Prandtl number dependence of Nusselt number in direct numerical simulations

Abstract

The dependence of the Nusselt number Nu on the Rayleigh Ra and Prandtl Pr number is determined for 10⁴ < Ra < 10⁷ and 0.07 < Pr < 7 using DNS with no-slip upper and lower boundaries and free-slip sidewalls in a 8 × 8 × 2 box. Nusselt numbers, velocity scales and boundary layer thicknesses are calculated. For Nu there are good comparisons with experimental data and scaling laws for all the cases, including Ra^2/7 laws at Pr = 0.7 and Pr = 7 and at low Pr, a Ra^1/4 regime. Calculations at Pr = 0.3 predict a new Nu ∼ Ra^2/7 regime at slightly higher Ra than the Pr = 0.07 calculations reported here and the mercury Pr = 0.025 experiments.