@Article{cmes.2009.048.083,
AUTHOR = {Alfredo  Nicolás, Blanca  Bermúdez, Elsa  Báez},
TITLE = {Effects of the Rayleigh Number and the Aspect Ratio on 2D Natural Convection Flows},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {48},
YEAR = {2009},
NUMBER = {1},
PAGES = {83--106},
URL = {http://www.techscience.com/CMES/v48n1/25368},
ISSN = {1526-1506},
ABSTRACT = {Numerical results of natural convection flows in two-dimensional cavities, filled with air, are presented to study the effects on the characteristics of the flows as some parameters vary: the Rayleigh number Ra and the aspect ratio <i>A</i> of the cavity. This kind of thermal flows may be modeled by the unsteady Boussinesq approximation in stream function-vorticity variables. The results are obtained with a simple numerical scheme, previously reported for isothermal/mixed convection flows, based mainly on a fixed point iterative process applied to the non-linear elliptic system that results after time discretization. The evolution of the flows, mainly flows converging to a steady state, depends on the variation of the parameters in the range: 10<sup>5</sup> ≤ <i>Ra</i> ≤ 10<sup>7</sup>, 1/4 ≤ <i>A</i> ≤ 4. The study is complemented with the corresponding heat transfer through the Nusselt numbers as well as the time <i>T<sub>ss</sub></i> when the steady state of the flow is reached; in connection with <i>T<sub>ss</sub></i>, the flow at different times less than <i>T<sub>ss</sub></i> is reported for <i>Ra</i> = 10<sup>6</sup> with <i>A</i> = 1, some findings become into light about transient phenomenon. The validation of the results is given through mesh size and time-step independence studies complemented with the corresponding independence of some characteristics of the flow; then, the validation process is not depending on the comparison with other works using different dimensionless forms.},
DOI = {10.3970/cmes.2009.048.083}
}