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Stability of ferrofluid flows in a horizontal channel subjected to a longitudinal temperature gradient and an oblique magnetic field

par Slavtchev, Slavtcho;Hennenberg, Marcel ;Valchev, Galin;Weyssow, Boris
Référence Microgravity, science and technology, 20, 3-4, page (199-203)
Publication Publié, 2008-09

Article révisé par les pairs

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Résumé :

The stability of thermoconvective flows of a ferrofluid in a horizontal channel subjected to a longitudinal temperature gradient and an oblique strong magnetic field is studied. The flows are governed by the mass, momentum, heat balance and Maxwell equations, in the Boussinesq approximation. Strong magnetic fields are characterized by a small parameter measuring the deviation of the magnetization across the layer from the external magnetic field. An approximate solution of the stationary hydrodynamic problem was found in analytical form in Hennenberg et al. (Phys Fluids 18:093602, 2006). The flow depends on the thermal (gravitational) and magnetic Rayleigh numbers. In the present paper the linear stability of that basic flow is studied by the Galerkin method. The analysis shows that for large Prandtl numbers, typical for ferrofluids, and relatively small magnetic Rayleigh numbers, only oscillatory instability can appear. For a given magnetic Rayleigh number, the critical wavenumber does not depend on the inclination of the magnetic field, while the critical thermal Rayleigh number slightly changes. For horizontal and vertical magnetic fields, both critical numbers decrease when increasing the magnetic Rayleigh number. © 2008 Springer Science+Business Media B.V.