Natural convection in cavity has become one of the classical heat transfer problems with a large volume of research performed both experimentally and numerically. There are several permutations of the cavity problem related to its shape, its boundary conditions, the properties of circulating fluid, etc. Among them, the most interesting one is that of a rectangular cavity, which is maintained at hot and cold temperatures on its opposing side walls while its horizontal walls are thermally insulated. Contrary to the past works, we study the cavity with small to high temperature differences. This produces a wide range of compressibility effects in the cavity, which need to be treated carefully by an algorithm capable of solving both incompressible and compressible flows. In this regard, an already developed algorithm for solving laminar flow in thermobuoyant domains is suitably extended for treating the turbulent thermobuoyant domains. A low-Reynolds-number k-E turbulence model is utilized to predict the correct turbulent behavior, which is largely affected by the transition effects. The extended algorithm is then utilized to solve thermally driven squared cavity problem at a fixed Rayleigh number of 4.9 x 1010 but a wide range of temperature differences, i.e., various compressibility effects. The current results indicate that the thermobuoyant fields with large temperature differences cannot be treated using classical methods relied on Boussinesq approximation. The deviation of the latter methods from the reality becomes noticeable as the temperature difference increases.
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