Linear stability of quasi-two-dimensional liquid metal duct flow subjected to a transverse magnetic field and vertical temperature stratification

T. Vo, A. Pothérat, G. J. Sheard

Research output: Chapter in Book/Report/Conference proceedingConference PaperOther


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–Bénard 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–Bénard flows are recovered with critical values that are in agreement with previous literature. As H → ∞, the relationships Rec ∞ H1/2 and Rac ∞ H are obtained. Neutral stability curves are obtained for fixed values of low Re and low Ra conditions and are mapped onto Rac–H and Rec–H regimes, respectively. The critical eigenmodes feature characteristics that are consistent with Tollmien–Schlichting waves and Rayleigh–Bénard convection cells.

Original languageEnglish
Title of host publicationProceedings of the 20th Australasian Fluid Mechanics Conference (AFMC)
Subtitle of host publication5-8th December, 2016, Perth, Western Australia
PublisherAustralasian Fluid Mechanics Society
Number of pages4
ISBN (Electronic)9781740523776
Publication statusPublished - 2016
EventAustralasian Fluid Mechanics Conference 2016 - The University of Western Australia, Perth, Australia
Duration: 5 Dec 20168 Dec 2016
Conference number: 20th

Publication series

NameProceedings of the 20th Australasian Fluid Mechanics Conference, AFMC 2016


ConferenceAustralasian Fluid Mechanics Conference 2016
Abbreviated titleAFMC 2016

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