We perform direct numerical simulations (DNS) of turbulent Rayleigh-Bénard convection coupled with surface-to-surface radiation in a rectangular enclosure filled with air to investigate whether this interaction influences the heat transfer, temperature distribution and the flow structures. To do so, horizontal solid plates with finite conductivity are employed for the considered Rayleigh-Bénard cell. Such boundary conditions allow local variations of the temperature at the hot and cold interfaces due to their interaction with the fluid and surface radiation. In order to investigate the maximum effect of those boundary conditions, both interfaces are treated as a blackbody (ε = 1) and the cell is filled with a radiatively non-participating fluid. The values of dimensionless control parameters and dimensional properties used in considered simulations are as follows.

The effects of radiation for highly conducting plates are shown and compared to the case where radiation is neglected. It is found that the temperature at the hot interface tends to decrease due to the radiative heat loss while the temperature at the cold interface slightly increases. Apart from that, we observe small changes in the temperature distribution at the interfaces due to surface-to-surface radiation. The analysis of the heat transfer reveals a slight drop of the convective Nusselt number. However, the total heat flux (convective plus radiative) at the interfaces increases nearly three times (see figure 2). Finally, it is shown that all mentioned variations caused by heat radiation between interfaces are too tiny to noticably change the large-scale  flow structures when highly conducting plates are employed.