title: On oscillatory convection with the Cattaneo-Christov hyperbolic heat-flow model.
abstract: Adoption of the hyperbolic Cattaneo-Christov heat-flow model in place of the more usual parabolic Fourier law is shown to raise the possibility of oscillatory convection in the classic Bénard problem of a Boussinesq fluid heated from below. By comparing the critical Rayleigh numbers for stationary and oscillatory convection,RcandRSrespectively, oscillatory convection is found to represent the preferred form of instability whenever the Cattaneo numberCexceeds a threshold valueCT≥8/27π2≈0.03. In the case of free boundaries, analytical approaches permit direct treatment of the role played by the Prandtl number [Formula: see text], which-in contrast to the classical stationary scenario-can impact on oscillatory modes significantly owing to the non-zero frequency of convection. Numerical investigation indicates that the behaviour found analytically for free boundaries applies in a qualitatively similar fashion for fixed boundaries, while the threshold Cattaneo numberCTis computed as a function of [Formula: see text] for both boundary regimes.
authors: Department of Mathematical Sciences , University of Durham , Durham City DH1 3LE, UK.
authors: J J
authors: JJ
authors: Bissell
keywords: Rayleigh–Bénard convection; buoyancy-driven instabilities; hyperbolic heat-flow; oscillatory convection; thermal convection