Abstract
We report on recent findings of natural convection resonance under time periodic horizontal heating. The transport phenomena is investigated numerically considering a rectangular enclosure filled with fluid or with fluid saturated porous medium. Numerical simulations, of various configurations, indicate that the natural convection activity within the enclosure peaks at several discrete frequencies, with the climax attained at a heating frequency referred to as the resonance frequency. A general estimate of the resonance frequency is obtained theoretically via a system of non linear equations, function of the average Rayleigh number, the Prandtl number, the enclosure aspect ratio, the heating amplitude, and the Darcy number for the porous medium case. Theoretical predictions considering various Prandtl numbers agree well with the numerical results. A simplified theoretical model antecipates the resonance frequency varying with Pr1/2 for the porous medium enclosure, a result confirmed by the numerical data. The convection intensity within the enclosure is shown to decreases with either increasing or decreasing Pr from its optimum value around 1. This behavior is explained as a dual effect: at low Pr the high thermal diffusivity reduces buoyancy inside the enclosure; at high Pr the high momentum diffusivity (viscosity) damps the flow wheel inside the enclosure. Both effects justify the observed reduction in the natural convection activity inside the enclosure.
