Open Access

ARTICLE

Effects of the Rayleigh Number and the Aspect Ratio on 2D Natural Convection Flows

Alfredo Nicolás¹, Blanca Bermúdez², Elsa Báez³

1 Depto. Matemáticas, 3er. Piso Ed. Diego Bricio, UAM-Iztapalapa, 09340 México D.F. México, e-mail: anc@xanum.uam.mx
2 Facultad de C. de la Computación, BUAP, Pue., México
3 Depto. Matemáticas Aplicadas y Sistemas, UAM-C; 01120 México D.F., México, correspondence to: Alfredo Nicolás

Computer Modeling in Engineering & Sciences 2009, 48(1), 83-106. https://doi.org/10.3970/cmes.2009.048.083

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 A 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: 10⁵ ≤ Ra ≤ 10⁷, 1/4 ≤ A ≤ 4. The study is complemented with the corresponding heat transfer through the Nusselt numbers as well as the time T_ss when the steady state of the flow is reached; in connection with T_ss, the flow at different times less than T_ss is reported for Ra = 10⁶ with A = 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.

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Keywords

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