Effects of nonperfect thermal sources in turbulent thermal convection

The effects of the plates thermal properties on the heat transfer in turbulent 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 Rf and the plates Rp; when this ratio is smaller than a threshold value (Rf/Rp ≈ 300 arbitrarily defined by requiring that the actual heat transfer differs by less than 2% from its ideal value), the finite conductivity of the plates limits the heat transfer in the cell. In addition, since Rf decreases for increasing Rayleigh numbers, any experimental apparatus is characterized by a threshold Rayleigh number that cannot be exceeded if the heat transfer in the cell has not to be influenced by the thermal properties of the plates. It has been also shown that the plate effects cannot be totally corrected by subtracting the temperature drop occurring within the plates from the measured total temperature difference. This is due to the changes produced in the thermal plume dynamics by the reduced local heat flux at the plate/fluid interface. A model with a correction factor has been derived to account for the plates effects and it gave the appropriate correction for a recent experiment in which the heat transfer measurements were systematically smaller than a theoretical prediction. In view of the present correction the discrepancy between theory and experiments addressed by Nikolaenko and Ahlers [Phys. Rev. Lett. 91, 084501 (2003)] can be therefore resolved. The application of the proposed correction to the results in the literature can also reconcile the heat transfer measurements for water and mercury that appear systematically smaller than in other fluids.