Prandtl number dependence of Nusselt number in direct numerical simulations

The dependence of the Nusselt number Nu on the Rayleigh Ra and Prandtl Pr n umber is determined for 10(4) < Ra < 10(7) and 0.07 < Pr < 7 using DNS with no-slip upper and lower boundaries and free-slip sidewalls in a 8 x 8 x 2 box. Nusselt numbers, velocity scales and boundary layer thicknesses are ca lculated. For Nu there are good comparisons with experimental data and scal ing laws for all the cases, including Ra-2/7 laws at Pr = 0.7 and Pr = 7 an d at low Pr, a Ra-1/4 regime. Calculations at Pr = 0.3 predict a new Nu sim ilar to Ra-2/7 regime at slightly higher Ra than the Pr = 0.07 calculations reported here and the mercury Pr = 0.025 experiments.