## Abstract

The effect of the viscosity-temperature relation,//(T), on the onset of convection in a horizontal fluid layer is discussed. Linear analysis shows that, for aqueous glycerol solutions, the critical Rayleigh numbers (Ra
_{crit}) obtained using the Arrhenius approximation, fi
_{A}(T), are in excellent agreement with those employing the actual//(T) data. The results for the exponential approximation fi
_{e} (T) differ to an extent that depends on the glycerol mass fraction and the temperature difference (AT) between the plates. The error associated with use of fj,
_{e} (T), while small, is of the same order as, or larger than, the uncertainty in careful experiments. For the broad class of liquids for which//
_{A} (T) is an excellent approximation to//, we have assessed the errors in Racrit associated with the widely used fi
_{e}(T). As AT and the viscosity contrast increase, the values of Racrit deviate increasingly from those predicted using//
_{A} (7
^{1}). Also, the relative error in Racrit is much smaller than the maximum relative error in the coefficients [involving//(T) and its derivatives with respect to T] of the linear disturbance equations.

Original language | English (US) |
---|---|

Pages (from-to) | 1380-1385 |

Number of pages | 6 |

Journal | Physics of Fluids |

Volume | 31 |

Issue number | 6 |

State | Published - 1988 |

## ASJC Scopus subject areas

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes