Influence of surface radiation on the transition to unsteadiness for a natural convection flow in a differentially heated cavity

Abstract

The influence of surface radiation on the transition to the unsteady state in natural convection is studied numerically. The configuration of the differentially heated square cavity with adiabatic horizontal walls is chosen to generate an internal natural convection flow. It is known that radiative transfers reduce the temperature difference between the adiabatic walls, which consequently reduces the thermal stratification of the central zone and increases the velocity flow. Many studies have focused on the stationary regime, but few of them have investigated the transition to unsteady flow. For this purpose, the effect of the wall emissivity on the critical Rayleigh number and the associated critical frequency was studied for a given cavity length. The cavity length and mean temperature of isothermal walls are set for the whole study. The results show that all these values are between the values obtained without radiation and those obtained for perfectly conducting horizontal walls. The critical Rayleigh number decreases with emissivity while the associated frequency increases. Moreover, the symmetry of fluctuating properties of the flow is changed when the radiation is taken into account.

Acknowledgments

The authors would also like to thank X. B. Nguyen for fruitful discussions.

Additional information

Funding

The authors acknowledge the CPER (2015-2020) and ERDF (2014-2020) programs for supporting this work through the funding of equipments.