### Abstract

Non-linear solutions and studies of their stability are presented for flows in a homogeneously heated fluid layer under the influence of a constant pressure gradient or when the mass flux across any lateral cross-section of the channel is required to vanish. The critical Grashof number is determined by a linear stability analysis of the basic state which depends only on the z-coordinate perpendicular to the boundary. Bifurcating longitudinal rolls as well as secondary solutions depending on the streamwise x-coordinate are investigated and their amplitudes are determined as functions of the supercritical Grashof number for various Prandtl numbers and angles of inclination of the layer. Solutions that emerge from a Hopf bifurcation assume the form of propagating waves and can thus be considered as steady flows relative to an appropriately moving frame of reference. The stability of these solutions with respect to three-dimensional disturbances is also analyzed in order to identify possible bifurcation points for evolving tertiary flows.

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 | FCV_10 |

ISBN (Print) | 9789038612744 |

Publication status | Published - May 2008 |

### Bibliographical note

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

- non-linear solutions
- homogeneously heated fluid layer
- constant pressure gradient
- critical Grashof number
- linear stability analysis
- bifurcating longitudinal rolls
- secondary
- solutions
- streamwise x-coordinate
- supercritical Grashof number
- Prandtl numbers
- angles of inclination
- Hopf bifurcation

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## Cite this

Generalis, S. C., & Busse, F. (2008). Transition in inclined internally heated fluid layers. In G. G. M. Stoffels, T. H. van der Meer, & A. A. van Steenhoven (Eds.),

*Proceedings 5th European Thermal-Sciences Conference*(pp. FCV_10). Eindhoven University of Technology. http://www.eurotherm2008.tue.nl/Proceedings_Eurotherm2008/papers/Forced_Convection/FCV_10.pdf