Low-Prandtl-number convection in a layer heated from below

Abstract

Steady solutions in the form of two-dimensional rolls are obtained numerically for convection in a horizontal layer of a low-Prandtl-number fluid heated from below. Prandtl numbers in the range 0·001 [les ] P [les ] 0·71 are investigated for Rayleigh numbers between the critical value, R = 1708, and R = 20,000 in the case of rigid boundaries. The calculations reveal that the convective heat transport is relatively independent of the Prandtl number at Rayleigh numbers greater than a finite critical value R2 of the order of 5 × 103. At R = 10,000 the convective heat transport varies by only about 30% for Prandtl numbers in the range investigated. As the Rayleigh number is increased above the critical value R2, the streamlines of the convection flow become circular, independent of the horizontal wavelength as long as the latter is larger than or about equal to twice the height of the layer.