Onset of Convection in Variable Viscosity Fluids: An Assessment of Approximate Viscosity-Temperature Relations

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.