The effect of a magnetic field on the onset of Bénard convection in variable viscosity couple-stress fluids using classical Lorenz model

Venkatesh Ramachandramurthy; Nagasundar Kavitha; Agrahara Sanjeevmurthy Aruna

Applications of Mathematics (2022)

  • Volume: 67, Issue: 4, page 509-523
  • ISSN: 0862-7940

Abstract

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The Rayleigh-Bénard convection for a couple-stress fluid with a thermorheological effect in the presence of an applied magnetic field is studied using both linear and non-linear stability analysis. This problem discusses the three important mechanisms that control the onset of convection; namely, suspended particles, an applied magnetic field, and variable viscosity. It is found that the thermorheological parameter, the couple-stress parameter, and the Chandrasekhar number influence the onset of convection. The effect of an increase in the thermorheological parameter leads to destabilization in the system, while the Chandrasekhar number and the couple-stress parameter have the opposite effect. The generalized Lorenz's model of the problem is essentially the classical Lorenz model but with coefficients involving the impact of three mechanisms as discussed earlier. The classical Lorenz model is a fifth-order autonomous system and found to be analytically intractable. Therefore, the Lorenz system is solved numerically using the Runge-Kutta method in order to quantify heat transfer. An effect of increasing the thermorheological parameter is found to enhance heat transfer, while the couple-stress parameter and the Chandrasekhar number diminishes the same.

How to cite

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Ramachandramurthy, Venkatesh, Kavitha, Nagasundar, and Aruna, Agrahara Sanjeevmurthy. "The effect of a magnetic field on the onset of Bénard convection in variable viscosity couple-stress fluids using classical Lorenz model." Applications of Mathematics 67.4 (2022): 509-523. <http://eudml.org/doc/298321>.

@article{Ramachandramurthy2022,
abstract = {The Rayleigh-Bénard convection for a couple-stress fluid with a thermorheological effect in the presence of an applied magnetic field is studied using both linear and non-linear stability analysis. This problem discusses the three important mechanisms that control the onset of convection; namely, suspended particles, an applied magnetic field, and variable viscosity. It is found that the thermorheological parameter, the couple-stress parameter, and the Chandrasekhar number influence the onset of convection. The effect of an increase in the thermorheological parameter leads to destabilization in the system, while the Chandrasekhar number and the couple-stress parameter have the opposite effect. The generalized Lorenz's model of the problem is essentially the classical Lorenz model but with coefficients involving the impact of three mechanisms as discussed earlier. The classical Lorenz model is a fifth-order autonomous system and found to be analytically intractable. Therefore, the Lorenz system is solved numerically using the Runge-Kutta method in order to quantify heat transfer. An effect of increasing the thermorheological parameter is found to enhance heat transfer, while the couple-stress parameter and the Chandrasekhar number diminishes the same.},
author = {Ramachandramurthy, Venkatesh, Kavitha, Nagasundar, Aruna, Agrahara Sanjeevmurthy},
journal = {Applications of Mathematics},
keywords = {Rayleigh-Bénard convection; Boussinesq-Stokes suspension; variable viscosity; magnetoconvection; Lorenz model},
language = {eng},
number = {4},
pages = {509-523},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The effect of a magnetic field on the onset of Bénard convection in variable viscosity couple-stress fluids using classical Lorenz model},
url = {http://eudml.org/doc/298321},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Ramachandramurthy, Venkatesh
AU - Kavitha, Nagasundar
AU - Aruna, Agrahara Sanjeevmurthy
TI - The effect of a magnetic field on the onset of Bénard convection in variable viscosity couple-stress fluids using classical Lorenz model
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 4
SP - 509
EP - 523
AB - The Rayleigh-Bénard convection for a couple-stress fluid with a thermorheological effect in the presence of an applied magnetic field is studied using both linear and non-linear stability analysis. This problem discusses the three important mechanisms that control the onset of convection; namely, suspended particles, an applied magnetic field, and variable viscosity. It is found that the thermorheological parameter, the couple-stress parameter, and the Chandrasekhar number influence the onset of convection. The effect of an increase in the thermorheological parameter leads to destabilization in the system, while the Chandrasekhar number and the couple-stress parameter have the opposite effect. The generalized Lorenz's model of the problem is essentially the classical Lorenz model but with coefficients involving the impact of three mechanisms as discussed earlier. The classical Lorenz model is a fifth-order autonomous system and found to be analytically intractable. Therefore, the Lorenz system is solved numerically using the Runge-Kutta method in order to quantify heat transfer. An effect of increasing the thermorheological parameter is found to enhance heat transfer, while the couple-stress parameter and the Chandrasekhar number diminishes the same.
LA - eng
KW - Rayleigh-Bénard convection; Boussinesq-Stokes suspension; variable viscosity; magnetoconvection; Lorenz model
UR - http://eudml.org/doc/298321
ER -

References

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