Thermal Instability in Rayleigh-Benard Configuration
by
B. S. Bhadauria
Department of Mathematics and Statistics, Jai Narain Vyas University Jodhpur, India-342001

Abstract: Thermal instability in a fluid layer confined between two horizontal rigid walls is studied with the help of the Floquet theory. The temperature distribution between the walls consists of a steady part and an oscillatory time-dependent part. The time-dependent part of the temperature is approximated by some function and expressed in Fourier series. Disturbances are assumed to be infinitesimal. Only even eigenfunctions are approximated. Numerical results for the critical Rayleigh numbers and wave numbers are obtained for various values of the parameters. It is found that time modulation of the wall temperatures can significantly affect the onset of instability. It can advance or delay the onset of convection. Also formation of convective cells in the fluid layer is studied with the help of the Floquet theory. It is found that the disturbances are either synchronous with the primary temperature field or have half its frequency. Some comparisons have also been made.

Key words and Phrases: Modulation, Instability, Rayleigh number, Even eigenfunctions, Thermal convection.

2000 Mathematics Subject Classification: 76E06, 76R10.

Date received: May 26, 2003