A STUDY OF THERMAL-CONVECTION IN AN ENCLOSURE INDUCED SIMULTANEOUSLY BY GRAVITY AND VIBRATION

Abstract

Thermal convection in a two-dimensional square enclosure induced simultaneously by gravity and vertical vibration is investigated numerically. A penalty finite element method with a Newton-Raphson iteration algorithm and a backward difference scheme dealing with the time term are adopted to solve the governing equations. In order to investigate the effects of the vibration frequency and Rayleigh number on the thermal convection in the enclosure, the vibration frequency is varied from 1 to 10(4) and three different values of the Rayleigh number of 0, 10(4) and 10(6) are considered. According to the results, the thermal convection can be divided into five regions: (i) quasi-static convection; (ii) vibration convection; (iii) resonant vibration convection; (iv) intermediate convection; and (v) high frequency vibration convection. In the high Rayleigh number (= 10(6)) case, the gravitational thermal convection dominates, and the vibration motion does not enhance the heat transfer rate remarkably. In contrast, in the low Rayleigh number (=10(4)) case, except in the quasi-static convection region, the vibration thermal convection is dominant, and the vibration enhances the heat transfer rate significantly. In addition, two analytic methods are proposed to predict the frequencies of the quasi-static convection and resonant vibration convection regions, respectively. The values predicted by the two methods are in agreement with that obtained from the numerical method.