Non-linear Chandrasekhar-Bénard convectionin temperature-dependent variable viscosity Boussinesq-Stokes suspension fluid with variable heat source/sink

Nagasundar Kavitha; Agrahara Sanjeevmurthy Aruna; MKoppalu Shankarappa Basavaraj; Venkatesh Ramachandramurthy

Applications of Mathematics (2023)

  • Volume: 68, Issue: 3, page 357-376
  • ISSN: 0862-7940

Abstract

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The generalized Lorenz model for non-linear stability of Rayleigh-Bénard magneto-convection is derived in the present paper. The Boussinesq-Stokes suspension fluid in the presence of variable viscosity (temperature-dependent viscosity) and internal heat source/sink is considered in this study. The influence of various parameters like suspended particles, applied vertical magnetic field, and the temperature-dependent heat source/sink has been analyzed. It is found that the basic state of the temperature gradient, viscosity variation, and the magnetic field can be conveniently expressed using the half-range Fourier cosine series. This facilitates to determine the analytical expression of the eigenvalue (thermal Rayleigh number) of the problem. From the analytical expression of the thermal Rayleigh number, it is evident that the Chandrasekhar number, internal Rayleigh number, Boussinesq-Stokes suspension parameters, and the thermorheological parameter influence the onset of convection. The non-linear theory involves the derivation of the generalized Lorenz model which is essentially a coupled autonomous system and is solved numerically using the classical Runge-Kutta method of the fourth order. The quantification of heat transfer is possible due to the numerical solution of the Lorenz system. It has been shown that the effect of heat source and temperature-dependent viscosity advance the onset of convection and thereby give rise to enhancing the heat transport. The Chandrasekhar number and the couple-stress parameter have stabilizing effects and reduce heat transfer. This problem has possible applications in the context of the magnetic field which influences the stability of the fluid.

How to cite

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Kavitha, Nagasundar, et al. "Non-linear Chandrasekhar-Bénard convectionin temperature-dependent variable viscosity Boussinesq-Stokes suspension fluid with variable heat source/sink." Applications of Mathematics 68.3 (2023): 357-376. <http://eudml.org/doc/299474>.

@article{Kavitha2023,
abstract = {The generalized Lorenz model for non-linear stability of Rayleigh-Bénard magneto-convection is derived in the present paper. The Boussinesq-Stokes suspension fluid in the presence of variable viscosity (temperature-dependent viscosity) and internal heat source/sink is considered in this study. The influence of various parameters like suspended particles, applied vertical magnetic field, and the temperature-dependent heat source/sink has been analyzed. It is found that the basic state of the temperature gradient, viscosity variation, and the magnetic field can be conveniently expressed using the half-range Fourier cosine series. This facilitates to determine the analytical expression of the eigenvalue (thermal Rayleigh number) of the problem. From the analytical expression of the thermal Rayleigh number, it is evident that the Chandrasekhar number, internal Rayleigh number, Boussinesq-Stokes suspension parameters, and the thermorheological parameter influence the onset of convection. The non-linear theory involves the derivation of the generalized Lorenz model which is essentially a coupled autonomous system and is solved numerically using the classical Runge-Kutta method of the fourth order. The quantification of heat transfer is possible due to the numerical solution of the Lorenz system. It has been shown that the effect of heat source and temperature-dependent viscosity advance the onset of convection and thereby give rise to enhancing the heat transport. The Chandrasekhar number and the couple-stress parameter have stabilizing effects and reduce heat transfer. This problem has possible applications in the context of the magnetic field which influences the stability of the fluid.},
author = {Kavitha, Nagasundar, Aruna, Agrahara Sanjeevmurthy, Basavaraj, MKoppalu Shankarappa, Ramachandramurthy, Venkatesh},
journal = {Applications of Mathematics},
keywords = {Rayleigh-Bénard convection; heat source/sink; Boussinesq-Stokes suspension; Boussinesq approximation; Lorenz model},
language = {eng},
number = {3},
pages = {357-376},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Non-linear Chandrasekhar-Bénard convectionin temperature-dependent variable viscosity Boussinesq-Stokes suspension fluid with variable heat source/sink},
url = {http://eudml.org/doc/299474},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Kavitha, Nagasundar
AU - Aruna, Agrahara Sanjeevmurthy
AU - Basavaraj, MKoppalu Shankarappa
AU - Ramachandramurthy, Venkatesh
TI - Non-linear Chandrasekhar-Bénard convectionin temperature-dependent variable viscosity Boussinesq-Stokes suspension fluid with variable heat source/sink
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 3
SP - 357
EP - 376
AB - The generalized Lorenz model for non-linear stability of Rayleigh-Bénard magneto-convection is derived in the present paper. The Boussinesq-Stokes suspension fluid in the presence of variable viscosity (temperature-dependent viscosity) and internal heat source/sink is considered in this study. The influence of various parameters like suspended particles, applied vertical magnetic field, and the temperature-dependent heat source/sink has been analyzed. It is found that the basic state of the temperature gradient, viscosity variation, and the magnetic field can be conveniently expressed using the half-range Fourier cosine series. This facilitates to determine the analytical expression of the eigenvalue (thermal Rayleigh number) of the problem. From the analytical expression of the thermal Rayleigh number, it is evident that the Chandrasekhar number, internal Rayleigh number, Boussinesq-Stokes suspension parameters, and the thermorheological parameter influence the onset of convection. The non-linear theory involves the derivation of the generalized Lorenz model which is essentially a coupled autonomous system and is solved numerically using the classical Runge-Kutta method of the fourth order. The quantification of heat transfer is possible due to the numerical solution of the Lorenz system. It has been shown that the effect of heat source and temperature-dependent viscosity advance the onset of convection and thereby give rise to enhancing the heat transport. The Chandrasekhar number and the couple-stress parameter have stabilizing effects and reduce heat transfer. This problem has possible applications in the context of the magnetic field which influences the stability of the fluid.
LA - eng
KW - Rayleigh-Bénard convection; heat source/sink; Boussinesq-Stokes suspension; Boussinesq approximation; Lorenz model
UR - http://eudml.org/doc/299474
ER -

References

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