Effects of variable viscosity and temperature modulation on linear Rayleigh-Bénard convection in Newtonian dielectric liquid

doi:10.1007/s10483-019-2537-9

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (11): 1601-1614.doi: https://doi.org/10.1007/s10483-019-2537-9

Effects of variable viscosity and temperature modulation on linear Rayleigh-Bénard convection in Newtonian dielectric liquid

P. G. SIDDHESHWAR¹, D. UMA², S. BHAVYA³

1. Department of Mathematics, Bangalore University, Bengaluru 560056, India;
2. Department of Computer Science and Engineering, PES University, Bengaluru 560085, India;
3. Department of Mathematics, Atria Institute of Technology, Bengaluru 560024, India

收稿日期:2019-02-27 修回日期:2019-06-05 出版日期:2019-11-01 发布日期:2019-10-28
通讯作者: S. BHAVYA E-mail:bhavyashivaraj@gmail.com

Effects of variable viscosity and temperature modulation on linear Rayleigh-Bénard convection in Newtonian dielectric liquid

P. G. SIDDHESHWAR¹, D. UMA², S. BHAVYA³

1. Department of Mathematics, Bangalore University, Bengaluru 560056, India;
2. Department of Computer Science and Engineering, PES University, Bengaluru 560085, India;
3. Department of Mathematics, Atria Institute of Technology, Bengaluru 560024, India

Received:2019-02-27 Revised:2019-06-05 Online:2019-11-01 Published:2019-10-28
Contact: S. BHAVYA E-mail:bhavyashivaraj@gmail.com

摘要/Abstract

摘要： The linear Rayleigh-Bénard electro-convective stability of the Newtonian dielectric liquid is determined theoretically subject to the temperature modulation with time. A perturbation method is used to compute the critical Rayleigh number and the wave number. The critical Rayleigh number is calculated as a function of the frequency of modulation, the temperature-dependent variable viscosity, the electric field dependent variable viscosity, the Prandtl number, and the electric Rayleigh number. The effects of all three cases of modulations are established to delay or advance the onset of the convection process. In addition, how the effect of variable viscosity controls the onset of convection is studied.

关键词: dielectric liquid, temperature dependent variable viscosity, electric field dependent variable viscosity, electric Rayleigh number, temperature modulation

Abstract: The linear Rayleigh-Bénard electro-convective stability of the Newtonian dielectric liquid is determined theoretically subject to the temperature modulation with time. A perturbation method is used to compute the critical Rayleigh number and the wave number. The critical Rayleigh number is calculated as a function of the frequency of modulation, the temperature-dependent variable viscosity, the electric field dependent variable viscosity, the Prandtl number, and the electric Rayleigh number. The effects of all three cases of modulations are established to delay or advance the onset of the convection process. In addition, how the effect of variable viscosity controls the onset of convection is studied.

Key words: dielectric liquid, temperature dependent variable viscosity, electric field dependent variable viscosity, electric Rayleigh number, temperature modulation

中图分类号:

P. G. SIDDHESHWAR, D. UMA, S. BHAVYA. Effects of variable viscosity and temperature modulation on linear Rayleigh-Bénard convection in Newtonian dielectric liquid[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(11): 1601-1614.

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Effects of variable viscosity and temperature modulation on linear Rayleigh-Bénard convection in Newtonian dielectric liquid

Effects of variable viscosity and temperature modulation on linear Rayleigh-Bénard convection in Newtonian dielectric liquid

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