### Abstract

Original language | English |
---|---|

Article number | 2014.0845 |

Pages (from-to) | 1 - 18 |

Number of pages | 18 |

Journal | Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences |

Volume | 471 |

Issue number | 2175 |

Early online date | 18 Feb 2015 |

DOIs | |

Publication status | Published - Mar 2015 |

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### Cite this

*Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences*,

*471*(2175), 1 - 18. [2014.0845]. https://doi.org/10.1098/rspa.2014.0845

**On oscillatory convection with the Cattaneo-Christov hyperbolic heat-flow model.** / Bissell, J. J.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences*, vol. 471, no. 2175, 2014.0845, pp. 1 - 18. https://doi.org/10.1098/rspa.2014.0845

}

TY - JOUR

T1 - On oscillatory convection with the Cattaneo-Christov hyperbolic heat-flow model

AU - Bissell, J. J.

PY - 2015/3

Y1 - 2015/3

N2 - 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, Rc and RS respectively, oscillatory convection is found to represent the preferred form of instability whenever the Cattaneo number C exceeds a threshold value CT≥8/27π2≈0.03. In the case of free boundaries, analytical approaches permit direct treatment of the role played by the Prandtl number P 1 , 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 CT is computed as a function of P 1 ∈[10 −2 ,10 +2 ] for both boundary regimes.

AB - 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, Rc and RS respectively, oscillatory convection is found to represent the preferred form of instability whenever the Cattaneo number C exceeds a threshold value CT≥8/27π2≈0.03. In the case of free boundaries, analytical approaches permit direct treatment of the role played by the Prandtl number P 1 , 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 CT is computed as a function of P 1 ∈[10 −2 ,10 +2 ] for both boundary regimes.

UR - http://dx.doi.org/10.1098/rspa.2014.0845

U2 - 10.1098/rspa.2014.0845

DO - 10.1098/rspa.2014.0845

M3 - Article

VL - 471

SP - 1

EP - 18

JO - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

SN - 1364-503X

IS - 2175

M1 - 2014.0845

ER -