Transient thermal convection in an enclosure induced simultaneously by gravity and vibration

Abstract

Transient thermal convection in a two-dimensional square enclosure induced simultaneously by gravity and vibration is investigated numerically. The enclosure, which is filled with air under a terrestrial environment, is insulated at both horizontal walls and kept at constant temperature at the vertical walls. For time t=0, the fluid is stationary with the same temperature as the vertical walls T c; as t > 0, the left wall temperature is raised to T h and the enclosure is vibrated with a constant frequency Ω and amplitude b simultaneously. In order to study the effect of vibration frequency on the transient thermal convection, four vibration frequencies (100, 900, 1100, 5000) are considered with fixed Rayleigh number ( Ra=10 4 ) and vibrational Grashof number ( G = 10 6 ). The results show that the transient process, from the stationary state to the steady flow state, is shortened by increasing the vibration frequency, and both the flow field and heat transfer mechanism are mainly determined by the vortex shedding rate, which has the same frequency as the vibration frequency near the upper and lower corners of the hot wall. For ω=100, a single main cell is formed and alternates the rotating direction with the variation of the buoyancy force direction. For ω=5000, the buoyancy force induced by the vibration is definitely dominant and the development of temperature distribution from left to right sides is initially symmetric at the center line of the vertical wall; afterwards, an instability of the thermal boundary layer causes an overshoot of the total Nusselt number and an increase of flow intensity before the periodic solution is approached. For ω=900 and 1100, the vortices shed continuously and alternately from the upper and lower corners near the hot wall, which causes the variation of the total Nusselt number to be irregular and inconsistent on the hot and cold walls for the ω=900 case; for the ω=1100 case the total Nusselt number varies irregularly in the transient processes, but a periodic solution is obtained at steady state.