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

Abstract

International audienceAbstract 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

Effect of radiation on the flow structure and heat transfer in a 2-D gray medium

“…A technique derived from the classical projection method is employed to solve the coupling between pressure and velocity. The Poisson equations for the pressure correction in the projection method are solved by standard multigrid techniques [15].…”

“…Other works dealing with combined natural convection-surface radiation in differentially heated cavities have received considerable attention in the literature, either in the case of Boussinesq approximation [10][11][12][13] or under Low Mach Number conditions [14,15].…”

Conduction, Convection, and Radiation in a Closed Cavity With a Local Radiant Heater

“…The view factors were determined by means of the Hottel's crossed string method (Hottel and Sarofim, 1967). Taking into account the above assumptions, the non-dimensional radiosity equation can be written as follows (Bouafia et. al., 2015):…”

“…Calculating the values of the i J , irradiation equation can be determined as follows (Bouafia et. al., 2015):…”

“…However, convective Nusselt number weakly depended on the surface emissivity in this case. The study of M. Bouafia et. al.…”