## Abstract

The linear stability of a magnetohydrodynamic duct flow with heating from below is investigated and serves as an extension to the class of Poiseuille–Rayleigh–B´enard flows. Such flows can be found in the blankets of nuclear fusion reactors and have been of great interest in recent times due to the endeavour of demonstrating the viability of nuclear fusion as a future energy source. The flow is described by the quasi-two-dimensional model proposed by Sommeria and Moreau [12] coupled with the energy transport equation through the Boussinesq approximation. The onset of several instability modes in this system is studied as functions of the non-dimensional governing parameters: Reynolds number

*Re*, Rayleigh number*Ra*, and modified Hartmann number*H*. As*H*→0, the classical plane plane Poiseuille and Rayleigh–B´enard flows are recovered with critical values that are in agreement with previous literature. As*H*→∞, the relationships*Re*∞ H_{c}^{1/2}and*Ra*∞ H are obtained. Neutral stability curves are obtained for fixed values of low Re and low Ra conditions and are mapped onto_{c}*Ra*and_{c}–H*Re*regimes, respectively. The critical eigenmodes feature characteristics that are consistent with Tollmien–Schlichting waves and Rayleigh–Benard convection cells._{c}–HOriginal language | English |
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Title of host publication | Proceedings of the 20th Australasian Fluid Mechanics Conference (AFMC) |

Subtitle of host publication | 5-8^{th} December, 2016, Perth, Western Australia |

Publisher | Australasian Fluid Mechanics Society |

Number of pages | 4 |

ISBN (Electronic) | 9781740523776 |

Publication status | Published - Dec 2016 |

Event | Australasian Fluid Mechanics Conference 2016 - The University of Western Australia, Perth, Australia Duration: 5 Dec 2016 → 8 Dec 2016 Conference number: 20th |

### Conference

Conference | Australasian Fluid Mechanics Conference 2016 |
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Abbreviated title | AFMC 2016 |

Country | Australia |

City | Perth |

Period | 5/12/16 → 8/12/16 |