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

Natural convection in a differentially heated cavity has been carried out under large temperature gradient. The study has been performed by direct simulations using a two-dimensional finite volume numerical code solving the time-dependent Navier-Stokes equations under the low Mach number approximation. The low Mach number model constitutes an important numerical problem for low speed flows. It is based on the filtering of acoustic waves from the complete Navier-Stokes equations. Various simulations were conducted including constant or variable transport coefficients and both small and large temperature differences. A comparison between an incompressible code based on the Boussinesq approximation and the low Mach number compressible code shows that the incompressible model is not sufficient to simulate natural convective flow for large temperature differences.

A perturbation method is used to solve an unsteady one-dimensional heat conduction problem in a cylinder. A simple second order explicit solution is obtained. It is shown that this solution is accurate even for high values of the Biot number in a region surrounding the center of the cylinder.

Nomenclature Cp= dimensionless specific heat F ij = geometry view factor g = gravitational acceleration H = dimension of the enclosure k = thermal conductivity Nr = dimensionless parameter of conduction-radiation,dimensionless fluid density σ = Stefan-Boltzmann constant Subscripts avg = average value BS = Boussinesq model CP = constant properties c = cold h = hot max = maximum value mid = midplane min = minimum value 0 = reference state

A numerical study of combined natural convection and radiation in a square cavity filled with a gray non-scattering semi-transparent fluid is conducted. The horizontal walls are adiabatic and the vertical are differentially heated. Convection is treated by the finite volumes approach and the discrete ordinates method is used to solve radiative transfer equation using S6 order of angular quadrature. Representative results illustrating the effects of the Rayleigh number, the optical thickness and the Planck number on the flow and temperature distribution are reported. In addition, the results in terms of the average Nusselt number obtained for various parametric conditions show that radiation modifies significantly the thermal behavior of the fluid within the enclosure.