Direct numerical simulation of thermal channel flow for medium–high Prandtl numbers up to [formula omitted

Abstract

A new set of DNS of a thermal channel flow have been conducted for friction Reynolds and Prandtl numbers up to 2000 and 10, respectively, reaching the Prandtl number of water, 7, for new Reynolds numbers, never simulated before. The Mixed Boundary Condition has been used as the thermal boundary condition. A new scaling of the thickness of the conductive sublayer is presented for medium–high Prandtl number values. The maximum of the intensity of the thermal field does not increase with the Reynolds number for the highest Prandtl numbers. This entails a good scaling near the wall of the viscous diffusion and the dissipation terms in the budgets of the temperature variance. The Nusselt number shows a power function behaviour with respect to the Prandtl number in a certain range of the friction Péclet number. Finally, the turbulent Prandtl number presents an increase near the wall for highest Prandtl numbers due to the reduction of the thermal eddy diffusivity. The statistics of all simulations can be downloaded from the web page of our group: http://personales.upv.es/serhocal/.