title: Thermal convection in a magnetized conducting fluid with the Cattaneo-Christov heat-flow model.
abstract: By substituting the Cattaneo-Christov heat-flow model for the more usual parabolic Fourier law, we consider the impact of hyperbolic heat-flow effects on thermal convection in the classic problem of a magnetized conducting fluid layer heated from below. For stationary convection, the system is equivalent to that studied by Chandrasekhar (Hydrodynamic and Hydromagnetic Stability,1961), and with free boundary conditions we recover the classical critical Rayleigh number [Formula: see text] which exhibits inhibition of convection by the field according to [Formula: see text] as [Formula: see text], whereQis the Chandrasekhar number. However, for oscillatory convection we find that the critical Rayleigh number [Formula: see text] is given by a more complicated function of the thermal Prandtl number [Formula: see text], magnetic Prandtl number [Formula: see text] and Cattaneo numberC. To elucidate features of this dependence, we neglect [Formula: see text] (in which case overstability would be classically forbidden), and thereby obtain an expression for the Rayleigh number that is far less strongly inhibited by the field, with limiting behaviour [Formula: see text], as [Formula: see text]. One consequence of this weaker dependence is that onset of instability occurs as overstability providedCexceeds a threshold valueCT(Q); indeed, crucially we show that whenQis large, [Formula: see text], meaning that oscillatory modes are preferred even whenCitself is small. Similar behaviour is demonstrated in the case of fixed boundaries by means of a novel numerical solution.
authors.affiliation: Department of Physics , University of Bath , BA2 7AY Bath, UK.
authors.forename: J J
authors.identifier: 0000-0002-8364-8085
authors.initials: JJ
authors.lastname: Bissell
keywords: Cattaneo–Christov model; Rayleigh–Bénard problem; buoyancy-driven instabilities; hyperbolic heat-flow; magnetized thermal convection; oscillatory convection