Convección natural de fluidos incompresibles y viscosos en cavidades rectangulares

Abstract

Natural convection numerical results for incompressible viscous flows are presented in rectangular cavities with different aspect ratios. This kind of flows may be governed by the time-dependent Boussinesq approximation in the stream function-vorticity formulation. The results are obtained with a simple numerical scheme previously reported for isothermal/thermal (mixed convection) flows. The numerical scheme is based mainly on a fixed point iterative process applied to the non-linear elliptic system that results after a second order time discretization is made. The iterative process leads to the solution of uncoupled, well-conditioned, symmetric linear elliptic problems. The evolution of the thermal flow depends on the parameters given by the Rayleigh number $Ra$, in the range $10^4\leq Ra \leq 10^6$, and the aspect ratio of the cavity $G$, in the range $1/3 \leq G \leq 3$. There are also shown a result related with cat's eyes instability, $G=16$, and other as an example of time-dependent thermal flows, $G=1/16$. To the best of our knowledge, some results with %$A \neq 1$ $G$ different of the unity are being reported for the first time.