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A computational procedure is presented with an accelerated full-multigrid scheme for an efficient modeling of time-dependent buoyancy-driven flows. The smoother is the iterative red-and-black successive overrelaxation (RBSOR) scheme. In order to improve the convergence, an acceleration parameter, C, is implemented in the classical full-multigrid procedure. It is shown that an optimal value of C ¼ 3.75 minimizes the number of iterations needed for convergence. Numerical results are presented and compared with available investigations for an 8:1 differentially heated enclosure and a square heated cavity. Solutions for Prandtl number Pr ¼ 0.71, Rayleigh number Ra ¼ 3.4 3 10 5 for the 8:1 heated enclosure, and 10 5 e Ra e 10 9 for the square cavity are presented and show excellent agreement.

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The effect of aspect ratio on natural convection flow in a cavity submitted to periodic temperature boundary, is investigated numerically. The temperature of the heated wall is either maintained constant or varied sinusoidally with time while the temperature of the opposite vertical wall is maintained constant. The results are given for a range of varied parameters as Rayleigh number ͑5 ϫ 10 3 ഛ Raഛ 10 6 ͒, cavity aspect ratio ͑1/6ഛ A ഛ 8͒, and period of the sinusoidally heated wall ͑1 ഛ ഛ 1600͒. The amplitude of oscillation ͑a = 0.8͒ and the Prandtl number ͑Pr= 0.71͒ were kept constant. The results obtained in the steady state regime show that the heat transfer averaged over the cold wall is maximum when the aspect ratio is in the range 1 ഛ A ഛ 2. In the case of a periodic temperature boundary, it is shown that the deviation between the mean heat transfer and the heat transfer of the constant heated case is larger for shallow cavities.

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