) ◽  
pp. 13-20
Author(s):  
Shalu Choudhary ◽  
Keyword(s):  
Porous Medium ◽  
Couple Stress ◽  
Linear Instability ◽  
Couple Stress Fluid ◽  
Brinkman Number ◽  
Onset Of Convection ◽  
Instability Theory ◽  
Diffusive Convection ◽  
Solute Gradient ◽  
Double Diffusive

Abstract We show that the global non-linear stability threshold for convection in a double-diffusive couple-stress fluid saturating a porous medium is exactly the same as the linear instability boundary. The optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It is also found that couple-stress fluid saturating a porous medium is thermally more stable than the ordinary viscous fluid, and the effects of couple-stress parameter (F ) , solute gradient ( S f ) and Brinkman number ( D a ) on the onset of convection is also analyzed.

scholarly journals Horizontally isotropic bidispersive thermal convection

2018 ◽  
Vol 474 (2213) ◽  
pp. 20180018 ◽  
Author(s):  
B. Straughan
Keyword(s):  
Thermal Conductivity ◽  
Nonlinear Stability ◽  
Thermal Convection ◽  
Vertical Direction ◽  
Interaction Coefficient ◽  
Linear Instability ◽  
Solid Skeleton ◽  
Stationary Convection ◽  
Symmetric Tensors ◽  
Stability Threshold

A bidispersive porous material is one which has usual pores but additionally contains a system of micro pores due to cracks or fissures in the solid skeleton. We present general equations for thermal convection in a bidispersive porous medium when the permeabilities, interaction coefficient and thermal conductivity are anisotropic but symmetric tensors. In this case, we show exchange of stabilities holds and fluid movement will commence via stationary convection, and additionally we show the global nonlinear stability threshold is the same as the linear instability one. Attention is then focused on the case where the interaction coefficient and thermal conductivity are isotropic, and the permeability is isotropic in the horizontal directions, although the permeability in the vertical direction is different. The nonlinear stability threshold is calculated in this case and numerical results are presented and discussed in detail.

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 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 Instability of Vertical Throughflows in Bidisperse Porous Media

Physics ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 821-828
Author(s):  
Florinda Capone ◽  
Roberta De Luca
Keyword(s):  
Porous Media ◽  
Rayleigh Number ◽  
Closed Form ◽  
Nonlinear Stability ◽  
Approximation Method ◽  
Galerkin Approximation ◽  
Fluid Motion ◽  
Linear Instability ◽  
Stability Threshold ◽  
Darcy Rayleigh Number

In this paper, the instability of a vertical fluid motion, or throughflow, is investigated in a horizontal bidisperse porous layer that is uniformly heated from below. By means of the order-1 Galerkin approximation method, the critical Darcy–Rayleigh number for the onset of steady instability is determined in closed form. The coincidence between the linear instability threshold and the global nonlinear stability threshold, in the energy norm, is shown.

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