Oscillatory Heating in Rayleigh-Benard Configuration
by
B. S. Bhadauria
Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur, India. Current: Department of Mathematics, Eritrean Institute of Technology Asmara, Eritrea (N. E. Africa)

Linear convective instability of a horizontal fluid layer confined between two rigid boundaries and heated from below is considered. The temperature distribution between the walls consists of two parts; a steady part and a time-dependent oscillatory part. The time-dependent part has been expressed in Fourier series. Disturbances are assumed to be infinitesimal. Only odd solutions are considered. The formation of convective cells in the fluid layer is studied with the help of the Floquet theory. Numerical results for the critical Rayleigh number are obtained for a Prandtl number of 0.71(air). It is found that the disturbances are either synchronous with the primary temperature field or have half its frequency.

Key words and Phrases: Modulation, Stability, Rayleigh number, Odd solution, Thermal convection.

2000 Mathematics Subject Classification: 76E06, 76R10.

Date received: October 9, 2004