Magnetofluidconvection in a Rotating Porous Layer Under Modulated Temperature on the Boundaries

2006 ◽  
Vol 129 (7) ◽  
pp. 835-843 ◽  
Author(s):  
B. S. Bhadauria
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Prandtl Number ◽  
Thermal Instability ◽  
Fluid Layer ◽  
Saturated Porous Medium ◽  
Critical Rayleigh Number ◽  
Temperature Modulation ◽  
Brinkman Model ◽  
Vertical Magnetic Field

Thermal instability in an electrically conducting fluid saturated porous medium, confined between two horizontal walls, has been investigated in the presence of an applied vertical magnetic field and rotation, using the Brinkman model. The temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent oscillatory part. Only infinitesimal disturbances are considered. The combined effect of permeability, rotation, vertical magnetic field, and temperature modulation has been investigated using Galerkin’s method and Floquet theory. The value of the critical Rayleigh number is calculated as function of amplitude and frequency of modulation, Chandrasekhar number, Taylor number, porous parameter, Prandtl number, and magnetic Prandtl number. It is found that rotation, magnetic field, and porous medium all have a stabilizing influence on the onset of thermal instability. Further, it is also found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation of the walls’ temperature. In addition the results corresponding to the Brinkman model and Darcy model have been compared for neutral instability.

Combined Effect of Temperature Modulation and Magnetic Field on the Onset of Convection in an Electrically Conducting-Fluid-Saturated Porous Medium

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
B. S. Bhadauria
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Saturated Porous Medium ◽  
Effect Of Temperature ◽  
Temperature Modulation ◽  
Vertical Magnetic Field ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Fluid Saturated Porous Medium

The effect of temperature modulation on the onset of thermal convection in an electrically conducting fluid-saturated-porous medium, heated from below, has been studied using linear stability analysis. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small. The porous medium is confined between two horizontal walls and subjected to a vertical magnetic field; flow in porous medium is characterized by Brinkman–Darcy model. Considering only infinitesimal disturbances, and using perturbation procedure, the combined effect of temperature modulation and vertical magnetic field on thermal instability has been studied. The correction in the critical Rayleigh number is calculated as a function of frequency of modulation, Darcy number, Darcy Chandrasekhar number, magnetic Prandtl number, and the nondimensional group number χ. The influence of the magnetic field is found to be stabilizing. Furthermore, it is also found that the onset of convection can be advanced or delayed by proper tuning of the frequency of modulation. The results of the present model have been compared with that of Darcy model.

Thermal Instability of a Fluid-Saturated Porous Medium Bounded by Thin Fluid Layers

1987 ◽  
Vol 109 (3) ◽  
pp. 677-682 ◽  
Author(s):  
G. Pillatsis ◽  
M. E. Taslim ◽  
U. Narusawa
Keyword(s):  
Porous Medium ◽  
Porous Layer ◽  
Thermal Instability ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Convective Motion ◽  
Wave Number ◽  
Thermal Conductivity Ratio ◽  
Fluid Layers

A linear stability analysis is performed for a horizontal Darcy porous layer of depth 2dm sandwiched between two fluid layers of depth d (each) with the top and bottom boundaries being dynamically free and kept at fixed temperatures. The Beavers–Joseph condition is employed as one of the interfacial boundary conditions between the fluid and the porous layer. The critical Rayleigh number and the horizontal wave number for the onset of convective motion depend on the following four nondimensional parameters: dˆ ( = dm/d, the depth ratio), δ ( = K/dm with K being the permeability of the porous medium), α (the proportionality constant in the Beavers–Joseph condition), and k/km (the thermal conductivity ratio). In order to analyze the effect of these parameters on the stability condition, a set of numerical solutions is obtained in terms of a convergent series for the respective layers, for the case in which the thickness of the porous layer is much greater than that of the fluid layer. A comparison of this study with the previously obtained exact solution for the case of constant heat flux boundaries is made to illustrate quantitative effects of the interfacial and the top/bottom boundaries on the thermal instability of a combined system of porous and fluid layers.

Onset of wall-attached convection in a rotating fluid layer in the presence of a vertical magnetic field

2008 ◽  
Vol 600 ◽  
pp. 427-443
Author(s):  
J. J. SÁNCHEZ-ÁLVAREZ ◽  
E. CRESPO DEL ARCO ◽  
F. H. BUSSE
Keyword(s):  
Magnetic Field ◽  
Rotation Rate ◽  
Magnetic Energy ◽  
Fluid Layer ◽  
Travelling Waves ◽  
Critical Rayleigh Number ◽  
Vertical Axis ◽  
Vertical Magnetic Field ◽  
Onset Of Convection ◽  
Magnetic Energy Density

A horizontal fluid layer heated from below and rotating about a vertical axis in the presence of a vertical magnetic field is considered. From earlier work it is known that the onset of convection in a rotating layer usually occurs in the form of travelling waves attached to the vertical sidewalls of the layer. It is found that this behaviour persists when a vertical magnetic field is applied. When the Elsasser number Λ is kept constant and the sidewall is thermally insulating the critical Rayleigh number Rc increases in proportion to the rotation rate described by the square root of the Taylor number, τ. This asymptotic relationship is found for an electrically highly conducting sidewall as well as for an electrically insulating one. At fixed rotation rate for Q≫τ, Rc grows in proportion to Q when the sidewall is electrically highly conducting, and in proportion to Q3/4 when the sidewall is electrically insulating. Here Q is the Chandrasekhar number which is a measure of the magnetic energy density, and a thermally insulating sidewall has been assumed. Of particular interest is the possibility that the magnetic field counteracts the stabilizing influence of rotation on the onset of sidewall convection in the case of thermally insulating sidewalls. When the sidewall is thermally highly conducting, Rc for the sidewall mode grows in proportion to τ4/3. This asymptotic behaviour is found for both cases of electrical boundary conditions, but it no longer precedes the onset of bulk convection for Λ ≳ 1.

Ferromagnetic Convection in a Densely Packed Porous Medium with Magnetic-Field-Dependent Viscosity – Revisited

2018 ◽  
Vol 73 (3) ◽  
pp. 181-189
Author(s):  
Jyoti Prakash ◽  
Pankaj Kumar ◽  
Kultaran Kumari ◽  
Shweta Manan
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Wave Number ◽  
Free Boundaries ◽  
Medium Permeability ◽  
Field Dependent ◽  
Mfd Viscosity ◽  
Dependent Viscosity

AbstractThe effect of magnetic-field-dependent (MFD) viscosity on the thermal convection in a ferromagnetic fluid in the presence of a uniform vertical magnetic field is investigated for a fluid layer saturating a densely packed porous medium using the Darcy model. A correction is applied to the model by Sunil et al. [Z. Naturforsch. 59, 397 (2004)], which is very important to predict the correct behaviour of MFD viscosity. A linear stability analysis is carried out for stationary modes. 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 illustrated graphically. It is shown that MFD viscosity has stabilizing effect on the system, whereas medium permeability has a destabilizing effect.

Thermal instability of a compressible finite-Larmor-radius Hall plasma in a porous medium

1996 ◽  
Vol 55 (1) ◽  
pp. 35-45 ◽  
Author(s):  
R. C. Sharma ◽  
Sunil
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Instability ◽  
Hall Current ◽  
Larmor Radius ◽  
Vertical Magnetic Field ◽  
Finite Larmor Radius ◽  
Medium Permeability ◽  
Hall Plasma

The thermal instability of a compressible plasma in a porous medium is considered in the presence of a uniform vertical magnetic field to include the Hall-current and finite-Larmor-radius effects. The system is found to be stable for (cp/g) β < 1, where cp, β and g are the specific heat at constant-pressure, the uniform adverse temperature gradient and the acceleration due to gravity respectively. The uniform vertical magnetic field, Hall-current and finite. Laimor-radius effects introduce oscillatory modes in the system for (cp/g) β ≤ 1, which were non-existent in their absence. The Hall current and finite Larmor radius (FLR) individually have destabilizing and stabilizing effects respectively on the system. In their simultaneous presence there is competition between the destabilizing role of the Hall current and the stabilizing role of the FLR, and each succeeds in stabilizing a certain wavenumber range. In the absence of a magnetic field (and hence the absence of an FLR and Hall current), the destabilizing effect of medium permeability is seen, but in the presence of a magnetic field (and hence the presence of an FLR and Hall current), the medium permeability may have a stabilizing or a destabilizing effect on the thermal instability of the plasma. The effect of compressibility is found to postpone the onset of thermal instability in plasma.

Sign in / Sign up

Export Citation Format

Share Document