Linear and Weakly Non-Linear Analyses of Gravity Modulation and Electric Field on the Onset of Rayleigh-Bénard Convection in a Micropolar Fluid

Authors

  • S. Pranesh Christ University
  • Sameena Tarannum Christ University, Bangalore
  • T. V. Joseph Christ University, Bangalore

DOI:

https://doi.org/10.24297/jam.v9i3.2426

Keywords:

Gravity modulation, Electric field, Micropolar fluid, Lorenz model.

Abstract

The effect of time periodic body force (or g-jitter or gravity modulation) on the onset of Rayleigh-B©nard electro-convention in a micropolar fluid layer is investigated by making linear and non-linear stability analysis. The stability of the horizontal fluid layer heated from below is examined by assuming time periodic body acceleration. This normally occurs in satellites and in vehicles connected with micro gravity simulation studies. A linear and non-linear analysis is performed to show that gravity modulation can significantly affect the stability limits of the system. The linear theory is based on normal mode analysis and perturbation method. Small amplitude of modulation is used to compute the critical Rayleigh number and wave number. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation. The non-linear analysis is based on the truncated Fourier series representation. The resulting non-autonomous Lorenz model is solved numerically to quantify the heat transport. It is observed that the gravity modulation leads to delayed convection and reduced heat transport.

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Author Biographies

S. Pranesh, Christ University

Department of Mathematics

Professor and coordinator

Sameena Tarannum, Christ University, Bangalore

Department of Professional Studies

T. V. Joseph, Christ University, Bangalore

Department of Mathematics

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Published

2014-08-25

How to Cite

Pranesh, S., Tarannum, S., & Joseph, T. V. (2014). Linear and Weakly Non-Linear Analyses of Gravity Modulation and Electric Field on the Onset of Rayleigh-Bénard Convection in a Micropolar Fluid. JOURNAL OF ADVANCES IN MATHEMATICS, 9(3), 2057–2082. https://doi.org/10.24297/jam.v9i3.2426

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Articles