scholarly journals Effects of Magnetic Field and Non-uniform Basic Temperature Gradient on the Onset of Rayleigh-Benard Convection in a Micropolar Fluid

2007 ◽  
Vol 6 (2) ◽  
pp. 1-33
Author(s):  
S. Pranesh
Keyword(s):  
Magnetic Field ◽  
Temperature Gradient ◽  
Suspended Particles ◽  
Conducting Fluid ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Benard Convection ◽  
Basic Temperature ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The effects of magnetic field and non-uniform basic temperature gradient on the onset of Rayleigh-Benard convection in an electrically conducting micro polar fluid are studied using the Garlerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal and adiabatic temperature conditions on the spin-vanishing boundaries. The eigenvalues are also obtained for lower rigid isothermal and upper free adiabatic boundaries with vanishing spin. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the electrically conducting fluid layer with suspended particles heated from below is more stable compared to the classically electrically conducting fluid without suspended particles. The critical wave number is found to be insensitive to the changes in the parameters but sensitive to the changes in the Chandrasekhar number.

scholarly journals Effects of Magnetic Field and Non-Uniform Basic Temperature Gradient

2002 ◽  
Vol 1 (1) ◽  
pp. 1-14
Author(s):  
S. Pranesh
Keyword(s):  
Magnetic Field ◽  
Temperature Gradient ◽  
Fluid Layer ◽  
Suspended Particles ◽  
Conducting Fluid ◽  
Wave Number ◽  
Uniform Temperature ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

The effects of a non-uniform temperature gradient and magnetic field on the onset of convection in a horizontal layer of Boussinesq fluid with suspended particles confined between an upper free/adiabatic boundary and a lower rigid/isothermal boundary have been considered. A linear stability analysis is performed. The microrotation is assumed to vanish at the boundaries. The Galerkin technique is used to obtain the Eigen values. The influence of various parameters on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the electrically conducting fluid layer with suspended particles heated from below is more stable compared to the classical electrically conducting fluid without Suspended particles. The critical wave number is found to be insensitive to the changes in the parameters but sensitive to the changes in the Chandrasekhar number.

Rayleigh–Bénard convection and pattern formation in magnetohydrodynamics

1998 ◽  
Vol 60 (3) ◽  
pp. 529-539 ◽  
Author(s):  
RENU BAJAJ ◽  
S. K. MALIK
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Thermal Instability ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
The Magnetic Field

A nonlinear thermal instability in a layer of electrically conducting fluid in the presence of a magnetic field is discussed. Steady-state bifurcation results in the formation of patterns: rolls, squares and hexagons. The stability of various patterns is also investigated. It is found that in the absence of a magnetic field only rolls are stable, but when the magnetic field strength exceeds a certain finite value, squares and hexagons also become stable.

scholarly journals Bulk scaling in wall-bounded and homogeneous vertical natural convection

2018 ◽  
Vol 841 ◽  
pp. 825-850 ◽  
Author(s):  
Chong Shen Ng ◽  
Andrew Ooi ◽  
Detlef Lohse ◽  
Daniel Chung
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Temperature Gradient ◽  
Power Law ◽  
Exact Relation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Previous numerical studies on homogeneous Rayleigh–Bénard convection, which is Rayleigh–Bénard convection (RBC) without walls, and therefore without boundary layers, have revealed a scaling regime that is consistent with theoretical predictions of bulk-dominated thermal convection. In this so-called asymptotic regime, previous studies have predicted that the Nusselt number ($\mathit{Nu}$) and the Reynolds number ($\mathit{Re}$) vary with the Rayleigh number ($\mathit{Ra}$) according to $\mathit{Nu}\sim \mathit{Ra}^{1/2}$ and $\mathit{Re}\sim \mathit{Ra}^{1/2}$ at small Prandtl numbers ($\mathit{Pr}$). In this study, we consider a flow that is similar to RBC but with the direction of temperature gradient perpendicular to gravity instead of parallel to it; we refer to this configuration as vertical natural convection (VC). Since the direction of the temperature gradient is different in VC, there is no exact relation for the average kinetic dissipation rate, which makes it necessary to explore alternative definitions for $\mathit{Nu}$, $\mathit{Re}$ and $\mathit{Ra}$ and to find physical arguments for closure, rather than making use of the exact relation between $\mathit{Nu}$ and the dissipation rates as in RBC. Once we remove the walls from VC to obtain the homogeneous set-up, we find that the aforementioned $1/2$-power-law scaling is present, similar to the case of homogeneous RBC. When focusing on the bulk, we find that the Nusselt and Reynolds numbers in the bulk of VC too exhibit the $1/2$-power-law scaling. These results suggest that the $1/2$-power-law scaling may even be found at lower Rayleigh numbers if the appropriate quantities in the turbulent bulk flow are employed for the definitions of $\mathit{Ra}$, $\mathit{Re}$ and $\mathit{Nu}$. From a stability perspective, at low- to moderate-$\mathit{Ra}$, we find that the time evolution of the Nusselt number for homogenous vertical natural convection is unsteady, which is consistent with the nature of the elevator modes reported in previous studies on homogeneous RBC.

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