Non-Boussinesq convection in a square cavity with surface thermal radiation

•Numerical study of natural convection with large temperature differences in a differentially heated square cavity.•Navier–Stokes equations under the low Mach number approximation.•Effect of thermal radiation on the flow and heat transfer for gray and diffuse surfaces.•Influence of radiation on the transition to unsteady flows.

The interaction of natural convection with surface radiation in a differentially heated square cavity filled with air is considered under large temperature differences. The study has been investigated by direct numerical simulations with a two-dimensional finite volume numerical code solving the time-dependent Navier–Stokes equations under the Low Mach Number (LMN) approximation. Calculations were performed for cases with strong non-Boussinesq effects. The results reveal that the fluid flow and heat transfer are influenced significantly by the surface radiation. At steady state, the top wall is cooled and the bottom wall is heated compared to the case without radiation. The air flow is reinforced near the horizontal walls and the thermal stratification at the core is reduced. The surface radiation reduces the convection heat transfer at the hot wall and increases it on the cold wall.Transition from steady to unsteady flow has also been investigated. By comparing the solutions in pure convection, the results in combined convection–radiation show that the radiation promotes the occurrence of instabilities leading to an early transition to the unsteadiness and contributes to the modification of the physical mechanism responsible for their onset.