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 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 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 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.

Rayleigh-Benard Convection With Second-Sound in a Viscoelastic Fluid-Filled High-Porosity Medium

2003 ◽  
Author(s):  
P. G. Siddheshwar ◽  
C. V. Srikrishna
Keyword(s):  
Heat Flux ◽  
Viscoelastic Fluid ◽  
Critical Rayleigh Number ◽  
Momentum Equation ◽  
Heat Propagation ◽  
High Porosity ◽  
Eigen Value ◽  
Heat Flux Law ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The linear stability of the Rayleigh-Benard situation in a viscoelastic fluid occupying a high-porosity medium is investigated. The viscoelastic correction to Brinkman momentum equation is effected by considering the modified form of Jeffrey constitutive equation. Further, the non-classical Maxwell-Cattaneo heat flux has been used in place of the classical Fourier heat flux law. The results of the study reveal that the non-classical theory predicts finite speeds of heat propagation. The eigen value is obtained for free-free, isothermal boundary combinations and it has been observed that the critical Rayleigh number is less than the corresponding value of the problem governed by the classical Fourier law. The study finds application in progressive solidification of polymeric melts and solutions, and also in the manufacture of composite materials.

scholarly journals Uniform Solution on the Combined Effect of Magnetic Field and Internal Heat Generation on Rayleigh–Bénard Convection in Micropolar Fluid

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
I. K. Khalid ◽  
N. F. M. Mokhtar ◽  
N. M. Arifin
Keyword(s):  
Magnetic Field ◽  
Heat Generation ◽  
Micropolar Fluid ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Combined Effect ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Combined effect of magnetic field and internal heat generation on the onset of Rayleigh–Bénard convection in a horizontal micropolar fluid layer is studied. The bounding surfaces of the liquids are considered to be rigid-free, rigid-rigid, and free-free with combination isothermal on the spin-vanishing boundaries. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. The influence of various parameters on the onset of convection has been analyzed. It is shown that the presence of magnetic field always has a stability effect on the Rayleigh–Bénard convection in micropolar fluid.

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