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

Alfredo Nicolás1, Blanca Bermúdez2, Elsa Báez3
Depto. Matemáticas, 3er. Piso Ed. Diego Bricio, UAM-Iztapalapa, 09340 México D.F. México, e-mail:
Facultad de C. de la Computación, BUAP, Pue., México
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.


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


unsteady Boussinesq approximation, Rayleigh number, aspect ratio, heat transfer

Cite This Article

Nicolás, A., Bermúdez, B., Báez, E. (2009). Effects of the Rayleigh Number and the Aspect Ratio on 2D Natural Convection Flows. CMES-Computer Modeling in Engineering & Sciences, 48(1), 83–106.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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