scholarly journals Effect of Non-Uniform Temperature Gradient on the Onset of Rayleigh–Bénard–Magnetoconvection in Micropolar Fluid with Maxwell–Cattaneo Law

2012 ◽  
Vol 11 (3) ◽  
pp. 193-214
Author(s):  
S Pranesh ◽  
R V Kiran
Keyword(s):  
Temperature Gradient ◽  
Micropolar Fluid ◽  
Isothermal Condition ◽  
Propagation Speed ◽  
Heat Propagation ◽  
Uniform Temperature ◽  
Onset Of Convection ◽  
Linear Temperature ◽  
Rayleigh Benard ◽  
Heat Propagation Speed

The effect of non-uniform temperature gradient on the onset of Rayleigh-Bénard magnetoconvection in a Micropolar fluid with Maxwell-Cattaneo law is studied using the Galerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal condition on the spin-vanishing boundaries. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. One linear and five non-linear temperature profiles are considered and their comparative influence on onset of convection is discussed. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (Second Sound) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed.

scholarly journals Gradient on Rayleigh–Bénard – Marangoni – Magnetoconvection in a Micropolar Fluid with Maxwell – Cattaneo Law

2015 ◽  
Vol 14 (3) ◽  
pp. 1-22
Author(s):  
R V Kiran ◽  
Attluri Kalyani
Keyword(s):  
Micropolar Fluid ◽  
Propagation Speed ◽  
Heat Propagation ◽  
Temperature Profiles ◽  
Wave Type ◽  
Onset Of Convection ◽  
Linear Temperature ◽  
Eigen Value ◽  
Rayleigh Benard ◽  
Heat Propagation Speed

The effect of non-uniform temperature gradient on the onset of Rayleigh-Bénard-Marangoni- Magneto-convection in a Micropolar fluid with Maxwell-Cattaneo law is studied using the Galerkin technique. The eigen value is obtained for rigid-free velocity boundary combination with isothermal and adiabatic condition on the spin-vanishing boundaries. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. One linear and five non-linear temperature profiles are considered and their comparative influence on onset is discussed. The classical approach predicts an infinite speed for the propagation of heat.  The present non-classical theory involves a wave type heat transport (Second Sound) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed.

scholarly journals Effect of Second Sound on the Onset of Rayleigh- Benard Convection in a Micropolar Fluid

2008 ◽  
Vol 7 (1) ◽  
pp. 26-40
Author(s):  
S. Pranesh
Keyword(s):  
Micropolar Fluid ◽  
Propagation Speed ◽  
Heat Propagation ◽  
Second Sound ◽  
Fourier Law ◽  
Wave Type ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Short Times ◽  
Heat Propagation Speed

The effects resulting from the substitution of the classical Fourier law by the non-classical Maxwell-Cattaneo law in Rayleigh-Benard convention in micropolar fluid is studied. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical sign values are less than the classical ones.

scholarly journals Effect of Second Sound on the Onset of Rayleigh-Benard Convection in a Coleman - Noll Fluid

2008 ◽  
Vol 7 (2) ◽  
pp. 1-9
Author(s):  
S. Pranesh
Keyword(s):  
Propagation Speed ◽  
Heat Propagation ◽  
Second Sound ◽  
Fourier Law ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Short Times ◽  
Heat Propagation Speed

This paper deals with linear stability analysis of the effects resulting from the substitution of the classical Fourier law by the non-classical Maxwell - Cattaneo law in Rayleigh - Benard convection in second order fluid is studies. Coleman-Noll constitutive equaion is used to give a viscoelastic correction. The eigenvalue is obtained for free - free isothernal boundary combination. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigenvalues are less than the classical ones.

scholarly journals Effects of Suction–Injection–Combination (SIC) on the onset of Rayleigh–Bénard Electroconvection in a Micropolar Fluid

2015 ◽  
Vol 14 (3) ◽  
pp. 23-42 ◽  
Author(s):  
S Pranesh ◽  
Tarannum Sameena ◽  
Baby Riya
Keyword(s):  
Stability Analysis ◽  
Micropolar Fluid ◽  
Fluid Layer ◽  
Suspended Particles ◽  
Wave Number ◽  
Critical Wave Number ◽  
Onset Of Convection ◽  
Temperature Boundary ◽  
The Stability ◽  
Rayleigh Benard

The effect of Suction – injection combination on the onset of Rayleigh – Bénard electroconvection micropolar fluid is investigated by making a linear stability analysis. The Rayleigh-Ritz technique is used to obtain the eigenvalues for different velocity and temperature boundary combinations. The influence of various parameters on the onset of convection has been analysed. It is found that the effect of Prandtl number on the stability of the system is dependent on the SIC being pro-gravity or anti-gravity. A similar Pe-sensitivity is found in respect of the critical wave number. It is observed that the fluid layer with suspended particles heated from below is more stable compared to the classical fluid layer without suspended particles.

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.

scholarly journals Rayleigh-Bѐnard Convection in a Second-Order Fluid with Maxwell-Cattaneo Law

2012 ◽  
Vol 2 ◽  
pp. 24-32 ◽  
Author(s):  
Smita Saklesh Nagouda ◽  
Subbarama Pranesh
Keyword(s):  
Boundary Conditions ◽  
Critical Rayleigh Number ◽  
Propagation Speed ◽  
Heat Propagation ◽  
Second Order ◽  
Onset Of Convection ◽  
Eigen Value ◽  
Eigen Values ◽  
Heat Flux Law ◽  
Short Times

The objective of the paper is to study the Rayleigh-Bѐnard convection in second order fluid by replacing the classical Fourier heat law by non-classical Maxwell-Cattaneo law using Galerkin technique. The eigen value of the problem is obtained using the general boundary conditions on velocity and third type of boundary conditions on temperature. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. The classical Fourier flux law over predicts the critical Rayleigh number compared to that predicted by the non-classical law. The present non-classical Maxwell-Cattaneo heat flux law involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigen values are less than the classical ones. Over stability is the preferred mode of convection.

Thermorheological and Magnetorheological Effects on Rayleigh-Bénard-Marangoni Convection in Ferromagnetic Liquids With Non-Uniform Basic Temperature Gradient

2013 ◽  
Author(s):  
Gummadi Narendra Sekhar ◽  
Jayalatha Gopal ◽  
Prakash Revanna
Keyword(s):  
Temperature Gradient ◽  
Heat Source ◽  
Variable Viscosity ◽  
Variable Coefficients ◽  
Tight Coupling ◽  
Onset Of Convection ◽  
Interesting Possibility ◽  
Basic Temperature ◽  
Source Sink ◽  
Rayleigh Benard

A linear stability analysis of buoyancy and surface tension driven convection in temperature and magnetic field sensitive Newtonian ferromagnetic liquid is studied. The importance of this problem lies in the interesting possibility of regulating convection using a heat source (sink). The problem discussed in this paper leads to a situation that the basic temperature gradient here is non-uniform. The governing equations thereby are of variable coefficients. The principle of exchange of stabilities is shown to be valid. The critical values are obtained using higher order Galerkin technique. The influence of various magnetic and nonmagnetic parameters on the onset of convection has been analyzed. It is found that there is tight coupling between Rayleigh and Marangoni numbers, with an increase in one resulting in a decrease in the other. Variable viscosity parameter and heat source destabilize the system. The effect of heat sink is to stabilize the system. Buoyancy magnetization parameter destabilizes the system both in presence/absence of heat source/sink.

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