International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 19, Pages 991-1001

Effects of modulation on Rayleigh-Benard convection. Part I

B. S. Bhadauria1,2 and Lokenath Debnath3

1Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur 342001, India
2Department of Mathematics, Eritrea Institute of Technology, Asmara, Eritrea
3Department of Mathematics, University of Texas - Pan American, Edinburg 78539-2999, TX, USA

Received 10 November 2002; Revised 9 February 2003

Copyright © 2004 B. S. Bhadauria and Lokenath Debnath. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The linear stability of a horizontal layer of fluid heated from below and above is considered. In addition to a steady temperature difference between the walls of the fluid layer, a time-dependent periodic perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. Numerical results for the critical Rayleigh number are obtained at various Prandtl numbers and for various values of the frequency. Some comparisons have been made with the known results.