On oscillatory convection with the Cattaneo-Christov hyperbolic heat-flow model

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, R_c and R_S respectively, oscillatory convection is found to represent the preferred form of instability whenever the Cattaneo number C exceeds a threshold value C_T≥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 number C_T is computed as a function of [Formula: see text] for both boundary regimes.