International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2572

Full Length Research Paper

Lattice Boltzmann simulation of the two-dimensional Poiseuille-Rayleigh-Benard flows instability

S. Atock A Nwatchok, C. Mbane Biouele* and H. Ekobena Fouda
Department of Physics, University of Yaoundé I, P. O. Box 812, Yaoundé, Cameroun.
Email: [email protected]

  •  Accepted: 27 May 2010
  •  Published: 31 July 2010


A numerical method based on the lattice Boltzmann equation (LBE) is developed in two dimensions to solve the equations of conservation of energy and momentum of a Poiseuille-Rayleigh-Benard (PRB) mixed-flow. The configuration considered in this work is a channel heated from below, cooled from the top and crossed by a fluid (Pr = 1). The study is conducted for a range of Rayleigh numbers (0 < Ra < 5000) and Reynolds (0 < Re < 500). For Re = 0 and Ra exceeds the critical value (1707.76), the Rayleigh-Benard (RB) mixed-flow appears. However, for Re values other than 0, the transition from Poiseuille flow in a cellular flow is obtained for the largest critical Ra (in limited area) and characteristics of cells depend on the intensity of the flow at the entrance of the channel.


Key words: Poiseuille-Rayleigh-Benard flow, Lattice Boltzmann equation (LBE), horizontal rectangular channel.