Selective control of Poiseuille–Rayleigh–Bénard instabilities by a spanwise magnetic field

Abstract

The stability of a pressure driven flow in an electrically conducting fluid heated from below and subjected to a spanwise constant magnetic field is investigated through a linear stability analysis. The numerical calculations show that such a magnetic field only affects the longitudinal stationary modes ͑L͒, which are stabilized, and has no effect on the transverse traveling modes ͑T͒. A direct consequence is the expansion of the domain where the transverse traveling ͑T͒ modes prevail. This expansion is controlled by the strength of the spanwise magnetic field, expressed through the Hartmann number ͑Ha, ratio of magnetic to viscous dissipation forces͒. Moreover, when Ha exceeds a limiting value depending on the Prandtl number, the ͑T͒ modes become the only dominant modes in the whole Re range. Particular attention was dedicated to the oblique modes ͑O͒ corresponding to fully three-dimensional disturbances in order to verify that they never become the dominant modes when the magnetic field is applied, similarly to what was found without magnetic field. From a practical point of view, these results could be of a great interest since it is known that the optimization of several processes involving the Poiseuille-Rayleigh-Bénard flow is achieved when the traveling ͑T͒ modes prevail.

Linear stability of horizontal, laminar fully developed, quasi-two-dimensional liquid metal duct flow under a transverse magnetic field and heated from below

“…Note that the critical Ra for the onset of peak II mode initially decreases with increasing H but begins to increase again beyond H = 100. It is worth mentioning that qualitatively similar stability diagrams have been produced by Fakhfakh et al [16] for different Prandtl number liquids in a flow heated from below with vertical and horizontal magnetic fields. However, that study investigated an infinite domain where friction from the Hartmann walls are absent and therefore direct comparisons with the present study cannot be performed.…”

“…Specifically, the stability (e.g. [15][16][17][18]) and heat transfer properties of a liquid metal flow is of great importance to the future designs of experimental fusion reactors where maximising heat transfer is a key criterion. The enhancement of heat transfer and instability growth in MHD flows can be achieved by implementing turbulent promoters such as bluff bodies [19][20][21] and current injection [22].…”

The linear stability of Hunt-Rayleigh-Bénard flow

“…Besides, the boundary curves of the absolute instability (AI) and convective instability (CI) were also given. Futhermore, in the studies of Fakhfakh et al, 20,21 their results showed that the spanwise magnetic field could stabilize the longitudinal stationary (L) modes but had no effect on the transverse traveling (T) modes, and the (T) modes became the only dominant modes in the whole Re range when Ha exceeded a limiting value. As for the duct flow, Pelekasis 22 adopted the linear stability analysis and dynamic simulations to study the free convection in a differentially heated cavity under a horizontal magnetic field.…”