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 The Effect of Magnetic Field Dependent Viscosity on Ferromagnetic Convection in a Rotating Sparsely Distributed Porous Medium - Revisited

2020 ◽  
Vol 25 (1) ◽  
pp. 142-158
Author(s):  
J. Prakash ◽  
P. Kumar ◽  
S. Manan ◽  
K.R. Sharma
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Critical Rayleigh Number ◽  
Wave Number ◽  
Stationary Mode ◽  
Free Boundaries ◽  
Field Dependent ◽  
Mfd Viscosity ◽  
Magnetic Field Dependent Viscosity ◽  
Dependent Viscosity

AbstractThe effect of magnetic field dependent (MFD) viscosity on the thermal convection in a ferrofluid layer saturating a sparsely distributed porous medium has been investigated by using the Darcy-Brinkman model in the simultaneous presence of a uniform vertical magnetic field and a uniform vertical rotation. A correction is applied to the study of Vaidyanathan et al. [11] which is very important in order to predict the correct behavior of MFD viscosity. A linear stability analysis has been carried out for stationary modes and oscillatory modes separately. The critical wave number and critical Rayleigh number for the onset of instability, for the case of free boundaries, are determined numerically for sufficiently large values of the magnetic parameter M1. Numerical results are obtained and are illustrated graphically. It is shown that magnetic field dependent viscosity has a destabilizing effect on the system for the case of stationary mode and a stabilizing effect for the case of oscillatory mode, whereas magnetization has a destabilizing effect.

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 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.

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