The influence of the rayleigh number on the flow of natural convection in a differentially heated cavity

In this work, we present a two-dimensional numerical study in a square cavity filled with air. The flow of natural convection is laminar in unsteady regime. The two vertical sides are subject to an isothermal temperature difference, while the other two horizontal walls are adiabatic. The objective of our study is to highlight the influence of Rayleigh numbers on the structure of the flow, the temperature distribution in the cavity and on heat transfer. The equations of conservation of mass, momentum and energy were solved by the COMSOL multiphysics computer code. The numerical method used is that of finite elements implemented in the COMSOL calculation code. A validation study in a differentially heated square cavity was carried out in order to compare our results to those of the literature. We studied pure natural convection by varying the Rayleigh number from 1 to 〖10〗^7. Results are presented as isotherms, pressure, streamlines and temperature fields. It emerges from this study that for a Rayleigh number less than 1000, the fluid presents a vertical thermal stratification due to heat transfer only by conduction which does not generate any convective flow. But for Ra greater than 1000, we see distortions due to the influence of the Rayleigh number on natural convection. The fluid is Newtonian for a Prandtl number P_r=0,71.