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Numerical study of natural convection in a square cavity under non-boussinesq conditions

Hamimid Saber (Laboratoire de Génie des Procédés Chimiques, Université de Sétif, Sétif, Algeria)
Guellal Messaoud (Laboratoire de Génie des Procédés Chimiques, Université de Sétif, Sétif, Algeria)
Bouafia Madiha (Laboratoire de Mécanique et Energétique d’Evry, Université d’Evry Val d’Essonne, France)

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 LMN 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 LMN compressible code shows that the incompressible model is not sufficient to simulate natural convective flow for large temperature differences.

Keywords: natural convection, low mach number approximation, numerical simulation