Thursday, 13. December 2018

Turbulent convection and thermal radiation in a Rayleigh-Bénard-Cell

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.




: Rayleigh number




: Prandtl number




: conduction - radiation number




: temperature ratio




: mean temperature




: temperature difference between the outer sides of the heating and cooling plates



500 mm

: height of the cell

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.

Instantaneous isosurfaces of temperature
Total heat flux at the interfaces versus time (for the case with and without radiation)


Tim Wetzel
German Aerospace Center (DLR)
Institute of Aerodynamics and Flow Technology, Department Ground Vehicles
Phone: +49 551 709-2727



German Aerospace Center (DLR), Institute of Aerodynamics and Flow Technology, SCART
Bunsenstraße 10, 37075 Göttingen, Germany