scholarly journals The Onset of Soret Driven Ferrothermoconvective Instability in the Presence of Darcy Porous Medium with Anisotropy Effect and MFD Viscosity

2021 ◽  
Vol 26 (1) ◽  
pp. 156-177
Author(s):  
D. Murugan ◽  
R. Sekar
Keyword(s):  
Porous Medium ◽  
Soret Effect ◽  
Stationary Mode ◽  
Onset Of Convection ◽  
System A ◽  
Anisotropy Effect ◽  
Field Dependent ◽  
Anisotropic Porous Medium ◽  
Mfd Viscosity ◽  
Mode Technique

AbstractThe effect of magnetic field dependent (MFD) viscosity on Soret driven ferrothermohaline convection in a densely packed anisotropic porous medium has been studied. The Soret effect is focused on the system. A linear stability analysis is carried out using a normal mode technique and a perturbation method is applied. It is found that a stationary mode is favorable for the Darcy model. Vertical anisotropy tends to destabilize the system and the magnetization effect is found to stabilize the system. It is also found that the MFD viscosity delays the onset of convection. Numerical computations are made and illustrated graphically.

Effect of magnetic field dependent viscosity on Soret-driven ferrothermohaline convection saturating an anisotropic porous medium of sparse particle suspension

2014 ◽  
Vol 11 (3) ◽  
pp. 213-228 ◽  
Author(s):  
R. Sekar ◽  
K. Raju
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Soret Effect ◽  
Anisotropy Ratio ◽  
Free Boundaries ◽  
Wide Range ◽  
Field Dependent ◽  
Anisotropic Porous Medium ◽  
Mfd Viscosity ◽  
Dependent Viscosity

Thermoconvective instability with Soret effect in multi-component fluids has wide range of applications in heat and mass transfer. This work deals with the theoretical investigation of the effect of magnetic field dependent (MFD) viscosity on Soret-driven ferrothermohaline convection heated and salted from below in an anisotropic porous medium subjected to a transverse uniform magnetic field. The resulting eigen value problem is solved using Brinkman model. An exact solution is obtained for the case of two free boundaries and the stationary and oscillatory instabilities are investigated by using linear stability analysis and normal mode technique for the vertical of anisotropic porous medium. The analysis has been made for different parameters like porosity, anisotropy, ratio of heat transport to mass transport, buoyancy magnetization, non-buoyancy magnetization, Soret parameter and Salinity Rayleigh number. The effect of MFD viscosity is assumed to be isotropy. It is found that the presence of MFD viscosity has a stabilizing effect, whereas magnetization has a destabilizing effect.

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 numerical technique and effect of magnetic field dependent (MFD) viscosity on thermal instability in a ferrofluid pores with Coriolis force for Darcy model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
D. Murugan ◽  
R. Sekar
Keyword(s):  
Magnetic Field ◽  
Coriolis Force ◽  
Fluid Layer ◽  
Taylor Number ◽  
Stationary Mode ◽  
Onset Of Convection ◽  
Content Type ◽  
Darcy Model ◽  
Field Dependent ◽  
Mfd Viscosity

Purpose The effect of magnetic field dependent (MFD) viscosity on the onset of convection in a ferromagnetic fluid layer heated from below saturating rotating porous medium in the presence of vertical magnetic field is investigated theoretically by using Darcy model. The resulting eigen value problem is solved using the regular perturbation technique. Both stationary and oscillatory instabilities have been obtained. It is found that increase in MFD viscosity and increase in magnetic Rayleigh number is to delay the onset of ferroconvection, while the nonlinearity of fluid magnetization has no influence on the stability of the system. Design/methodology/approach The thermal perturbation method is employed for analytical solution. A theory of linear stability analysis and normal mode technique have been carried out to analyze the onset of convection for a fluid layer contained between two impermeable boundaries for which an exact solution is obtained. Findings The conditions for the system to stabilize both by stationary and oscillatory modes are studied. Even for the oscillatory system of particular frequency dictated by physical conditions, the critical Rayleigh numbers for oscillatory mode of the system were found to be greater than for the stationary mode. The system gets destabilized for various physical parameters only through stationary mode. Hence, the analysis is restricted to the stationary mode. To the Coriolis force, the Taylor number Ta is calculated to discuss the results. It is found that the system stabilizes through stationary mode for values of and for oscillatory instability is favored for Ta > 104. Therefore the Taylor number Ta leads to stability of the system. For larger rotation, magnetization leads to destabilization of the system. The MFD viscosity is found to stabilize the system. Originality/value This research paper is new and original.

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.

Thermovibrational Instability in a Fluid Saturated Anisotropic Porous Medium

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
S. Saravanan ◽  
T. Sivakumar
Keyword(s):  
Porous Medium ◽  
Dynamic Instability ◽  
Instability Threshold ◽  
Momentum Balance ◽  
Onset Of Convection ◽  
Time In Literature ◽  
Anisotropic Porous Medium ◽  
Arbitrary Amplitude ◽  
Vibration Parameters ◽  
First Time

A comprehensive investigation is made to understand the effect of harmonic vibration on the onset of convection in a horizontal anisotropic porous layer heated either from below or from above. The layer is subject to vertical mechanical vibrations of arbitrary amplitude and frequency. The porous medium is assumed to be both mechanically and thermally anisotropic, and Brinkman’s law is invoked to model the momentum balance. Both continued fraction and Hill’s infinite determinant methods are used to determine the convective instability threshold with the aid of Floquet theory. The synchronous and subharmonic resonant regions of dynamic instability are determined and their critical boundaries are found. The results show that anisotropy in permeability favors convection whereas that in thermal conductivity suppresses it with a wider cellular pattern at the instability threshold. The influence of vibration parameters and heating condition on the anisotropy effects and the competition between the synchronous and subharmonic modes are discussed. This study also reveals the existence of a closed disconnected instability region in certain areas of the parameter space for the first time in literature.

scholarly journals Effect of Soret and Temperature Dependent Viscosity on Thermohaline Convection in a Ferrofluid Saturating a Porous Medium

2014 ◽  
Vol 19 (2) ◽  
pp. 321-336
Author(s):  
R. Sekar ◽  
K. Raju
Keyword(s):  
Porous Medium ◽  
Fluid Layer ◽  
Effect Of Temperature ◽  
Stationary Mode ◽  
Free Boundaries ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Onset Of Convection ◽  
Wide Range ◽  
Dependent Viscosity

Abstract Soret driven ferrothermoconvective instability in multi-component fluids has a wide range of applications in heat and mass transfer. This paper deals with the theoretical investigation of the effect of temperature dependent viscosity on a Soret driven ferrothermohaline convection heated from below and salted from above subjected to a transverse uniform magnetic field in the presence of a porous medium. The Brinkman model is used in the study. It is found that the stationary mode of instability is preferred. For a horizontal fluid layer contained between two free boundaries an exact solution is examined using the normal mode technique for a linear stability analysis. The effect of salinity has been included in magnetization and density of the fluid. The critical thermal magnetic Rayleigh number for the onset of instability is obtained numerically for sufficiently large values of the buoyancy magnetization parameter M1 using the method of numerical Galerkin technique. It is found that magnetization and permeability of the porous medium destabilize the system. The effect of temperature dependent viscosity stabilizes the system on the onset of convection.

scholarly journals Hall Effect on Bénard Convection of Compressible Viscoelastic Fluid through Porous Medium

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Mahinder Singh ◽  
Chander Bhan Mehta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Instability ◽  
Linear Stability Theory ◽  
Stationary Convection ◽  
Onset Of Convection ◽  
Medium Permeability ◽  
Rayleigh Numbers ◽  
The Magnetic Field ◽  
Mode Technique

An investigation made on the effect of Hall currents on thermal instability of a compressible Walter’s B′ elasticoviscous fluid through porous medium is considered. The analysis is carried out within the framework of linear stability theory and normal mode technique. For the case of stationary convection, Hall currents and compressibility have postponed the onset of convection through porous medium. Moreover, medium permeability hasten postpone the onset of convection, and magnetic field has duel character on the onset of convection. The critical Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection have been obtained and the behavior of various parameters on critical thermal Rayleigh numbers has been depicted graphically. The magnetic field, Hall currents found to introduce oscillatory modes, in the absence of these effects the principle of exchange of stabilities is valid.

scholarly journals Stability analysis of soret effect on thermohaline convection in dusty ferrofluid saturating a Darcy porous medium

2015 ◽  
Vol 3 (1) ◽  
pp. 37
Author(s):  
R. Sekar ◽  
K. Raju
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Soret Effect ◽  
Dust Particles ◽  
Stationary Mode ◽  
Free Boundaries ◽  
Thermohaline Convection ◽  
Particle Parameter ◽  
Thermoconvective Instability ◽  
Oscillatory Instabilities

<p>The Soret–driven ferro thermoconvective instability of multi–component fluid in a porous medium heated from below and salted from above in the presence of dust particles subjected to a transverse uniform magnetic field has been analyzed using Darcy model for various values of permeability of the porous medium. The salinity effect has been contained in magnetization and density of the ferrofluid. A small thermal perturbation imparted on the basic state and a linear stability analysis is used for this model for which normal mode technique is applied. An exact solution is obtained for the case of two free boundaries and both stationary and oscillatory instabilities have been investigated. It is found that the system destabilizes only through stationary mode. The non-buoyancy magnetization parameter, the dust particle parameter and the permeability of the porous medium are found to destabilize the system. The results are depicted graphically.</p>

Sign in / Sign up

Export Citation Format

Share Document