Effect of non perfect thermal sources in turbulent thermal convection

The effects of the plates thermal properties on the heat transfer in thermal convection are investigated by direct numerical simulations of the Navier-Stokes equations with the Boussinesq approximation. It has been found that the governing parameter is the ratio of the thermal resistances of the fluid layer $R_f$ and of the plates $R_p$; when this ratio is smaller than a threshold value ($R_f/R_p \approx 300$) the finite conductivity of the plates limits the heat transfer in the cell. In addition, since $R_f$ decreases for increasing Rayleigh numbers, each experimental apparatus is characterized by a threshold Rayleigh number that can not be exceeded if the heat transfer in the cell has not to be influenced by the thermal properties of the plates. A model with a correction factor has been derived to account for the plates effects and it gave the appropriate correction for an experiment in which the heat transfer measurements were systematically smaller than a theoretical prediction. A recent experimental study has confirmed the present findings. Due to changes of the thermal plume dynamics caused by the locally reduced heat flux at the plate/fluid interface the plate effect can not be trivially corrected by accounting for the temperature drop at the plates.