Effect of internal-heating on weakly non-linear stability analysis of Rayleigh-Bénard convection under g-jitter

B. S. Bhadauria, I. Hashim, P. G. Siddheshwar

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In this paper, we study the combined effect of internal-heating and time-periodic gravity modulation on thermal instability in a viscous fluid layer, heated from below. The time-periodic gravity modulation, considered in this problem can be realized by vertically oscillating the fluid layer. A weak non-linear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number has been obtained in terms of the amplitude of convection which is governed by the non-autonomous Ginzburg-Landau equation derived for the stationary mode of convection. Effects of various parameters such as internal Rayleigh number, Prandtl number, and amplitude and frequency of gravity modulation have been analysed on heat transport. It is found that the response of the convective system to the internal Rayleigh number is destabilizing. Further, it is found that the heat transport can be controlled by suitably adjusting the external parameters of the system.

Original languageEnglish
Pages (from-to)35-42
Number of pages8
JournalInternational Journal of Non-Linear Mechanics
Volume54
DOIs
Publication statusPublished - 2013

Fingerprint

Nonlinear Stability
Jitter
Nonlinear Analysis
Rayleigh
Convection
Heating
Stability Analysis
Gravity
Gravitation
Modulation
Internal
Heat Transport
Rayleigh number
Nonautonomous Equation
Power Series Expansion
Fluids
Ginzburg-Landau Equation
Nusselt number
Prandtl number
Viscous Fluid

Keywords

  • Ginzburg-Landau equation
  • Gravity modulation
  • Internal heating
  • Non-linear stability analysis

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Applied Mathematics

Cite this

Effect of internal-heating on weakly non-linear stability analysis of Rayleigh-Bénard convection under g-jitter. / Bhadauria, B. S.; Hashim, I.; Siddheshwar, P. G.

In: International Journal of Non-Linear Mechanics, Vol. 54, 2013, p. 35-42.

Research output: Contribution to journalArticle

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N2 - In this paper, we study the combined effect of internal-heating and time-periodic gravity modulation on thermal instability in a viscous fluid layer, heated from below. The time-periodic gravity modulation, considered in this problem can be realized by vertically oscillating the fluid layer. A weak non-linear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number has been obtained in terms of the amplitude of convection which is governed by the non-autonomous Ginzburg-Landau equation derived for the stationary mode of convection. Effects of various parameters such as internal Rayleigh number, Prandtl number, and amplitude and frequency of gravity modulation have been analysed on heat transport. It is found that the response of the convective system to the internal Rayleigh number is destabilizing. Further, it is found that the heat transport can be controlled by suitably adjusting the external parameters of the system.

AB - In this paper, we study the combined effect of internal-heating and time-periodic gravity modulation on thermal instability in a viscous fluid layer, heated from below. The time-periodic gravity modulation, considered in this problem can be realized by vertically oscillating the fluid layer. A weak non-linear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number has been obtained in terms of the amplitude of convection which is governed by the non-autonomous Ginzburg-Landau equation derived for the stationary mode of convection. Effects of various parameters such as internal Rayleigh number, Prandtl number, and amplitude and frequency of gravity modulation have been analysed on heat transport. It is found that the response of the convective system to the internal Rayleigh number is destabilizing. Further, it is found that the heat transport can be controlled by suitably adjusting the external parameters of the system.

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