Abstract

BERMUDEZ, B  and  NICOLAS, A. Convección natural de fluidos incompresibles y viscosos en cavidades rectangulares. Rev. mex. fis. [online]. 2008, vol.54, n.3, pp.236-246. ISSN 0035-001X.

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 10⁴ < Ra < 10⁶, and the aspect ratio of the cavity G, in the range 1/3 < G < 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 G different of the unity are being reported for the first time.

Keywords : Boussinesq aproximation; fixed point iterative process; Rayleigh number; rectangular cavities.

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