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 which exhibits inhibition of convection by the field according to as , where Q is the Chandrasekhar number. However, for oscillatory convection we find that the critical Rayleigh number is given by a more complicated function of the thermal Prandtl number , magnetic Prandtl number and Cattaneo number C. To elucidate features of this dependence, we neglect (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 , as . One consequence of this weaker dependence is that onset of instability occurs as overstability provided C exceeds a threshold value CT(Q); indeed, crucially we show that when Q is large, , meaning that oscillatory modes are preferred even when C itself is small. Similar behaviour is demonstrated in the case of fixed boundaries by means of a novel numerical solution.
- Received August 23, 2016.
- Accepted October 17, 2016.
- © 2016 The Author(s)
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