### Abstract

In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.

Original language | English |
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Title of host publication | Proceedings 5th European Thermal-Sciences Conference |

Editors | G.G.M. Stoffels, T.H. van der Meer, A.A. van Steenhoven |

Place of Publication | Eindhoven (NL) |

Publisher | Eindhoven University of Technology |

Pages | NCV_2 |

ISBN (Print) | 9789038612744 |

Publication status | Published - May 2008 |

### Bibliographical note

5th European Thermal-Sciences Conference, 18-21 May 2008, Eindhoven (NL).### Keywords

- equilibrium states
- periodic finite amplitude flow
- horizontal channel
- differential heating
- rigid boundaries
- Navier-Stokes equations
- Landau coefficients
- Newton-Raphson iterative method
- Fourier expansion
- Prandtl numbers

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## Cite this

Generalis, S. C., & Fujimura, K. (2008). Range of validity of weakly non-linear theory in Rayleigh-Bénard convection. In G. G. M. Stoffels, T. H. van der Meer, & A. A. van Steenhoven (Eds.),

*Proceedings 5th European Thermal-Sciences Conference*(pp. NCV_2). Eindhoven University of Technology. http://www.eurotherm2008.tue.nl/Proceedings_Eurotherm2008/papers/Natural_Convection/NCV_2.pdf